Chapter 4

\- Two forces act on a \(5.0-\mathrm{kg}\) object sitting on a frictionless horizontal surface. One force is \(30 \mathrm{~N}\) in the \(+x\) -direction, and the other is \(35 \mathrm{~N}\) in the \(-x\) -direction. What is the acceleration of the object?

A net force of 4.0 N gives an object an acceleration of \(10 \mathrm{~m} / \mathrm{s}^{2} .\) What is the mass of the object?

Consider a \(2.0-\mathrm{kg}\) ball and a \(6.0-\mathrm{kg}\) ball in free fall. (a) What is the net force acting on each? (b) What is the acceleration of each?

IE oo A hockey puck with a weight of \(0.50 \mathrm{lb}\) is sliding freely across a section of very smooth (frictionless) horizontal ice. (a) When it is sliding freely, how does the upward force of the ice on the puck (the normal force) compare with the upward force when the puck is sitting permanently at rest: (1) The upward force is greater when the puck is sliding; (2) the upward force is less when it is sliding; (3) the upward force is the same in both situations? (b) Calculate the upward force on the puck in both situations.

IE oo (a) You are told that an object has zero acceleration. Which of the following is true: (1) The object is at rest; (2) the object is moving with constant velocity; (3) either (1) or (2) is possible; or (4) neither 1 nor 2 is possible. (b) Two forces on the object are \(F_{1}=3.6 \mathrm{~N}\) at \(74^{\circ}\) below the \(+x\) -axis and \(F_{2}=3.6 \mathrm{~N}\) at \(34^{\circ}\) above the \(-x\) -axis. Is there a third force on the object? Why or why not? If there is a third force, what is it?

. \(\bullet\) A 1.5 -kg object moves up the \(y\) -axis at a constant speed. When it reaches the origin, the forces \(F_{1}=5.0 \mathrm{~N}\) at \(37^{\circ}\) above the \(+x\) -axis, \(F_{2}=2.5 \mathrm{~N}\) in the \(+x\) -direction, \(F_{3}=3.5 \mathrm{~N}\) at \(45^{\circ}\) below the \(-x\) -axis, and \(F_{4}=1.5 \mathrm{~N}\) in the \(-y\) -direction are applied to it. (a) Will the object continue to move along the \(y\) -axis? (b) If not, what simultaneously applied force will keep it moving along the \(y\) -axis at a constant speed?

IE .?? Three horizontal forces (the only horizontal ones) act on a box sitting on a floor. One (call it \(F_{1}\) ) acts due east and has a magnitude of \(150 \mathrm{lb}\). A second force (call it \(F_{2}\) ) has an easterly component of \(30.0 \mathrm{lb}\) and a southerly component of \(40.0 \mathrm{lb}\). The box remains at rest. (Neglect friction.) (a) Sketch the two known forces on the box. In which quadrant is the unknown third force: (1) the first quadrant; (2) the second quadrant; (3) the third quadrant; or (4) the fourth quadrant? (b) Find the unknown third force in newtons and compare your answer to the sketched estimate.

A 6.0 -N net force is applied to a 1.5 -kg mass. What is the object's acceleration?

A force acts on a \(1.5-\mathrm{kg},\) mass, giving it an acceleration of \(3.0 \mathrm{~m} / \mathrm{s}^{2} .\) (a) If the same force acts on a 2.5 -kg mass, what acceleration would be produced? (b) What is the magnitude of the force?

A loaded Boeing 747 jumbo jet has a mass of \(2.0 \times 10^{5} \mathrm{~kg} .\) What net force is required to give the plane an acceleration of \(3.5 \mathrm{~m} / \mathrm{s}^{2}\) down the runway for takeoffs?

IE \(\bullet\) A \(6.0-\mathrm{kg}\) object is brought to the Moon, where the acceleration due to gravity is only one-sixth of that on the Earth. (a) The mass of the object on the Moon is (1) zero, \((2) 1.0 \mathrm{~kg},(3) 6.0 \mathrm{~kg}\) (4) 36 kg. Why? (b) What is the weight of the obiect on the Moon?

A gun is fired and a \(50-\mathrm{g}\) bullet is accelerated to a muzzle speed of \(100 \mathrm{~m} / \mathrm{s}\). If the length of the gun barrel is \(0.90 \mathrm{~m}\), what is the magnitude of the accelerating force? (Assume the acceleration to be constant.)

In a college homecoming competition, eighteen students lift a sports car. While holding the car off the ground, each student exerts an upward force of \(400 \mathrm{~N}\). (a) What is the mass of the car in kilograms? (b) What is its weight in pounds?

