physics 105 homework problems, fall 2007 files... · 2007-09-17 · 2-6. a firefighter, [08] m...

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Physics 105 Homework Problems, Fall 2007 Sec. 3, Stephanie Magleby These problems are adapted from Serway and Faughn, College Physics, and are used with permission from Harcourt Brace College Publishers. 1-1. At the Olympics, an athlete runs the marathon in 2 h, 9 min, [01] s. (This is near the record time.) The marathon distance is 26 mi, 385 yd (1 yd = 3 ft). Determine the average speed of this athlete. Caution: Find the distance in miles and the time in hours to high precision. 1-2. A person travels by car from one city to another with different constant speeds between pairs of cities. She drives [02] min at 83.7 km/h, 11.8 min at 126 km/h, and 45.5 min at [03] km/h, and spends 15.1 min eating lunch and buying gas. (a) Determine the distance between the initial and final cities along this route. (b) Determine the average speed for the trip. 1-3. A tennis player moves in a straight-line path as shown in the figure. On the vertical axis in the figure, x 1 = [04] m and x 2 = [05] m. Find her average velocities in the time intervals (a) 0 to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 5.0 s, and (d) 0 to 5.0 s. 1-4. The space shuttle orbits [06] mi above the surface of the earth. If the average speed of the shuttle is [07] mi/h, determine the time required for it to circle the Earth. The Earth’s radius is 3963 miles. 1-5. A car traveling in a straight line has a velocity of +[08] m/s at some instant. After [09] s, its velocity is +8.49 m/s. What is its average acceleration in this time interval? 1-6. A tennis ball is thrown perpendicularly at a wall. Before striking the wall, the ball’s velocity is +[10] m/s (moving towards the right). After striking the wall, the ball rebounds in the opposite direction with a velocity equal to -8.32 m/s (moving towards the left). If the ball is in contact with the wall for [11] ms, what is the average acceleration of the ball while it is in contact with the wall? (Be sure to include the correct sign on the answer.)

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Physics 105 Homework Problems, Fall 2007

Sec. 3, Stephanie Magleby

These problems are adapted from Serway and Faughn, College Physics, and are usedwith permission from Harcourt Brace College Publishers.

1-1. At the Olympics, an athlete runs the marathon in 2 h, 9 min, [01] s. (This is

near the record time.) The marathon distance is 26 mi, 385 yd (1 yd = 3 ft). Determine

the average speed of this athlete. Caution: Find the distance in miles and the time in

hours to high precision.

1-2. A person travels by car from one city to another with different constant speeds between

pairs of cities. She drives [02] min at 83.7 km/h, 11.8 min at 126 km/h, and

45.5 min at [03] km/h, and spends 15.1 min eating lunch and buying gas.

(a) Determine the distance between the initial and final cities along this route.

(b) Determine the average speed for the trip.

1-3. A tennis player moves in a straight-line path as shown

in the figure. On the vertical axis in the figure,

x1 = [04] m and x2 = [05] m.

Find her average velocities in the time intervals (a) 0

to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 5.0 s, and (d) 0 to

5.0 s.

1-4. The space shuttle orbits [06] mi above the surface of the earth. If the average

speed of the shuttle is [07] mi/h, determine the time required for it to circle

the Earth. The Earth’s radius is 3963 miles.

1-5. A car traveling in a straight line has a velocity of +[08] m/s at some instant.

After [09] s, its velocity is +8.49 m/s. What is its average acceleration in this

time interval?

1-6. A tennis ball is thrown perpendicularly at a wall. Before striking the wall, the ball’s

velocity is +[10] m/s (moving towards the right). After striking the wall, the

ball rebounds in the opposite direction with a velocity equal to −8.32 m/s (moving

towards the left). If the ball is in contact with the wall for [11] ms, what is

the average acceleration of the ball while it is in contact with the wall? (Be sure to

include the correct sign on the answer.)

1-7. A certain bacterium swims with a speed of [12] µm/s. How long would it take

this bacterium to swim across a petri dish having a diameter of [13] cm?

1-8. A car accelerates uniformly from rest to a speed of [14] mi/h in

[15] s. (a) Find the acceleration of the car and (b) the distance the car

travels during this time.

1-9. A jet plane lands with a speed of [16] m/s and can accelerate at a maximum

rate of −5.31 m/s2 as it comes to rest. (a) From the instant the plane touches the

runway, what is the minimum time needed before it can come to rest. (b) What is the

minimum distance needed?

2-1. A ball is thrown vertically upward with a speed of [01] m/s. (a) How high

does it rise? (b) How long does it take to reach its highest point? (c) How long after it

reaches its highest point does it take to return to the level from which it started?

(d) What is its velocity when it returns to the level from which it started? (Use negative

sign for downward velocity.)

2-2. A model rocket is launched straight upward with an initial speed of [02] m/s.

It accelerates with a constant acceleration of [03] m/s2 until its engines stop

at an altitude of [04] m. (a) What is the maximum height reached by the

rocket? (b) How long after lift-off does the rocket reach its maximum height? (c) How

long is the rocket in the air?

2-3. A car, capable of a constant acceleration of 2.5 m/s2, is stopped at a traffic light. When

the light turns green, the car starts from rest with this acceleration. Also, as the light

turns green, a truck traveling with a constant velocity of [05] km/h passes the

car. Clearly, the car will eventually travel faster than the truck and will overtake it. How

far from the traffic light will the car catch up with the truck?

