Download Chapter 4 – Laws of Motion – Even Problems

Chapter 4 – Laws of Motion – Even Problems
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2. A car with m = 850kg is moving right with constant speed of 1.44 m/s (no direction
change either!). (a) What is the force on the car? (b) What is the force on the car if it is
moving to the left?
4. A bag of sugar weighs 5lb on Earth. What should it weigh in newtons on the moon
where the acceleration due to gravity is 1/6 that on Earth? Repeat for Jupiter where g is
2.64 times Earth’s gravity field. Find the mass in each location in kg.
6. (a) Draw a free-body diagram indicating all the forces acting on a vertically falling
baseball. For each force drawn, indicate the reaction force to it. (b) Repeat part (a) for a
baseball moving as a projectile toward an outfielder.
8. A box weighing 20N is to be pushed across a smooth floor with a horizontal force of
5N. What acceleration magnitude will be produced?
10. The engine on a 0.2kg model airplane exerts a forward force on the plane of 10N. If the
plane accelerates at 2m/s2, what is the magnitude of the resistive force due to the wind
acting on the airplane.
12*. The force of the wind on the sails of a sailboat is 390N north. The water exerts a force
of 180N east. If the boat including the crew has a mass of 270kg, what is the acceleration
(magnitude and direction) of the sailboat?
14*. A boat moves through the water with two forces acting on it. One is a 2000N forward
push by the motor, while the second is an 1800N resisitive force due to the water. (a) What
is the acceleration of the 1000kg boat? (b) If it starts from rest, how far will it move in
10s? (c) What will be its speed at the end of this time?
16. Two horses are pulling a sled along an icy road; assume that friction between the sled
and the road is negligible. A farmer keeps the sled along the proper path by pulling on it
with a rope attached at the point where the cables from two horses are attached. A noise
startles the horses and they move toward opposite sides as shown below. What are the
magnitude and direction of the force that the farmer will have to exert on the sled to keep it
moving along the road at a constant velocity?
Problem 16
Problem 18
18. A 150N bird feeder is supported by three cables as shown above. Find the tension in
each cable.
Chapter 4 – Laws of Motion – Even Problems
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20. The leg in the cast in the figure below weighs 220N (w1). Determine the weight (w2)
and angle  in order that there be no force exerted on the hip joint J by the leg in the cast.
22. A shopper in a supermarket pushes a loaded cart with a horizontal force of 10N. If the
cart is 30kg and she places her 30N child in the cart, how far will the cart move in 3sec
assuming she starts from rest?
24*. A train has a mass of 5.22 x 106 kg and is moving with a speed of 90.0 km/h. The
engineer applies the brakes, which results in a net backward force of 1.87 x 106 N on the
train. The brakes are held on for 30.0s. (a) What is the new speed of the train? (b) How far
does the train travel during this period?
26*. A 2kg mass starts from rest and slides down an inclined plane 80cm long in 5s. What
is the net force magnitude acting along the incline?
28*. A shopper pushes a 40kg cart up a 20 smooth ramp. What force directed along the
incline must the shopper exert to give the cart an acceleration of .5m/s2?
30. A 5kg bucket of water is raised from a well by a rope attached to the bucket. If the
upward acceleration of the bucket is 3m/s2, find the force exerted by the rope.
32*. On takeoff, the combined action of the engines and the wings of an airplane exerts a
force of 8000N on the plane upward at an angle of 65 above the horizontal. The plane
rises with constant speed in the vertical direction while accelerating in the horizontal
direction. (a) What is the weight of the plane? (b) What is the horizontal acceleration of the
plane?
34*. A car with a mass of 1000kg is pulling a trailer with a mass of 300kg. Together, the
car and the trailer have an acceleration of 2.15m/s2 in the forward direction. Neglecting
frictional forces on the trailer, determine (a) the net force on the car (b) the net force on the
trailer (c) the force of the trailer on the car (d) the force of the car on the road.
36*. A 5kg mass resting on a smooth horizontal table is connected to a string that passes
over a pulley and then is fastened to a hanging 10kg mass as shown below. Find the
tension in the string and the acceleration of the two objects.
Chapter 4 – Laws of Motion – Even Problems
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38. (a) A 10kg box of books rests on a horizontal surface. If the coefficient of static
friction between box and floor is 0.4, find the maximum horizontal force that can be
applied to the box before it slips. (b) The coefficient of kinetic friction is 20% less that that
of static friction. If the force found in part (a) is exerted on the box once it is in motion,
find the acceleration of the box.
40. A dockworker loading crates on a ship finds that a 20kg crate, initially at rest on a
rough horizontal surface, requires a 75N horizontal force to set it into motion. However,
after it is in motion, a horizontal force of 60N is required to keep the crate moving at a
constant speed. Find the coefficients of static and kinetic friction between the crate and the
floor.
42*. A man doing his spring cleaning pulls a 150N vacuum cleaner across the floor at a
constant velocity by exerting a force on it at an angle of 30 with the horizontal. If the
required force is 35N, what is the kinetic coefficient of friction between floor and vacuum?
44* A crate is held at rest on a frictionless 53 ramp by a rope parallel to the incline. If the
tension in the rope is 7000N, what is the mass of the crate?
46*. A person standing on crutches (shown below) weighs 170lb. The crutches each make
an angle of 22 with the vertical as viewed from the front. Half of the person’s weight is
supported by the crutches. The other half is supported by the vertical forces of the ground
the feet. Assume the force of the ground on the crutches acts along the crutches and
determine (a) the coefficient of friction of the crutches on the ground and (b) the
magnitude of the compression force supported by each crutch.
