physics for scientist and engineers third edition...

1/19 Conservation of Energy problems.pdf (#4)2012-09-14 18:15:29

Conservation of Energy Problems

Example Problem

A 1000 kg roller coaster car moves from pint A which is 15 m above the bottom to point B which is 10

m above point A. Then it drops to point C which is 25 m below point B. A) what is the gravitational

potential energy at B and C relative to point A. That is take y=o at point A. B) What is the change in

potential energy when it goes from B to C C) Repeat parts A and B, but take the reference point (y=0)

to be at point C

Variables

Drawing

Solution

Answer: -1.5 E 5 J; -2.5 E 5 J; -2.5 E5 J

Physics for Scientist and Engineers third edition

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2/19 Conservation of Energy problems.pdf (2/13)2012-09-14 18:15:29


Example Problem

If the original height of the stone is y1= h= 3.0 m, calculate the stone’s speed when it has fallen 1.0 m

above the ground

Variables

Drawing

Solution

Answer: 6.3 m/s


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Example Problem

Assuming the height of the hill is 40 m and the roller-coaster car starts from rest at the top, calculate

A) the speed of the roller-coaster car at the bottom of the hill, and B) at what height it will have half

the speed. Takey=0 ( and U=0) at the bottom of the hill

Variables

Drawing

Solution

Answer: 28 m/s


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Example Problem

Estimate the kinetic energy and the speed required for a 70 kg pole vaulter to just pass over a bar 5.0 m

hight. Assume the vaulter’s center of mass is initially 0.90 m off the ground and reaches its maximum

height at the level of the bar itself

Variables

Drawing

Solution

Answer: 8.9 m/s


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Example Problem

A dart of mass 0.100 kg is pressed against the spring of a toy dart gun. The spring (with spring

constant k=250 N/m) is compressed 6.0 cm and released. If the dart detaches from the spring when the

latter reaches its normal length (x=0), what speed does the dart acquire?

Variables

Drawing

Solution

Answer: 3.0 m/s^2


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Example Problem

A ball of mass m= 2.60 kg starting from rest, falls a vertical distance h= 55.0 cm before striking a

vertical coiled spring, which it compresses an amount Y= 15.0 cm. Determine the spring constant of

the spring. Assume the spring has negligible mass. measure all distances from the point where the

ball first touches the uncompressed spring (y=0 at this point)

Variables

Drawing

Solution

Answer: 1580 N/m


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Example Problem

Dave jumps off a bridge with a bungee cord tied around his ankle. He falls for 15 meters before the

bungee cord begins to stretch. Dave’s mass is 75 kg and we assume the cord obeys Hooke’s Law with

k= 50 N/m. If we neglect air resistance estimate how far below the bridge Dave will fall before

coming to a stop. Ignore the mass of the cord.

Variables

Drawing

Solution

Answer: 55 m


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Example Problem

The simple pendulum has a small bob of mass m suspended by a massless cord of length l. The bob is

released at t=0, where the cord makes and angle ø=ø0 to the vertical. A) describe the motion of the

bob in terms of kinetic energy and potential energy. Then determine the speed of the bob b) as a

function of position ø as it swings back and forth and C) at the lowest point of the swing D) find the

Tension in the cord

Variables

Drawing

Solution

Answer:


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Example Problem

The roller coaster car starts at a height y1= 40 m is found to reach a vertical height of only 25 m on the

second hill before coming to a stop. It traveled a total distance of 400 m. Estimate the average friction

force (assume constant) on the car, whose mass is 1000 kg

Variables

Drawing

Solution

Answer: 370 N


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Example Problem

A block of mass m sliding along a rough horizontal surface is traveling at a speed V0 when it strikes a

massless spring head on and compresses the spring a maximum distance X. If the spring has stiffness

constant k, determine the coefficent of kinetic friction between block and surface.

Variables

Drawing

Solution

Answer:


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Example Problem

A box of empty film canisters is dumped from a rocket traveling outward from Earth at a speed of

1800 m/s when 1600 km above the Earth’s surface. The package eventually falls to the Earth.

Estimate its speed just before impact. Ignore air resistance

Variables

Drawing

Solution

Answer: 5320 m/s


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Example Problem

A) Compare the escape velocities of a rocket from the Earth and from the moon B) compare the

energies required to launch the rockets. For the Moon Mm= 7.35 E 22 kg and rm= 1.74 E 6 m, and for

the Earth Me= 5.97 E 24 kg and re= 6.38 E 6 m

Variables

Drawing

Solution

Answer: 4.7


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Example Problem

A 70 kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m. A)

Estimate the jogger’s power output in watts and horsepower B) how much energy did this require?

Variables

Drawing

Solution

Answer: 770 W, 1 hp; 3100 J


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14/19 Work and Energy Problems.pdf (#3)2012-09-14 18:15:31

Work and Energy Problems

Example Problem

a 50 kg crate is pulled 40 m along a horizontal floor by a constant force exerted by a person, Fp=

100N, which acts at a 37˚ angle. The floor is rough and exerts a friction force Ffr= 50 N. Determine

the work done by each force acting on the crate, and the net work done on the crate.

Variables

Drawing

Solution

Answer: 3200 J, -2000J, 1200 J


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15/19 Work and Energy Problems.pdf (2/6)2012-09-14 18:15:31


Example Problem

A) Determine the work a hiker must do on a 15.0 kg backpack to carry it up a hill of height h= 10.0 m.

Determine also B) the work done by gravity on the backpack C) the net work done on the backpack.

For simplicity, assume the motion is smooth and at a constant velocity

Variables

Drawing

Solution

Answer: 1470 J, -1470 J, o


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Example Problem

A person pulls on the spring stretching it 3.0 cm, which requires a maximum force of 75 N. How

much work does the person do?

Variables

Drawing

Solution

Answer: 1.1 J


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Example Problem

A 145 g- baseball is thrown with a speed of 25 m/s A) what is the kinetic energy B) How much work

was done to reach this speed starting from rest?

Variables

Drawing

Solution

Answer: 45 J, 45 J


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Example Problem

A horizontal spring has a spring constant of k=360 N/m A) how much work is required to compress it

down to its uncompressed length (x=0) to x=11.0 cm B) If a 1.85 kg block is placed against the spring

and the spring is released, what will be the speed of the block when it separates from the spring at x=0

C) Repeat part B but assume that the block is moving on a table and that the coefficent of friction is

µk= 0.38

Variables

Drawing

Solution

Answer: 2.18 J; 1.54 m/s^2; 1.24 m/s


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Example Problem

How much work is required to accelerate a 1000 kg car from 20 m/s to 30 m/s

Variables

Drawing

Solution

Answer: 2.5 E 5 J


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