2-4. A rowboat crosses a river with a velocity of 3.37 mi/h at an angle 62.5◦ north of west

relative to the water. The river is 0.505 mi wide and carries an eastward current of

[06] mi/h. How far upstream is the boat when it reaches the opposite shore?

2-5. A student decides to measure the muzzle velocity of a pellet from his gun. He points the

gun horizontally. He places a target on a vertical wall a distance 3.27 m away from the

gun. The pellet hits the target a vertical distance [07] m below the gun.

What is the speed of the pellet?

2-6. A firefighter, [08] m away from a burning building, directs a stream of water

from a ground level fire hose at an angle of [09] ◦ above the horizontal. If the

speed of the stream as it leaves the hose is [10] m/s, at what height will the

stream of water strike the building?

2-7. (a) If a person can jump a maximum horizontal distance (by using a 45◦ projection

angle) of [11] m on Earth, what would be his maximum range on the Moon,

where the free-fall acceleration is 1

6g (g = 9.80 m/s2)? (b) Repeat for Mars, where the

acceleration due to gravity is 0.38g.

2-8. One strategy in a snowball fight is to throw a snowball at a high angle over level ground.

While your opponent is watching the first one, you throw a second snowball at a low

angle timed to arrive before or at the same time as the first one. Assume both snowballs

are thrown with a speed of 25.3 m/s. The first one is thrown at an angle of

[12] ◦ with respect to the horizontal. (a) At what angle should the second

snowball be thrown to arrive at the same point as the first? (b) How many seconds later

should the second snowball be thrown after the first to arrive at the same time?

3-1. A football punter accelerates a football from rest to a speed of [01] m/s

during the time in which his toe is in contact with the ball (about 0.247 s). If the football

has a mass of [02] g, what average force does the punter exert on the ball?

3-2. A freight train has a mass of [03] kg. If the locomotive can exert a

constant pull of 7.54 × 105 N, how long does it take to increase the speed of the train

from rest to [04] km/h?

3-3. A performer in a circus is fired from a cannon as a “human cannonball” and leaves the

cannon with a speed of [05] m/s. The performer’s mass is 82.6 kg. The

cannon barrel is 9.29 m long. Find the average net force exerted on the performer while

he is being accelerated inside the cannon.

3-4. Two cables support a cat burglar. In the figure,

W = [06] N, and θ = [07] ◦. Find (a) the

tension in the cable connected to the ceiling and (b) the tension

in the cable connected to the wall on the left. Neglect the mass

of the cables.

3-5. A [08] -N bird feeder is supported

by three cables as shown in the figure. Find

the tension in (a) cable A, (b) cable B, and

(c) cable C.

3-6. A block of mass m = [09] kg is held in

equilibrium on an incline of angle

θ = [10] ◦ by the horizontal force F, as

shown in the figure. (a) Determine the value of F .

(b) Determine the normal force exerted by the

incline on the block. Ignore friction.

3-7. Assume that the three blocks in the figure move on a frictionless surface. In the figure,

m1 = [11] kg, m2 = [12] kg, and m3 = [13] kg. The

42.1-N force acts as shown on the right block. Determine (a) the acceleration of the

blocks, (b) the tension in the cord connecting the left and right blocks, and (c) the force

exerted on the center block by the left block.

3-8. Two blocks are fastened to the ceiling of an

elevator, as in the figure. In the figure,

m2 = [14] kg (bottom block) and

m1 = [15] kg (top block). The elevator

accelerates upward at a = [16] m/s2.

Find the tension in (a) the rope CD and (b) the

rope AB.

4-1. Two objects are connected by a light string that passes

over a frictionless pulley as in the figure. One object lies

on a smooth incline. In the figure,

m1 = [01] kg, m2 = [02] kg, and

θ = [03] ◦. Find (a) the magnitude of the

acceleration of the objects and (b) the tension in the

string.

4-2. A mass, m1 = [04] kg, resting on a

frictionless horizontal table is connected to a

cable that passes over a pulley and then is

fastened to a hanging mass,

m2 = [05] kg, as in the figure.

Find (a) the acceleration of the masses and

(b) the tension in the cable. Neglect the mass

of the cable and pulley.

4-3. A dockworker loading crates on a ship finds that a [06] -kg crate, initially at

rest on a horizontal surface, requires a 75-N horizontal force to set it in motion. However,

after the crate is in motion, a horizontal force of 60 N is required to keep it moving with

a constant speed. Find the coefficients of (a) static and (b) kinetic friction between crate

and floor.

4-4. Objects with masses m1 = 8.83 kg and

m2 = [07] kg are connected by

a light string that passes over a frictionless

pulley as in the figure. If, when the system

starts from rest, m2 falls 1.28 m in 1.22 s,

determine the coefficient of kinetic friction

between m1 and the table.

4-5. Find the acceleration experienced by each of the two

objects shown in the figure if the coefficient of kinetic

friction between the 7.00-kg object and the plane is

[08] .

4-6. A 2.00-kg block is held in equilibrium on an incline

of angle θ = [09] ◦ by a horizontal

force F applied in the direction shown in the figure.

If the coefficient of static friction between the block

and incline is µs = 0.334, determine (a) the

minimum value of F and (b) the normal force of the

incline on the block.