(a) A horizontal force acts on an object on a frictionless horizontal surface. If the force is halved and the mass of the object is doubled, the acceleration will be (1) four times, (2) two times, (3) one-half, (4) one-fourth as great. (b) If the acceleration of the object is \(1.0 \mathrm{~m} / \mathrm{s}^{2},\) and the force on it is doubled and its mass is halved, what is the new acceleration?

A force of \(50 \mathrm{~N}\) acts on a mass \(m_{1}\), giving it an acceleration of \(4.0 \mathrm{~m} / \mathrm{s}^{2}\). The same force acts on a mass \(m_{2}\) and produces an acceleration of \(12 \mathrm{~m} / \mathrm{s}^{2} .\) What acceleration will this force produce if the total system is \(m_{1}+m_{2}\) ?

A student weighing \(800 \mathrm{~N}\) crouches on a scale and suddenly springs vertically upward. His roommate notices that the scale reads 900 N momentarily just as he leaves the scale. With what acceleration does he leave the scale?

The engine of a 1.0 -kg toy plane exerts a 15-N forward force. If the air exerts an 8.0 -N resistive force on the plane, what is the magnitude of the acceleration of the plane?

When a horizontal force of \(300 \mathrm{~N}\) is applied to a 75.0 \(\mathrm{kg}\) box, the box slides on a level floor, opposed by a force of kinetic friction of \(120 \mathrm{~N}\). What is the magnitude of the acceleration of the box?

A rocket is far away from all planets and stars, so gravity is not a consideration. It is using its rocket engines to accelerate upward with an acceleration \(a=9.80 \mathrm{~m} / \mathrm{s}^{2} .\) On the floor of the main deck is a crate (object with brick pattern) with a mass of \(75.0 \mathrm{~kg}\) (a) How many forces are acting on the crate: (v Fig. 4.35). (1) zero; (2) one; (3) two; (4) three? (b) Determine the normal force on the crate and compare it to the normal force the crate would experience if it were at rest on the surface of the Earth.

In an emergency stop to avoid an accident, a shoulder-strap seatbelt holds a 60 -kg passenger in place. If the car was initially traveling at \(90 \mathrm{~km} / \mathrm{h}\) and came to a stop in \(5.5 \mathrm{~s}\) along a straight, level road, what was the average force applied to the passenger by the seatbelt?

A student is assigned the task of measuring the startup acceleration of a large RV (recreational vehicle) using an iron ball suspended from the ceiling by a long string. In accelerating from rest, the ball no longer hangs vertically, but at an angle to the vertical. (a) Is the angle of the ball forward or backward from the vertical? (b) If the string makes an angle of 3.0 degrees from the vertical, what is the initial acceleration of the RV?

A 2.0 -kg object has an acceleration of \(1.5 \mathrm{~m} / \mathrm{s}^{2}\) at \(30^{\circ}\) above the \(-x\) -axis. Write the force vector producing this acceleration in component form.

In a pole-sliding game among friends, a \(90-\mathrm{kg}\) man makes a total vertical drop of \(7.0 \mathrm{~m}\) while gripping the pole which exerts and upward force (call it \(F_{\mathrm{p}}\) ) on him. Starting from rest and sliding with a constant acceleration, his slide takes 2.5 s. (a) Draw the man's free body diagram being sure to label all the forces. (b) What is the magnitude of the upward force exerted on the man by the pole? (c) A friend whose mass is only \(75 \mathrm{~kg}\), slides down the same distance, but the pole force is only \(80 \%\) of the force on his buddy. How long did the second person's slide take?

A book is sitting on a horizontal surface. (a) There is (are) (1) one, (2) two, or (3) three force(s) acting on the book. (b) Identify the reaction force to each force on the book.

In an Olympic figure-skating event, a 65-kg male skater pushes a \(45-\mathrm{kg}\) female skater, causing her to accelerate at a rate of \(2.0 \mathrm{~m} / \mathrm{s}^{2}\). At what rate will the male skater accelerate? What is the direction of his acceleration?

A sprinter of mass \(65.0 \mathrm{~kg}\) starts his race by pushing horizontally backward on the starting blocks with a force of \(200 \mathrm{~N}\). (a) What force causes him to accelerate out of the blocks: (1) his push on the blocks; (2) the downward force of gravity; or (3) the force the blocks exert forward on him? (b) Determine his initial acceleration as he leaves the blocks.

