CHAPTER 7 SOLUTIONS TO PROBLEMS AND QUESTIONS

Citation: Jacqueline D. Spears and Dean Zollman, Instructor's Guide for The Fascination of Physics, (The Benjamin /Cummings Publishing Company, Inc., Menlo Park, CA 1985). Permission granted by the publisher.

A. Review of Chapter Material

A1. The answers to the "A1" questions are found directly in the text. Look for each term printed in boldface type.

A2. Newton's first law states that when the net force acting on an object is zero, the object's momentum does not change. Newton's second law states that the net force acting on an object is the product of its mass and its acceleration. Newton's third law states that for every force there is a reaction force which is equal in magnitude and opposite in direction to the original force. The applied and reaction forces act on different objects.

A3. The principle of inertia and Newton's first law describe the same observations. The principle of inertia describes an object's tendency to remain stationary or moving at a constant velocity as a property of the object. Newton's first law describes these same characteristics in terms of a relationship between force and acceleration.

A4. In equilibrium, the net force acting on an object is zero. Therefore, the acceleration of the object is zero.

A5. Newton's first law tells us that the object can be moving at any velocity, but that its velocity must not change.

A6. When an object moves in a circle, it is constantly changing the direction of its velocity. An object accelerates when either the magnitude or the direction of its velocity changes.

A7. As a car travels around a curve, passengers not rigidly attached to the car continue to move in a straight line. As the car turns, the passengers move closer to the doors of the car. Thinking of the car as a stationary reference frame, the passengers report that they are thrown to the outside of the circle.

A8. If a fictitious force is present, the reference frame must be accelerating.

A9. The reaction force acts on a different object from the original force.

A10. Newton's third law states that when we exert a force on an object, the object pushes back on us with an equally large but oppositely directed force. If we think of a force as the change in momentum divided by the time interval in which the force acts, then Newton's third law tells us that the object's change in momentum equals our change in momentum, but in the opposite direction. If the object's momentum increases, our momentum decreases. Given a closed system consisting of ourself and the object, Newton's third law predicts the same results as the law of conservation of momentum.

B. Using Chapter Material

B1. Newton's first law states that when a car stops suddenly, objects which are not rigidly attached to the car will continue moving at a constant velocity. These objects could strike a passenger, causing injury.

B2. When the strap breaks, the force causing the bicycle to turn is not transmitted to the package. The package keeps moving in a straight line while the bicycle turns. The diagram below shows this motion.

B3. While the engines are fired, the spaceship is acted upon by a force in a direction opposite to the motion of the exhaust gases (Newton's third law). The spaceship accelerates, its velocity increasing (Newton's second law). After the engines are turned off, no net force acts on the spaceship. In accordance with Newton's first law, the spaceship continues to move with the velocity it reached the instant before the engines were turned off.

B4. Acceleration = force/mass = 8000 N, forward/2000 kg = 4 (m/s)/s, forward. After the first three minutes, the engines are shut off and the net force acting on the spaceship is zero. The spaceship's acceleration is zero also.

B5. While the objects are falling, everything around them is falling at the same rate. Relative to one another, the objects are floating about. This simulates the weightlessness felt in space.

B6. In this situation the object which was accelerated was the airplane, not the plate. The author was using an accelerated reference frame, the airplane, to describe the motion of the plate.

B7. The rocket pushes the fuel backwards as it accelerates the gas out the back of the rocket. According to Newton's third law, the gas molecules exert an equal, but oppositely directed force on the rocket. Newton's second law tells us that this force causes the rocket to move forward.

B8. m e size of the force acting downward on you is equal to your mass times the acceleration due to gravity. Since you are not accelerating, the net force acting on you is zero. The floor must be pushing upward with a force equal to your mass times the acceleration due to gravity.

B9. When a moving billiard ball strikes an identical stationary one, the moving ball applies a force to the stationary one. In turn, the stationary ball applies a reaction force to the moving ball. These forces must be equal in magnitude and opposite in direction. One force stops the moving ball while the second force accelerates the stationary ball until it is moving at the same velocity that the moving ball had before the interaction.

C. Extensions to New Situations

C1. (a) The net force and acceleration acting on a car struck from behind are toward the front of the car. (b) A force that pushes the car forward will push the torso forward, but not the head. (c) Because the seat reaches up behind the head as well as behind the torso, the same force is exerted on both the head and torso. As the torso is pushed forward, the head is pushed forward as well. (d) The passenger's head in seat 2 has a force applied to it as soon as the rest of the body is accelerated forward. Because the head does not "stay behind, injuries to the neck are less likely.

C2. (a) A force directed toward the center of the circle, called a centripetal force, acts on the clothes. m is force is applied by the rotating tub of the washing machine. (b) If the clothes were not spinning, they would fall to the bottom of the washing machine. (c) As the tub starts to rotate, Newton's first law tells us that the wet clothes will try to move in a straight line. The holes are large enough to let drops of water escape, but too small to let the clothes escape. m e water and the clothes are quickly separated.