4-7. A weight lifter lifts a 359-N set of weights from ground level to a position over his head, a

vertical distance of [10] m. How much work does the weight lifter do,

assuming he moves the weights at constant speed?

4-8. A 6.93-kg bowling ball moves at [11] m/s. How fast must a [12] -g

Ping-Pong ball move so that the two balls have the same kinetic energy?

4-9. A 2.00-kg ball is attached to a ceiling by a [13] -m-long string. The height of

the room is 3.18 m. What is the gravitational potential energy associated with the ball

relative to (a) the ceiling? (b) the floor? (c) a point at the same elevation as the ball?

5-1. A 72.9-kg base runner begins his slide into second base when moving at a speed of

[01] m/s. The coefficient of friction between his clothes and Earth is

[02] . He slides so that his speed is zero just as he reaches the base. (a) How

much mechanical energy is lost due to friction acting on the runner? (b) How far does he

slide?

5-2. A 1.85-g bullet leaves the barrel of a gun at a speed of [03] m/s. (a) Find its

kinetic energy. (b) Find the average force exerted on the bullet by the expanding gases as

the bullet moves the length of the [04] -cm-long barrel.

5-3. A 2150-kg car moves down a level highway under the actions of two forces. One is a

1030-N forward force exerted on the drive wheels by the road; the other is a 950-N

resistive force. Use the work-kinetic energy theorem to find the speed of the car after is

has moved a distance of [05] m, assuming it starts from rest.

5-4. A bead of mass m = 5.00 kg is

released from point A at a

height h = [06] m and

slides on the frictionless track shown

in the figure. Determine (a) the

bead’s speed at point B, (b) its speed

at point C and (c) the net work done

by the force of gravity in moving the

bead from A to C.

5-5. A 51.3-kg pole vaulter running at [07] m/s vaults over the bar. Her speed

when she is over the bar is [08] m/s. Neglect air resistance, as well as any

energy absorbed by the pole, and determine her altitude as she crosses the bar.

5-6. A 378-g bead slides on a curved wire, starting from rest at

point A in the figure. In the figure, y1 = [09] m

and y2 = [10] m. If the wire is frictionless, find

the speed of the bead (a) at B and (b) at C.

5-7. A [11] -kg child on a 2.26-m-long swing is released from rest when the swing

supports make an angle of [12] ◦ with the vertical. (a) Neglecting friction, find

the child’s speed at the lowest position. (b) If the speed of the child at the lowest

position is 1.51 m/s, what is the mechanical energy lost due to friction?

5-8. A skier of mass 74.9 kg is pulled up a slope by a motor-driven cable. (a) How much work

is required to pull him 63.2 m up a [13] ◦-slope (assumed frictionless) at a

constant speed of [14] m/s? (b) How many horsepower must a motor have to

perform this task?

6-1. High-speed stroboscopic photographs show that the head of a 232-g golf club is traveling

at 54.9 m/s just before it strikes a [01] -g golf ball at rest on a tee. After the

collision, the club head travels (in the same direction) at [02] m/s. Find the

speed of the golf ball just after impact.

6-2. A rifle with a weight of [03] N fires a [04] -g bullet with a speed of

309 m/s. (a) Find the recoil speed of the rifle. (b) If a 685-N man holds the rifle firmly

against his shoulder, find the recoil speed of man and rifle.

6-3. A railroad car of mass [05] kg moving at [06] m/s collides and

couples with two coupled railroad cars, each of the same mass as the single car and

moving in the same direction at 1.24 m/s. (a) What is the speed of the three coupled

cars after the collision? (b) How much kinetic energy is lost in the collision?

6-4. A [07] -kg object moving to the right at 22.5 cm/s makes an elastic head-on

collision with a 11.2-kg object that is initially at rest. Find (a) the velocity of the 11.2-kg

object after the collision and (b) the fraction of the initial kinetic energy transferred to

the 11.2-kg object.

6-5. An 8.29-kg mass moving east at [08] m/s on a frictionless horizontal surface

collides with a 18.5-kg mass that is initially at rest. After the collision, the first mass

moves south at [09] m/s. What is (a) the magnitude and (b) the direction of

the velocity of the second mass after the collision? (c) What percentage of the initial

kinetic energy is lost in the collision? Note that the first mass changes the direction of its

motion. Use the approach as in the example, “Collision at an Intersection”, in the

textbook (Example 6.8 in the 7th edition, Example 6.9 in the 6th edition, and Example

6.10 in the 5th edition).

6-6. A friend claims that he can hold on to a 12.4-kg child in a [10] -mi/h collision

lasting for 0.052 s as long as he has his seat belt on. (a) Calculate the average force the

child exerts on the other person during the collision. (b) Can he hold on to the child? (A

child should always be in a toddler seat secured with a seat belt in the back seat of a car.)

6-7. A [11] -g bullet is fired into a 1.57-kg ballistic pendulum. The bullet emerges

from the block with a speed of 212 m/s, and the block rises to a maximum height of

12.7 cm. Find the initial speed of the bullet.

6-8. Consider a frictionless track as shown in the figure. A block of mass

m1 = [12] kg is released from A. It makes a head-on elastic collision at B with

a block of mass m2 = 12.4 kg that is initially at rest. Calculate the maximum height to

which m1 rises after the collision.

6-9. Two automobiles of equal mass approach an intersection. One vehicle is traveling with

velocity [13] mi/h toward the east and the other is traveling north with

speed v. Neither driver sees the other. The vehicles collide in the intersection and stick

together, leaving parallel skid marks at an angle of 55.6◦ north of east. What was the

speed of the northward-moving vehicle when the collision occurred?