Jane and John, with masses of \(50 \mathrm{~kg}\) and \(60 \mathrm{~kg}\), respectively, stand on a frictionless surface \(10 \mathrm{~m}\) apart. John pulls on a rope that connects him to Jane, giving Jane an acceleration of \(0.92 \mathrm{~m} / \mathrm{s}^{2}\) toward him. (a) What is John's acceleration? (b) If the pulling force is applied constantly, where will Jane and John meet?

During a daring rescue, a helicopter rescue squad initially accelerates a little girl (mass \(25.0 \mathrm{~kg}\) ) vertically off the roof of a burning building. They do this by dropping a rope down to her, which she holds on to as they pull her up. Neglect the mass of the rope. (a) What force causes the girl to accelerate vertically upward: (1) her weight; (2) the pull of the helicopter on the rope; (3) the pull of the girl on the rope; or (4) the pull of the rope on the girl? (b) Determine the pull of the rope (the tension) if she initially accelerates upward at \(0.750 \mathrm{~m} / \mathrm{s}^{2}\)

A 75.0 -kg person is standing on a scale in an elevator. What is the reading of the scale in newtons if the elevator is (a) at rest, (b) moving up at a constant velocity of \(2.00 \mathrm{~m} / \mathrm{s},\) and \((\mathrm{c})\) accelerating up at \(2.00 \mathrm{~m} / \mathrm{s}^{2} ?\)

(a) When an object is on an inclined plane, the normal force exerted by the inclined plane on the object is (1) less than, (2) equal to, (3) more than the weight of the object. Why? (b) For a \(10-\mathrm{kg}\) object on a \(30^{\circ}\) inclined plane, what are the object's weight and the normal force exerted on the object by the inclined place?

The weight of a 500 -kg object is 4900 N. (a) When the object is on a moving elevator, its measured weight could be (1) zero, (2) between zero and \(4900 \mathrm{~N}\), (3) more than \(4900 \mathrm{~N},\) (4) all of the preceding. Why? (b) Describe the motion if the object's measured weight is only \(4000 \mathrm{~N}\) in a moving elevator.

A \(3000-\mathrm{kg}\) truck tows a \(1500-\mathrm{kg}\) car by a chain. If the net forward force on the truck by the ground is \(3200 \mathrm{~N}\), (a) what is the acceleration of the car, and (b) what is the tension in the connecting chain?

A block of mass \(25.0 \mathrm{~kg}\) slides down a frictionless surface inclined at \(30^{\circ} .\) To ensure that the block does not accelerate, what is the smallest force that you must exert on it and what is its direction?

\(\bullet\) (a) An Olympic skier coasts down a slope with an angle of inclination of \(37^{\circ} .\) Neglecting friction, there is (are) (1), one, (2) two, (3) three force(s) acting on the skier. (b) What is the acceleration of the skier? (c) If the skier has a speed of \(5.0 \mathrm{~m} / \mathrm{s}\) at the top of the slope, what is his speed when he reaches the bottom of the 35 -m-long slope?

A car coasts (engine off) up a \(30^{\circ}\) grade. If the speed of the car is \(25 \mathrm{~m} / \mathrm{s}\) at the bottom of the grade, what is the distance traveled by the car before it comes to rest?

A rope is fixed at both ends on two trees and a bag is hung in the middle of the rope (causing the rope to sag vertically). (a) The tension in the rope depends on (1) only the tree separation, (2) only the sag, (3) both the tree separation and \(\operatorname{sag},(4)\) neither the tree separation nor the sag. \((b)\) If the tree separation is \(10 \mathrm{~m},\) the mass of the bag is \(5.0 \mathrm{~kg},\) and the sag is \(0.20 \mathrm{~m}\), what is the tension in the line?

A 55-kg gymnast hangs vertically from a pair of parallel rings. (a) If the ropes supporting the rings are attached to the ceiling directly above, what is the tension in each rope? (b) If the ropes are supported so that they make an angle of \(45^{\circ}\) with the ceiling, what is the tension in each rope?

A physicist's car has a small lead weight suspended from a string attached to the interior ceiling. Starting from rest, after a fraction of a second the car accelerates at a steady rate for about \(10 \mathrm{~s}\). During that time, the string (with the weight on the end of it) makes a backward (opposite the acceleration) angle of \(15.0^{\circ}\) from the vertical. Determine the car's (and the weight's) acceleration during the 10 -s interval.