C3. (a) In the vertical direction the net force acting on the bale is zero. The downward force due to gravity is balanced by an upward force exerted by the airplane. In the horizontal direction the bale is moving at a constant velocity, 20 m/s, east. Its horizontal acceleration is zero. The net horizontal force acting on the bale is zero. (b) Just before it is released, the bale has a horizontal velocity of 20 m/s, east and a vertical velocity of zero. (c) After it has been released, the bale has a horizontal force due to air resistance acting on it. Two vertical forces also act. A force due to gravity acts downward while a much smaller force due to air resistance acts upward. (d) Neglecting air resistance, the bale continues to move at a constant velocity in the horizontal direction, 20 m/s, east. (e) The bale will accelerate downward because the net force acting on the bale acts downward. (f) If we neglect air resistance, the bale continues to move eastward at a velocity of 20 m/s and begins to accelerate downward due to the force of gravity.

C4. When we are running horizontally along the ground, we have no net force acting in the vertical direction. m e downward force due to gravity is balanced by the force with which the ground pushes upward. If we were to run off a cliff, we would immediately have a net force acting downward on us. Our motion would be similar to that of the hay bale in Problem C3.

C5. (a) You exert an upward force of 50 N on your shoes, which in turn transmits this force to your body. (b) The reaction force with which the shoes pull down on you is 50 N. (c) The net force acting on you is 50 N, up + 50 N, down = 0. (d) You do not accelerate because the net force on you is zero. All forces are internal to the object (you) so no acceleration occurs.

C6. (a) If we ignore air resistance, the balls have no force acting on them in the horizontal direction. (b) While sitting on the table the ball on the right was acted upon by a horizontal force. When that force stopped acting, the ball had a velocity in the horizontal direction. According to Newton's first law, the ball will keep moving at this velocity unless acted upon by an outside force. (c) In the vertical direction, both balls experience a force due to gravity. They accelerate downward at the same rate. The horizontal motion of one ball does not influence the acceleration it experiences because of the force due to gravity.

C7. Because of its rotation, the earth can be treated as a spinning object. Newton's first law tells us that objects will continue moving in a straight line until acted upon by an outside force. Land and water near the equator move at a greater velocity than land and water near each pole. Consequently, land and water near the equator will tend to move out until a force acts to stop it. This process has been going on for millions of years and has led to the slight bulge at the equator.

C8. (a) In a spinning space station, objects not attached to the station would continue to move along a straight line (Newton's first law). Objects attached to the space station would experience a centripetal force toward the axis about which the station rotates (Newton's second law). (b) The direction in which an object fell when it was dropped would be defined as down. This direction would be toward the outside of the spinning circle, in a direction opposite to the center of the space station.

C9. (a) Velocity = acceleration x time = 9.8 (m/s)/s, down x 0.5 s = 4.9 m/s, down. Momentum = 1 kg x 4.9 m/s, down = 4.9 kg m/s, down for the empty glass. Momentum = 2 kg x 4.9 m/s, down = 9.8 kg m/s, down for the full glass. (b) To stop the glass, the floor must exert a force upward. (c) Force = change in momentum/time = (0 - 4.9 kg m/s, down)/0.01 s = 490 N, up for the empty glass. Force = (0 - 9.8 kg m/s, down)/0.01 s = 980 N, up for the full glass. (d) The full glass is-more likely to break because the force acting on it will be greater than that exerted on the empty glass.

C10. (a) Before the collision, one ball is moving at a constant velocity while the other is not moving. Each ball has zero net force acting on it. During the collision each ball has a horizontal force acting on it due to the other ball. Ball A experiences a net force towards the west, while ball B feels a net force towards the east. After the collision, ball A is stationary and ball B is moving at a constant velocity of 1 m/s, east. Each ball has zero net force acting on it. (b) Before the collision momentum = mass x velocity = 0.5 kg x 1 m/s, east = 0.5 kg m/s, east. After the collision momentum = 0 for ball A. (c) Momentum = 0 before the collision for ball B. After the collision momentum = 0.5 kg x 1 m/s, east = 0.5 kg m/s, east. (d) The change in the momentum of ball B is from 0 to 0.5 kg m/s, east. Force = (0.5 kg m/s, east - 0)/0.01 s = 50 N, east. This force is applied by ball A. (e) The change in momentum of ball A is from 0.5 kg m/s to 0. Force = (0 - 0.5 kg m/s, east)/0.01 s = -50 N, east = 50 N, west. This force is applied by ball B. (f) The force applied by each ball on the other is equal in magnitude and opposite in direction. Since the two balls have identical masses, the accelerations that result from these forces will be equal in magnitude but opposite in direction. This means that the decrease in the velocity of ball A will be exactly matched by the increase in the velocity of ball B. Thus, momentum is conserved.

C11. (a) Acceleration = (1000 N, up)/60 2kg = 16.7 (m/s)/s, up. (b) Acceleration = (1000 N, down)/(6 x 1024 kg) = 1.6 x 10-2 (m/s)/s down. (c) If all the people jumped right where they were now, they would be rather evenly spread around the globe. The net force they would exert would be close to zero. (d) In this case each person would cause the earth to accelerate downward at 1.6 x 10-2 (m/s)/s. The net acceleration would be 1.6 x 10-22 (m/s)/s X (5 X 1O9) = 8 x 10-13 (m/s)/s, downward.