7-1. A potter’s wheel moves from rest to an angular speed of 0.247 rev/s in [01] s.

Find its angular acceleration.

7-2. A machine part rotates at an angular speed of 0.66 rad/s. Its speed is then increased to

[02] rad/s at an angular acceleration of 0.713 rad/s2. Find the angle through

which the part rotates before reaching the final speed.

7-3. A mass attached to a 57.8-cm-long string starts from rest and is rotated

[03] times in 60.0 s before reaching a final angular speed. (a) Determine the

angular acceleration of the mass, assuming that it is constant. (b) What is the final

angular speed of the mass?

7-4. An airplane is flying in a horizontal circle at a speed of [04] m/s. The

[05] -kg pilot does not want her radial acceleration to exceed 7g. (a) What is

the minimum radius of the circular path? (b) At this radius, what is the force causing

the centripetal acceleration of the pilot?

7-5. An air puck of mass 255 g is tied to a string and

allowed to revolve in a circle of radius 1.04 m on a

frictionless horizontal table. The other end of the

string passes through a hole in the center of the table,

and a mass of [06] g is tied to it. The

suspended mass remains in equilibrium while the puck

on the tabletop revolves. (a) What is the tension in

the string? (b) What is the force causing the

centripetal acceleration of the puck? (c) What is the

speed of the puck?

7-6. A pail of water is rotated in a vertical circle of radius [07] m (the approximate

length of a person’s arm). What must be the minimum speed of the pail at the top of the

circle if no water is to spill out?

7-7. A satellite has mass of 142 kg and is located at h = [08] m above Earth’s

surface. (a) What is the potential energy associated with the satellite at this location?

(b) What is the magnitude of the gravitational force on the satellite?

7-8. Two objects attract each other with a gravitational force of magnitude [09] N

when separated by 23.6 cm. If the total mass of the two objects is 5.16 kg, what is the

mass of the object with the greater mass?

7-9. Geosynchronous satellites have a angular velocity that matches the rotation of the Earth

and follow circular orbits in the equatorial plane of the Earth. (Almost all

communications satellites are geosynchronous and appear to be stationary above a point

on the Equator.) Consider a satellite in geosynchronous orbit about a planet similar to

the Earth except that its mass is [10] kg and the period of the

rotation about its axis is [11] h. What must be the radius of the orbit of this

satellite?

7-10. Use the data in the textbook to find the net gravitational force exerted by Earth and the

Moon on a spaceship with mass [12] kg located halfway between them.

8-1. The chewing muscle, the masseter, is one of the

strongest in the human body. It is attached to the

mandible (lower jawbone). The jawbone is pivoted

about a socket just in front of the auditory canal.

The forces acting on the jawbone are equivalent to

those acting on the curved bar as shown in the

figure. C is the force exerted against the jawbone

by the food being chewed, T is the tension in the

masseter, and R is the force exerted on the

mandible by the socket. Find (a) T and (b) R if

you bite down on a piece of steak with a force of

[01] N.

8-2. A steel band exerts a horizontal force F of

[02] N on a tooth at point B in the figure.

What is the magnitude of the torque on the root of the

tooth at point A?

8-3. A uniform plank of length 2.26 m and mass [03] kg is supported by three

ropes, as indicated by the vectors in the figure. In the figure, θ = [04] ◦. A

705-N person is standing 0.52 m from the left end. Find the tensions (a) T2, (b) T1, and

(c) T3.

8-4. A hungry 728-N bear walks out on a beam in an attempt

to retrieve some ”goodies” hanging at the end (see figure).

The beam is uniform, weighs 216 N, and is

[05] m long; the goodies weigh 82 N. When the

bear is at x = 1.00 m, find (a) the tension on the wire and

(b) the magnitude of the reaction force at the hinge. (c) If

the wire can withstand a maximum tension of 900 N, what

is the maximum distance the bear can walk before the wire

breaks?

8-5. An 8.31-m, 267-N uniform ladder rests against a smooth wall. The coefficient of static

friction between the ladder and the ground is 0.582, and the ladder makes a 52.6◦ angle

with the ground. How far up the ladder can a [06] -N person climb before the

ladder begins to slip?

8-6. As part of a physical therapy program following a

knee operation, a 10.0-kg object is attached to an

ankle, and leg lifts are done as sketched in the

figure. The value of d in the figure is

[07] cm. Calculate the torque about

the knee due to this weight for the position at

(a) 0◦, (b) 30◦, (c) 60◦, and (d) 90◦.

8-7. Grade summary goes here.

9-1. A potter’s wheel having a radius of 0.561 m and a moment of inertia of 12.5 kg·m2 is

rotating freely at 53.7 rev/min. The potter can stop the wheel in [01] s by

pressing a wet rag against the rim and exerting a radially inward force of 68.2 N. Find

the effective coefficient of kinetic friction between the wheel and the wet rag.

9-2. A 149-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius

[02] m is set in motion by wrapping a rope about the rim of the disk and

pulling on the rope. What constant force would have to be exerted on the rope to bring

the merry-go-round from rest to an angular speed to 0.532 rev/s in 2.09 s?