At the end of most landing runways in airports, an extension of the runway is constructed using a special substance called formcrete. Formcrete can support the weight of cars, but crumbles under the weight of airplanes to slow them down if they run off the end of a runway. If a plane of mass \(2.00 \times 10^{5} \mathrm{~kg}\) is to stop from a speed of \(25.0 \mathrm{~m} / \mathrm{s}\) on a \(100-\mathrm{m}\) -long stretch of formcrete, what is the average force exerted on the plane by the formcrete?

A rifle weighs \(50.0 \mathrm{~N}\) and its barrel is \(0.750 \mathrm{~m}\) long. It shoots a 25.0-g bullet, which leaves the barrel at a speed (muzzle velocity) of \(300 \mathrm{~m} / \mathrm{s}\) after being uniformly accelerated. What is the magnitude of the force exerted on the rifle by the bullet?

A horizontal force of \(40 \mathrm{~N}\) acting on a block on a frictionless, level surface produces an acceleration of \(2.5 \mathrm{~m} / \mathrm{s}^{2} .\) A second block, with a mass of \(4.0 \mathrm{~kg}\), is dropped onto the first. What is the magnitude of the acceleration of the combination of blocks if the same force continues to act? (Assume that the second block does not slide on the first block.)

One mass, \(m_{1}=0.215 \mathrm{~kg},\) of an ideal Atwood machine (see Fig. 4.42) rests on the floor \(1.10 \mathrm{~m}\) below the other mass, \(m_{2}=0.255 \mathrm{~kg},\) (a) If the masses are released from rest, how long does it take \(m_{2}\) to reach the floor? (b) How high will mass \(m_{1}\) ascend from the floor? (Hint: When \(m_{2}\) hits the floor, \(m_{1}\) continues to move upward.)

IE . co Two blocks are connected by a light string and accelerated upward by a pulling force \(F\). The mass of the upper block is \(50.0 \mathrm{~kg}\) and that of the lower block is \(100 \mathrm{~kg}\). The upward acceleration of the system as a whole is \(1.50 \mathrm{~m} / \mathrm{s}^{2} .\) Neglect the mass of the string. (a) Draw the free-body diagram of each block. Use the diagrams to determine which of the following is true for the magnitude of the string tension \(T\) compared to other forces: \((1) T>w_{2}\) and \(Tw_{2}\) and \(T>F ;\) (3) \(T

Two blocks on a level, frictionless table are in contact. The mass of the left block is \(5.00 \mathrm{~kg}\) and the mass of the right block is \(10.0 \mathrm{~kg}\), and they accelerate to the left at \(1.50 \mathrm{~m} / \mathrm{s}^{2}\). A person on the left exerts a force \(\left(F_{1}\right)\) of \(75.0 \mathrm{~N}\) to the right. Another person exerts an unknown force \(\left(F_{2}\right)\) to the left. (a) Determine the force \(F_{2}\). (b) Calculate the force of contact \(N\) between the two blocks (that is, the normal force at their vertical touching surfaces).

A 20-kg box sits on a rough horizontal surface. When a horizontal force of \(120 \mathrm{~N}\) is applied, the object accelerates at \(1.0 \mathrm{~m} / \mathrm{s}^{2} .\) (a) If the applied force is doubled, the acceleration will (1) increase, but less than double; (2) also double; (3) increase, but more than double. Why? (b) Calculate the acceleration to prove your answer to part (a).

The coefficients of static and kinetic friction between a \(50.0-\mathrm{kg}\) box and a horizontal surface are 0.500 and 0.400 respectively. (a) What is the acceleration of the object if a 250-N horizontal force is applied to the box? (b) What is the acceleration if the applied force is \(235 \mathrm{~N}\) ?

In moving a 35.0 -kg desk from one side of a classroom to the other, a professor finds that a horizontal force of \(275 \mathrm{~N}\) is necessary to set the desk in motion, and a force of \(195 \mathrm{~N}\) is necessary to keep it in motion at a constant speed. What are the coefficients of (a) static and (b) kinetic friction between the desk and the floor?

A 40 -kg crate is at rest on a level surface. If the coefficient of static friction between the crate and the surface is 0.69 , what horizontal force is required to get the crate moving?

A packing crate is placed on a \(20^{\circ}\) inclined plane. If the coefficient of static friction between the crate and the plane is \(0.65,\) will the crate slide down the plane if released from rest? Justify your answer.

A hockey player hits a puck with his stick, giving the puck an initial speed of \(5.0 \mathrm{~m} / \mathrm{s}\). If the puck slows uniformly and comes to rest in a distance of \(20 \mathrm{~m}\), what is the coefficient of kinetic friction between the ice and the puck?