Problem 46
48*. A box slides down a 30 ramp with an acceleration of 1.2m/s2. Determine the
coefficient of kinetic friction between the box and the ramp.
50*. A racing car accelerates uniformly from 0 to 80mph in 8s. The external force that
accelerates the car is the frictional force between the tires and the road. If the tires do not
spin, determine the minimum coefficient of friction between the tires and the road.
52. A box weighing 5400N is being pulled up an inclined plane that rises 1.3m for every
7.5 of length measured along the incline. If the coefficient of friction is .6, determine the
force applied parallel to the incline necessary to move the box upward at a constant speed.
Chapter 4 – Laws of Motion – Even Problems
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54*. In order to determine the coefficients of friction between rubber and various surfaces,
a student uses a rubber eraser and an inclined board. In one experiment, the eraser slips
down the incline when the angle of inclination is 36 , and then moves down the incline
with a constant speed when the angle is reduced to 30 . From these data, determine the
coefficients of static and kinetic friction for this experiment.
56*. Find the acceleration experienced by the two masses shown below if the coefficient
of friction between the 5kg mass and the plane is .25 and the incline angle is 37 .
Problem 56
58*. A tractor is pulling two logs in tandem. The logs are fastened together by a chain.
Each log weighs 1750N, and the logs are moving with constant velocity. The tractor exerts
a 1600N force on the front log, and this same log is acted upon by a friction force of 900N.
Find the tension in the chain between the logs and the force of friction on the back log.
60. A man attempting to train his dog is shown below. He’s pulling on the dog with a force
of 70N at an angle of 30 to the horizontal. Find the x- and y-components of this force.
Problem 60
Problem 62
62. (a) What is the resultant force exerted by the two cables supporting the traffic light
shown above. (b) What is the weight of the light?
64. Some baseball pitchers are capable of throwing a fastball at 100mph. The pitcher
achieves this speed by moving his arm through a distance of 1.5m. What average force
must he exert on the .15kg ball during this time?
66. A car is at rest at the top of a driveway that has a slope of 20 . If the brake of the car is
released, find (a) the acceleration of the car down the drive and (b) the time it takes for the
car to reach the street 10m away.
68. A girl coasts down a hill on a sled, reaching the bottom of the hill with a speed of
7m/s. If the coefficient of friction between the runners and the snow is .05 and the girl and
sled together weigh 600N, how far does the sled travel on the level surface before
stopping?
70. Two barrels of masses 4kg and 7kg (shown below) are pulled across a frictionless,
frozen pond. The ice fisherman pulls with a force of 30N on the first barrel. Determine the
acceleration of the system and the tension in the cord connecting the barrels.
72*. A 1200N go-cart is being pulled up a 25 incline by a rope that makes a 35 angle
with the horizontal. Neglecting all frictional forces, determine the tension in the rope
necessary to pull the cart up the incline at a constant speed.
74. A solid sphere of radius R and mass M is placed in a wedge as shown below. The inner
surfaces of the wedge are frictionless. Determine the forces exerted by the wedge on the
sphere at the two contact points.
76. (a) What is the minimum force of friction required to hold the pulley system (shown
above) in equilibrium? (b) What coefficient of static friction between the 100N block and
the table would ensure equilibrium? (c) If the kinetic coefficient of friction between the
100N and the table is .25, what hanging weight should replace the 50N weight to allow the
system to move at a constant speed when set in motion?
78*. A 10,000N force is exerted on a car by a cable pulling the car up a loading ramp
which is inclined at 30 . If the car has a mass of 1500kg, determine the acceleration of the
system (neglecting frictional effects).
80*. A 3kg block starts from rest at the top of a 30 incline and slides a distance of 2m
down the incline in 1.5s. Find (a) the acceleration of the block, (b) the kinetic coefficient
of friction, (c) the frictional force acting on the block and the plane, and (d) the speed of
the block after it has slid 2m.
82*. A 3kg mass hangs from a rope attached to a support on a railroad car. When the car
accelerates to the right, the cord makes a 4 angle with the vertical as shown below. Find
the acceleration of the car.
84*. No friction. m1=10kg, m2=20kg. A pulling force of 50N is applied to the 20kg block.
(a) Find the acceleration and the tension in the cord. (b) Repeat the problem with  k  .1
Chapter 4 – Laws of Motion – Even Problems
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86*. A book of mass 0.9kg is projected up a 30 ramp with an initial speed of 3m/s. The
coefficient of kinetic friction is .2. Determine (a) how far up the incline the book will go
before coming to rest, (b) its acceleration as it slides back down the incline, and (c) its
speed when it reaches the bottom of the incline.
88**. A horizontal force, F, is applied to a frictionless pulley of mass m2 as shown below.
The horizontal surface is smooth. (a) Show that the acceleration of the block of mass m1 is
twice the acceleration of the pulley. Find (b) the accelerations of the pulley and the block
and (c) the tension in the string. (Assume a constant supporting force on the pulley to
offset its weight.)
Problem 88
Problem 90
90**. Horizontal force, F = 18N, is applied to the 3 blocks as shown above.
m1 = 2kg, m2 = 3kg, m3 = 4kg and there is kinetic friction!  k  .1
Find (a) the acceleration of the blocks, (b) the resultant force on each block, and (c) the
magnitude of the contact (normal) forces between the blocks.
92**. The three blocks shown below are connected by two light strings that pass over
frictionless pulleys (of negligible mass). The acceleration of the system is 2m/s 2 to the left
and the surfaces are rough. Find (a) the tension in each string and (b) the coefficient of
kinetic friction between the blocks and the surface. (Assume the same  k for both blocks.)
Note the 25 angle of the incline.