9-3. Four objects are held in position at the corners of a

rectangle by light rods as shown in the figure. If

m = [03] kg, find the moment of inertia of the

system about (a) the x axis, (b) the y axis, and (c) an axis

through O and perpendicular to the page.

9-4. A 13.7-kg cylinder rolls without slipping on a rough surface. At an instant when its

center of gravity has a speed of [04] m/s, determine (a) the translational

kinetic energy of its center of gravity, (b) the rotational kinetic energy about its center of

gravity, and (c) its total kinetic energy. Note: the answer does not depend on the radius

of the cylinder.

9-5. A light string is wrapped around a solid cylindrical spool of radius

0.565 m and mass [05] kg. A 5.04 kg mass is hung from the

string, causing the spool to rotate and the string to unwind. Assume

that the system starts from rest and no slippage takes place between

the string and the spool. By direct application of Newton’s second

law, determine the angular speed of the spool after the mass has

dropped 4.19 m. Caution: The tension T in the string is not equal to

the weight of the hanging mass. You must write down Newton’s

second law for the mass as well as for the spool. This will result in two

equations and two unknowns, α and T (assuming that you used

a = αr for the hanging mass).

9-6. A light string is wrapped around a solid cylindrical spool of radius

0.565 m and mass [06] kg. A 5.04 kg mass is hung from the

string, causing the spool to rotate and the string to unwind. Assume

that the system starts from rest and no slippage takes place between

the string and the spool. Use conservation of energy to determine the

angular speed of the spool after the mass has dropped 4.19 m.

9-7. A car is designed to get its energy from a rotating flywheel which is a solid cylinder with

a radius of 2.54 m and a mass of 476 kg. Before a trip, the flywheel is attached to an

electric motor, which brings the flywheel’s rotational speed up to

[07] rev/min. (a) Find the kinetic energy stored in the flywheel. (b) If the

flywheel is to supply energy to the car as would a 11.3-hp motor, find the length of time

the car could run before the flywheel would have to be brought back up to speed.

9-8. A student sits on a rotating stool holding two 3.09-kg masses. When his arms are

extended horizontally, the masses are 1.08 m from the axis of rotation, and he rotates

with an angular speed of [08] rad/s. The moment of inertia of the student

plus stool is 3.25 kg·m2 and is assumed to be constant. (Note that this moment of inertia

does not include the two 3.09-kg masses.) The student then pulls the masses horizontally

to 0.34 m from the rotation axis. (a) Find the new angular speed of the student. Find

the kinetic energy of the rotating system (student, stool, and masses) (b) before and

(c) after the masses are pulled in.

10-1. If the elastic limit of steel is 5.26 × 108 Pa, determine the minimum diameter a steel wire

can have if it is to support a [01] -kg circus performer without its elastic limit

being exceeded.

10-2. Water is to be pumped to the top of a skyscraper, which is [02] ft high. What

gauge pressure is needed in the water line at the base of the building to raise the water to

this height? (This building is about the same height as the Empire State Building in

New York City.)

10-3. A [03] -kg ballet dancer stands on her toes during a performance with

26.5 cm2 in contact with the floor. What is the pressure exerted by the floor over the

area of contact (a) if the dancer is stationary, and (b) if the dancer is leaping upwards

with an acceleration of 4.41 m/s2?

10-4. A collapsible plastic bag contains a glucose solution. If the

average gauge pressure in the artery is [04] Pa, what

must be the minimum height h of the bag in order to infuse

glucose into the artery? Assume that the specific gravity of the

solution is 1.02.

10-5. The figure shows the essential parts of a hydraulic

brake system. The area of the piston in the master

cylinder is [05] cm2 and that of the piston

in the brake cylinder is 1.75 cm2. The coefficient of

friction between shoe and wheel drum is 0.541. If the

wheel has a radius of 34.4 cm, determine the frictional

torque about the axle when a force of 43.9 N is exerted

on the brake pedal.

10-6. A frog in a hemispherical pod finds that he just floats without

sinking in a fluid of density 1.27 g/cm3. If the pod has a

radius of [06] cm and negligible mass, what is the

mass of the frog?

10-7. A 1.54-kg beaker contains 2.67 kg of oil (density =

916 kg/m3). A [07] -kg block of iron is

suspended from a spring scale and completely submerged in

the oil, as shown in the figure. Note that the force of the

oil on the block of iron is upward. By Newton’s third law,

the force of the block on the oil must then be downward.

Find the equilibrium reading of (a) the top scale and

(b) the bottom scale.

10-8. Water is pumped into a storage tank from a well delivering 17.8 gallons of water in 30.0 s

through a pipe of [08] in.2 cross-sectional area. What is the average velocity

of the water in the pipe as the water is pumped from the well?

10-9. When a person inhales, air moves down the bronchus (windpipe) at [09] cm/s.

The average flow speed of the air doubles through a constriction in the bronchus.

Assuming incompressible flow, determine the pressure drop in the constriction. Neglect

the change of pressure due to change in height y in the wind pipe. Use 1.20 kg/m3 for

the density of air.

10-10. A large storage tank, open to the atmosphere at the top and filled with water, develops a

small hole in its side at a point [10] m below the water level. If the rate of

flow from the leak is 2.53 × 10−3 m3/min, determine (a) the speed at which the water

leaves the hole and (b) the diameter of the hole.

