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Ch 4

Class problems section 4.3

1. An airplane has a mass of 3.1 x 104 kg and takes off under the influence of a constant net

force of 3.7 x 104 N. What is the net force that acts on the planes 78-kg pilot?

2. Two horizontal forces, 1F and ,2F are acting on a box, but only 1F is shown in the drawing.

2F can point either to the right or to the left. The box moves only along the x axis. There is no friction

between the box and the surface. Suppose that 1F=+9.0 N and the mass of the box is 3.0 kg. Find the

magnitude and direction of 2F when the acceleration of the box is (a) +5.0 m/s2, (b) -5.0 m/s2, and (c) 0 m/s2.

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3. When a 58-g tennis ball is served, it accelerates from rest to a speed of 45 m/s. The impact with the racket gives the ball a constant acceleration over a distance of 44 cm.

What is the magnitude of the net force acting on the ball?

4. A 1580-kg car is traveling with a speed of 15.0 m/s. What is the magnitude of the horizontal net force that is required to bring the car to a halt in a distance of 50.0 m?

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Ch 4

5. A person with a black belt in karate has a fist that has a mass of 0.70 kg. Starting from

rest, this fist attains a velocity of 8.0 m/s in 0.15 s. What is the magnitude of the average

net force applied to the fist to achieve this level of performance?

6. Two forces AF and BF are applied to an object whose mass is 8.0 kg. The larger force is

.AF When both forces point due east, the objects acceleration has a magnitude of 0.50

m/s2. However, when AF points due east and BF points due west, the acceleration is 0.40

m/s2, due east. Find (a) the magnitude of AF and (b) the magnitude of BF .

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Ch 4

Section 4.4

7. Two forces, 1F and ,2F act on the 7.00-kg block shown in the

drawing. The magnitudes of the forces are F1 = 59.0 N and F2 = 33.0 N. What is the horizontal acceleration (magnitude and

direction) of the block?

8. A rocket of mass 4.50 x 105 kg is in flight. Its thrust is directed at an angle of 55.0 above the horizontal and has a magnitude of 7.50 x 106 N. Find the magnitude and direction of

the rockets acceleration. Give the direction as an angle above the horizontal.

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9. Airplane flight recorders must be able to survive catastrophic crashes. Therefore, they are typically encased in crash-resistant steel or titanium boxes that are subjected to rigorous

testing. One of the tests is an impact shock test, in which the box must survive being thrown at high speeds against a barrier. A 41-kg box is thrown at a speed of 220 m/s and

is brought to a halt in a collision that lasts for a time of 6.5 ms. What is the magnitude of the average net force that acts on the box during the collision?

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Ch 4

10. A duck has a mass of 2.5 kg. As the duck paddles, a force of 0.10 N acts on it in a direction due east. In addition, the current of the water exerts a force of 0.20 N in a

direction of 52o south of east. When these forces begin to act, the velocity of the duck is 0.11 m/s in a direction due east. Find the magnitude and direction (relative to due east) of

the displacement that the duck undergoes in 3.0 s while the forces are acting.

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Ch 4

11. A boat moves through the water with two forces acting on it. One is a 2000-N forward push by the water on the propeller, and the other is a 1 800-N resistive force due to the

water around the bow. (a) What is the acceleration of the 1000-kg boat? (b) If it starts from rest, how far will the boat move in 10.0 s? (c) What will its velocity be at the end of

that time?

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Ch 4

12. A 325-kg boat is sailing 15.0O north of east at a speed of 2.00 m/s. Thirty seconds later, it is sailing 35.0O north of east at a speed of 4.00 m/s. During this time, three forces act

on the boat: a 31.0-N force directed 15.0O north of east (due to an auxiliary engine), a

23.0-N force directed 15.0O south of west (resistance due to the water), and wF (due to

the wind). Find the magnitude and direction of the force .wF Express the direction as an angle with respect to due east.

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Ch 4

13. Two forces are applied to a car in an effort to move it,

as shown in the Figure (a) What is the resultant of these

two forces? (b) If the car has a mass of 3 000 kg, what

acceleration does it have? Ignore friction.

14. After falling from rest from a height of 30 m, a 0.50-kg ball rebounds upward, reaching a

height of 20 m. If the contact between ball and ground lasted 2.0 ms, what average force

was exerted on the ball?

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Ch 4

15. The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a

force of 180 N east. If the boat (including its crew) has a mass of 270 kg, what are the

magnitude and direction of its acceleration?

Section 4.7 The Gravitational Force

16. A space traveler whose mass is 115 kg leaves earth. What are his weight and mass (a) on earth and (b) in interplanetary space where there are no nearby planetary objects?