10-11. A liquid (ρ = 1.65 g/cm3) flows through two horizontal sections of tubing joined end to

end. In the first section the cross-sectional area is 10.0 cm2, the flow speed is 275 cm/s,

and the pressure is 1.20 × 105 Pa. In the second section the cross-sectional area is

[11] cm2. Calculate the smaller section’s (a) flow speed and (b) pressure.

11-1. A 605-kg weather balloon is designed to lift a [01] -kg package. What volume

should the balloon have after being inflated with helium at standard temperature and

pressure (STP) in order that the total load can be lifted? Be sure to include the weight of

the helium. Note that the densities of gases at STP are given in Table 9.3 on p. 262 in

the textbook (Table 9.2 in the 5th edition of the textbook).

11-2. A pair of eyeglass frames are made of epoxy plastic (coefficient of linear expansion =

134 × 10−6 ◦C−1). At room temperature (21.9◦C) the frames have circular lens holes

2.232 cm in radius. To what temperature must the frames be heated in order to insert

lenses [02] cm in radius?

11-3. Gas is contained in an 8.71-L vessel at a temperature of [03] ◦C and a pressure

of 9.37 atm. (a) Determine the number of moles of gas in the vessel. (b) How many

molecules are in the vessel?

11-4. Two concrete spans of a 250-m-long bridge are placed end to end so that no room is

allowed for expansion [Figure (a)]. If the temperature increases by [04] ◦C,

what is the height y to which the spans rise when they buckle [Figure (b)]?

11-5. A weather balloon is designed to expand to a maximum radius of [05] m when

in flight at its working altitude, where the air pressure is 0.0282 atm and the temperature

is −65◦C. If the balloon is filled at 0.873 atm and 21◦C, what is its radius at lift-off?

11-6. A [06] -g sample of copper is at 25.6◦C. If 1250 J of heat energy is added to

the copper, what is its final temperature?

11-7. Lead pellets, each of mass 1.04 g, are heated to 219◦C. How many pellets must be added

to 532 g of water that is initially at 20.9◦C to make the equilibrium temperature

[07] ◦C? Neglect any heat transfer to or from the container.

11-8. A 137-g ice cube at 0◦C is placed in [08] g of water at 24.8◦C. What is the

final temperature of the mixture?

11-9. A Styrofoam box has a surface area of 0.832 m2 and a wall thickness of 2.09 cm. The

temperature of the inner surface is 4.8◦C, and that outside is 25.5◦C. If it takes

[09] h for 5.54 kg of ice to melt in the container, determine the thermal

conductivity of the Styrofoam.

11-10. Steam at 100◦C is added to ice at 0◦C. Find (a) the amount of ice melted and (b) the

final temperature when the mass of steam is [10] g and the mass of ice 51.4 g.

Find (c) the amount of ice melted and (d) the final temperature when the mass of steam

is [11] g and the mass of ice is the same as before..

11-11. An iron nail is driven into a block of ice by a single blow of a hammer. The hammerhead

has a mass of 0.53 kg and an initial speed of [12] m/s. Nail and hammer are

at rest after the blow. How much ice melts? Assume the temperature of the nail is 0.0◦C

before and after. Also, assume all of the kinetic energy lost ends up as heat which melts

the ice.

12-1. A 0.432-kg object is attached to a spring with a spring constant [01] N/m so

that the object is allowed to move on a horizontal frictionless surface. The object is

released from rest when the spring is compressed 0.158 m. Find (a) the force on the

object and (b) its acceleration at this instant.

12-2. An archer pulls her bow string back 0.412 m by exerting a force that increases uniformly

from zero to [02] N. (a) What is the equivalent spring constant of the bow?

(b) How much work is done in pulling bow?

12-3. A 1.54-kg block at rest on a tabletop is attached to a horizontal spring having constant

18.2 N/m as in the figure. The spring is initially unstretched. A constant

[03] -N horizontal force is applied to the object causing the spring to stretch.

(a) Determine the speed of the block after it has moved 0.331 m from equilibrium if the

surface between the block and tabletop is frictionless. (b) Answer part (a) if the

coefficient of kinetic friction between block and tabletop is 0.192.

12-4. A [04] -g block is released from rest and

slides down a frictionless track that begins 2.00 m

above the horizontal, as shown in the figure. At the

bottom of the track, where the surface is horizontal,

the block strikes and sticks to a light spring with a

spring constant of 18.3 N/m. Find the maximum

distance the spring is compressed.

12-5. A 5.21-g bullet moving with an initial speed of

439 m/s is fired into and passes through a 1.00-kg

block, as in the figure. The block, initially at rest

on a frictionless horizontal surface, is connected to

a spring with a spring constant of 883 N/m. If the

block moved [05] cm to the right after

impact, find (a) the speed at which the bullet

emerges from the block and (b) the mechanical

energy lost in the collision.

12-6. A slingshot consists of a light leather cup containing a stone that is pulled back against

two rubber bands. It takes a force of [06] N to stretch the bands 1.08 cm.

(a) What is the potential energy stored in the bands when a 55.4-g stone is placed in the

cup and pulled back 17.6 cm from the equilibrium position? (b) With what speed does

the stone leave the slingshot?

12-7. When four people with a combined mass of 321 kg sit down in a car, they find that the

car drops [07] mm lower on its springs. Then they get out of the car and

bounce it up and down. What is the frequency of the car’s vibration if its mass when

empty is 2370 kg?

12-8. If the frequency of oscillation of the wave emitted by an FM radio station is

[08] MHz, determine the wave’s (a) period of vibration and (b) wavelength.

(Hint: Radio waves travel at the speed of light, 3.00 × 108 m/s.)

12-9. A circus performer stretches a tightrope between two towers. He strikes one end of the

rope and sends a wave along it toward the other tower. He notes that it takes the wave

[09] s to reach the opposite tower, 28.2 m away. If 1.00 meter of the rope has

a mass of 0.356 kg, find the tension in the tightrope.

13-1. You are watching a pier being constructed on the far shore of a saltwater inlet when

some blasting occurs. You hear the sound in the water [01] s before it reaches

you through the air. How wide is the inlet? (Hint: See Table 14.1. Assume the air

temperature is 25◦C. Be sure to use the speed of sound in “Sea water”, not “Water”.)

13-2. A family ice show is held at an enclosed arena. The skaters perform to music with level

81.7 dB. This is too loud for your baby who yells at [02] dB. (a) What total

sound intensity engulfs you? (b) What is the combined sound level?

13-3. A stereo speaker (considered a small source) emits sound waves with a power output of

[03] W. (a) Find the intensity 10.5 m from the source. (Assume that the

sound is emitted uniformly in all directions from the speaker.) (b) Find the intensity

level, in decibels, at this distance. (c) At what distance would you experience the sound

at the threshold of pain, 120 dB?

13-4. A skyrocket explodes at a height

h = [04] m above the

ground (see figure). Three observers

are spaced 100 m apart, with

observer A directly under the point of

the explosion. (a) What is the ratio

of sound intensities heard by

observers A and B? (b) What is the

ratio of intensities heard by observers

A and C? Neglect the height of the

observers.

13-5. An airplane traveling at [05] m/s emits a sound of frequency 5.41 kHz. At

what frequency does a stationary listener hear the sound (a) as the plane approaches?

(b) after it passes? Use 345 m/s for the speed of sound.

13-6. Two trains on separate tracks move toward one another. Train 1 has a speed of

[06] km/h and train 2 a speed of 93 km/h. Train 2 blows its horn, emitting a

frequency of 532.9 Hz. What is the frequency heard by the engineer on train 1? Use

345 m/s for the speed of sound.

13-7. The sound interferometer shown in the figure is

driven by a speaker emitting a

[07] -Hz note. If destructive

interference occurs at a particular instant, how

much must the path length in the U-shaped tube

be increased in order to hear (a) constructive

interference and (b) destructive interference

once again? Use 345 m/s for the speed of sound.

13-8. In the arrangement shown in the figure, an object of mass m = [08] kg hangs

from a cord around a light pulley. The length of the cord between point P and the pulley

is L = 2.0 m. When the vibrator is set to a frequency of 150 Hz, a standing wave with six

loops is formed. What must be the linear mass density of the cord?

13-9. Grade summary goes here.

Answers to Homework Problems, Physics 105, Fall Semester, 2007Sec. 3, Stephanie Magleby

1-1. 12.100, 12.200 mi/h1-2a. 70.0, 120.0 km1-2b. 45.0, 65.0 km/h1-3a. 3.00, 5.00 m/s1-3b. −0.25, −0.75 m/s1-3c. −0.75, −1.25 m/s1-3d. 01-4. 1.20, 1.50 h1-5. 0.60, 1.20 m/s2

1-6. −1400, −1800 ±10 m/s2

1-7. 5.00, 9.00 h1-8a. 1.10, 1.90 m/s2

1-8b. 100, 170 m1-9a. 15.0, 25.0 s1-9b. 0.60, 1.50 km2-1a. 20.0, 50.0 m2-1b. 2.00, 3.20 s2-1c. 2.00, 3.20 s2-1d. −20.0, −30.0 m/s2-2a. 240, 390 m2-2b. 7.0, 10.0 s2-2c. 14.0, 19.0 s2-3. 50, 250 m2-4. 200, 500 ft2-5. 10.0, 20.0 m/s2-6. 4.0, 32.0 m2-7a. 10.00, 20.00 m2-7b. 5.00, 10.00 m2-8a. 10.0, 30.0◦

2-8b. 1.50, 4.50 s3-1. 13.0, 30.0 N3-2. 4.00, 12.00 min3-3. 600, 1500 ± 10 N3-4a. 700, 1100 N3-4b. 500, 900 N3-5a. 130, 180 N3-5b. 70, 100 N3-5c. 150, 200 N3-6a. 35.0, 65.0 N3-6b. 40.0, 70.0 N3-7a. 6.00, 8.00 m/s2

3-7b. 19.0, 23.0 N

3-7c. 12.0, 16.0 N3-8a. 110, 140 N3-8b. 220, 250 N4-1a. 2.50, 5.00 m/s2

4-1b. 40.0, 60.0 N4-2a. 6.00, 8.00 m/s2

4-2b. 30.0, 40.0 N4-3a. 0.20, 0.604-3b. 0.20, 0.604-4. 0.150, 0.5004-5. 3.00, 4.00 m/s2