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Ch 4

17. Saturn has an equatorial radius of 6.00 x 107 m and a mass of 5.67 x 1026 kg. (a) Compute the acceleration of gravity at the equator of Saturn. (b) What is the ratio of a persons weight on Saturn to that on earth?

Section 4.8 The Normal Force, Section 4.9 Static and Kinetic Frictional Forces

18. A 35-kg crate rests on a horizontal floor, and a 65-kg person is standing on the crate.

Determine the magnitude of the normal force that (a) the floor exerts on the crate and (b) the crate exerts on the person.

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Ch 4

19. In a European country a bathroom scale displays its reading in kilograms. When a man stands on this scale, it reads 92.6-kg. When he pulls down on a chin-up bar installed over

the scale, the reading decreases to 75.1 kg. What is the magnitude of the force he exerts on the chin-up bar?

20. A person pushes on a 57-kg refrigerator with a horizontal force of -267 N; the minus sign indicates that the force points in the -x direction. The coefficient of static friction is

0.65. (a) If the refrigerator does not move, what are the magnitude and direction of the static frictional force that the floor exerts on the refrigerator? (b) What is the magnitude

of the largest pushing force that can be applied to the refrigerator before it just begins to move?

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Ch 4

21. A dockworker loading crates on a ship finds that a 20-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 static and kinetic friction between crate and floor.

22. A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle above the horizontal. She pulls on

the strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. Draw a free-body diagram of the suitcase. (a) What angle does

the strap make with the horizontal? (b) What normal force does the ground exert on the suitcase?

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Ch 4

23. A 10.0 kg sled is resting on a hill. The angle the sled makes with the horizontal is 30o. The sled is stationary on the hill

a) Please draw a FBD of the sled. Show all the forces acting on the sled

b) Use Newtons 2nd law to calculate the force exerted by the hill on the sled, i.e. the normal force, FN.

c) Calculate the friction force between the sled and the hill.

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Ch 4

24. The coefficient of static friction between the 3.00-kg crate and the 35.0 incline of Figure P4.41 is 0.300. What minimum

force F

must be applied to the crate perpendicular to the

incline to prevent the crate from sliding down the incline?

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25. Traveling at a speed of 16.1 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the

road is 0.720. What is the speed of the automobile after 1.30 s have elapsed? Ignore the effects of air resistance.

26. The drawing shows a 25.0-kg crate that is initially at rest. Note that the view is one looking down on

the top of the crate. Two forces, 1F and ,2F are

applied to the crate, and it begins to move. The coefficient of kinetic friction between the crate and

the floor is k =0.350. Determine the magnitude and direction (relative to the x axis) of the acceleration of the crate.

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Ch 4

Section 4.10 The Tension Force, Section 4.11 Equilibrium

Applications of Newtons Laws of Motion

27. Find the tension in each cable supporting the 600-N cat burglar in

the Figure.

28. The leg and cast in the Figure weigh 220 N

(w1). Determine the weight w2 and the angle

needed so that no force is exerted on the

hip joint by the leg plus the cast.

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Ch 4

29. Three forces act on a moving object. One force has a magnitude of 80.0 N and is directed due north. Another has a magnitude of 60.0 N and is directed due west. What must be the

magnitude and direction of the third force, such that the object continues to move with a constant velocity?

Section 4.12 Nonequilibrium Applications of Newtons Laws of Motion

30. A 95.0-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.80 m/s2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.30

m/s2?

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Ch 4

31. A 1450-kg submarine rises straight up toward the surface. Seawater exerts both an upward buoyant force of 16 140 N on the submarine and a downward resistive force of

1030 N. What is the submarines acceleration?

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Ch 4

32. A 40.0-kg wagon is towed up a hill inclined at 18.5 with respect to the horizontal. The

tow rope is parallel to the incline and has a tension of 140 N. Assume that the wagon

starts from rest at the bottom of the hill, and neglect friction. How fast is the wagon going

after moving 80.0 m up the hill?

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Ch 4

33. A 1000-N crate is being pushed across a level

floor at a constant speed by a force F

of 300

N at an angle of 20.0 below the horizontal,

as shown in the Figure. (a) What is the coefficient of kinetic friction between the crate and the floor? (b) If the 300-N force is

instead pulling the block at an angle of 20.0 above the horizontal, as shown, what will be the acceleration of the crate? Assume that the coefficient of friction is the same as that

found in (a).

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Ch 4

34. A fisherman is fishing from a bridge and is using a 45-N test line. In other words, the line will sustain a maximum force of 45 N without breaking. What is the weight of the

heaviest fish that can be pulled up vertically when the line is reeled in (a) at a constant speed and (b) with an acceleration whose magnitude is 2.0 m/s2?