4-6a. 10.0, 25.0 N4-6b. 20.0, 30.0 N4-7. 680, 760 J4-8. 125, 200 m/s4-9a. −8.0, −40.0 J4-9b. 20.0, 60.0 J4-9c. 0.0, 0.0 J5-1a. 400, 800 J5-1b. 0.80, 1.60 m5-2a. 50.0, 120.0 J5-2b. 100, 300 N5-3. 1.20, 1.80 m/s5-4a. 3.50, 7.50 m/s5-4b. 6.00, 9.00 m/s5-4c. 90, 200 J5-5. 4.00, 6.20 m5-6a. 8.50, 11.00 m/s5-6b. 5.00, 10.00 m/s5-7a. 2.00, 3.00 m/s5-7b. 15.0, 90.0 J5-8a. 19000, 27000 ±100 J5-8b. 0.60, 1.50 hp6-1. 40.0, 120.0 m/s6-2a. 30.0, 60.0 cm/s6-2b. 1.80, 2.40 cm/s6-3a. 1.60, 2.00 m/s6-3b. 7000, 43000 ±100 J6-4a. 10.0, 20.0 cm/s6-4b. 0.850, 0.9506-5a. 4.50, 9.50 m/s6-5b. 8.0, 30.0◦ north of east

6-5c. 15.0, 60.0%6-6a. 900, 1500 ± 10 lbs6-7. 500, 750 m/s6-8. 0.90, 2.00 m6-9. 35.0, 55.0 mi/h7-1. 0.0300, 0.0800 rad/s2

7-2. 2.50, 4.50 rad7-3a. 0.100, 0.200 rad/s2

7-3b. 6.00, 11.00 rad/s7-4a. 160, 210 m7-4b. 5100, 5900 ±10 N7-5a. 7.80, 9.40 N7-5b. 7.80, 9.40 N7-5c. 5.60, 6.20 m/s7-6. 3.20, 3.70 m/s7-7a. −6.00 × 109, −8.00 × 109 J7-7b. 800, 1100 N7-8. 3.50, 5.00 kg7-9. 32000, 39000 ±100 km7-10. 200, 500 N8-1a. 120, 190 N8-1b. 80, 130 N8-2. 0.400, 0.800 N·m8-3a. 740, 770 N8-3b. 600, 1000 N8-3c. 500, 900 N8-4a. 350, 450 N8-4b. 600, 800 N8-4c. 3.00, 5.00 m8-5. 6.50, 7.50 m8-6a. 0, −50 N·m8-6b. 0, −50 N·m8-6c. 0, −50 N·m8-6d. 0, −50 N·m8-7. 0, 100%9-1. 0.250, 0.4009-2. 150, 210 N9-3a. 80.0, 100.0 kg·m2

9-3b. 30.0, 50.0 kg·m2

9-3c. 120.0, 150.0 kg·m2

9-4a. 400, 600 J9-4b. 200, 300 J

9-4c. 600, 900 J9-5. 14.0, 16.0 rad/s9-6. 14.0, 16.0 rad/s9-7a. 1.70 × 108, 3.60 × 108 J9-7b. 5.00, 12.00 h9-8a. 1.80, 2.20 rad/s9-8b. 2.50, 3.40 J9-8c. 6.50, 9.00 J10-1. 1.00, 1.50 mm10-2. 3.70 × 106, 4.20 × 106 Pa10-3a.10-3b.10-4. 1.25, 1.45 m10-5. 2.00, 2.40 N·m10-6. 0.300, 0.950 kg10-7a. 20.0, 70.0 N10-7b. 44.0, 50.0 N10-8. 2.30, 3.20 m/s10-9. −0.010, −0.040 Pa10-10a. 13.0, 20.0 m/s10-10b. 1.50, 2.00 mm10-11a. 5.0, 12.0 m/s10-11b. 20000, 120000 ± 100 Pa11-1. 4300, 5100 ±10 m3

11-2. 60.0, 100.0◦C11-3a. 3.00, 3.50 mol11-3b. 1.80 × 1024, 2.10 × 1024

11-4. 1.0, 5.0 m11-5. 5.00, 9.00 m11-6. 70.0, 110.0◦C11-7. 400, 90011-8. 7.0, 11.0◦C11-9. 0.0600, 0.1100 J/s·m·

◦C11-10a. 51.4, 51.4 g11-10b. 30.0, 90.0◦C11-10c. 8.0, 17.0 g11-10d. 0.0, 0.0◦C11-11. 3.0, 8.0 mg12-1a. 10.0, 30.0 N12-1b. 30.0, 60.0 m/s2

12-2a. 350, 750 N/m12-2b. 30.0, 65.0 J

12-3a. 2.00, 4.00 m/s12-3b. 2.00, 4.00 m/s12-4. 1.00, 1.40 m12-5a. 90, 250 m/s12-5b. 350, 500 J12-6a. 30.0, 60.0 J12-6b. 30.0, 50.0 m/s12-7. 1.90, 2.20 Hz12-8a. 9.0× 10−9, 12.0× 10−9

± 0.1× 10−9 s12-8b. 2.70, 3.40 m12-9. 350, 600 N13-1. 2.00, 3.00 km13-2a. 1.50 × 10−4, 1.90 × 10−4 W/m2

13-2b. 82.0, 84.0 dB13-3a. 5.0, 70.0 mW/m2

13-3b. 95.0, 110.0 dB13-3c. 0.50, 3.00 m13-4a. 1.0, 5.013-4b. 2.0, 20.013-5a. 8.00, 11.00 kHz13-5b. 3.60, 4.10 kHz13-6. 640.0, 660.0 Hz13-7a. 40, 180 cm13-7b. 90, 350 cm13-8. 2.0, 7.0 g/m13-9. 0, 100%