Newton's Laws of Motion Review
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Part C: Forced Choice and Short Answer
8a. Big Bubba has a mass of 100 kg on the earth. What is Big Bubba's mass on the moon where the force of gravity is approximately 1/6-th that of Earth's? ________ Explain or show your work.
Answer: 100 kg
Mass is a quantity which is independent of the location of the object. So if Big Bubba has a mass of 100 kg on Earth, then he also has a mass of 100 kg on the moon. Only the weight would change as Big Bubba is moved from the Earth to the moon. He weighs ~1000 N on Earth and 1/6-th this value (~167 N) on the moon.
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8b. Little Billie weighs 360 N on Earth. What is Little Billie's mass on the moon where the force of gravity is approximately 1/6-th that of Earth's? ________ Explain or show your work.
Answer: ~36 kg
The mass of an object is related to weight by the equation W = m•g where g = ~10 m/s/s on Earth and one-sixth this value (~1.67) on the moon. So if Billy weighs 360 N on Earth, then his mass is approximately ~36 kg. His mass on the moon will be the same as his mass on Earth. Only his weight changes when on the moon; rather than being 360 N, it is 60 N. His weight on the moon could be found by multiplying his mass by the value of g on the moon: (36 kg) • (9.8/6 m/s/s) = ~60 N
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9. TRUE or FALSE:
An object which is moving rightward has a rightward force acting upon it.
Answer: False
An object which is accelerating rightward must have a rightward force and a rightward net force acting upon it. But an object which is merely moving rightward does not necessarily have a rightward force upon it. A car that is moving rightward and skidding to a stop would not have a rightward force acting upon it.
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10. The amount of net force required to keep a 5-kg object moving rightward with a constant velocity of 2 m/s is ____.
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a. 0 N
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b. 0.4 N
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c. 2 N
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d. 2.5 N
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e. 5 N
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Answer: A
Net force is always m•a. In this case, the velocity is constant so the acceleration is zero and the net force is zero. Constant velocity motion can always be associated with a zero net force.
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11. TRUE or FALSE:
For an object resting upon a non-accelerating surface, the normal force is equal to the weight of the object.
Answer: False
Quite surprisingly to many, the normal force is not necessarily always equal to the weight of an object. Suppose that a person weighs 800 N and sits at rest upon a table. Then suppose another person comes along and pushes downwards upon the persons shoulders, applying a downward force of 200 N. With the additional downward force of 200 N acting upon the person, the total upward force must be 1000 N. The normal force supplies the upward force to support both the force of gravity and the applied force acting upon the person. Its value is equal to 1000 N which is not the same as the force of gravity of the person.
12. Which one(s) of the following force diagrams depict an object moving to the right with a constant speed? List all that apply.
Answer: AC
If an object is moving at a constant speed in a constant rightward direction, then the acceleration is zero and the net force must be zero. Choice B and D show a rightward net force and therefore a rightward acceleration, inconsistent with the described motion.
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13. According to Newton's third law, every force is accompanied by an equal and opposite reaction force. The reason that these forces do not cancel each other is ____.
a. the action force acts for a longer time period
b. the two forces are not always in the same direction
c. one of the two forces is greater than the other
d. the two forces act upon different objects; only forces on the same object can balance each other.
e. ... nonsense! They do cancel each other. Objects accelerate because of the presence of a third force.
Answer: D
Action and reaction forces always act upon the interacting objects for the same amount of time with the same magnitude. So if object A pushes on object B, then object B simultaneously pushes on object A with the same amount of force. The force on object B will be one of perhaps many forces which will govern its motion. But the reaction force is on object A and cannot contribute to object B's motion since it is not acting upon object B. Action-reaction forces can NEVER cancel each other.
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14. As you sit in your chair and study your physics (presuming that you do), the force of gravity acts downward upon your body. The reaction force to the force of the Earth pulling you downward is ___.
a. the force of the chair pushing you upward
b. the force of the floor pushing your chair upward
c. the force of the Earth pushing you upward
d. the force of air molecules pushing you upwards
e. the force of your body pulling the Earth upwards
f. ... nonsense! Gravity is a field force and there is no such reaction force.
Answer: E
The most common wrong answer is a - the force of the chair pushing you upward. As you sit in your chair, the chair is indeed pushing you upward but this is not the reaction force to the force of the Earth pulling you downward. The chair pushing you upward is the reaction force to you sitting on it and pushing the chair downward. To determine the action-reaction force pairs if given a statement of the form object A pulls X-ward on object B, simply take the subject and the object in the sentence and switch their places and then change the direction to the opposite direction (so the reaction force is object B pulls object A in the opposite direction of X). So if the Earth pulls you downward, then the reaction force is you pull the Earth upward.
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15. A golf pro places a ball at rest on the tee, lines up his shot, draws back his club, and lets one rip. During the contact of the golf club with the golf ball, the force of the club on the ball is ____ the force of the ball on the club and the acceleration of the club is ____ than the acceleration of the ball.
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a. greater than, greater than
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b. greater than, equal to
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c. greater than, less than
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d. less than, less than
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e. less than, equal to
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f. less than, greater than
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g. equal to, equal to
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h. equal to, greater than
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i. equal to, less than
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Answer: I
For every action, there is an equal and opposite reaction force. In this case, the force on the club is equal to the force on the ball. The subsequent accelerations of the interacting objects will be inversely dependent upon mass. The more massive club will have less acceleration than the less massive ball.
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Each one of Newton's Laws can play a role in any one particular situation. However, one of the laws is often most obviously dominant in governing the motion of a situation. Pick which of Newton's most governs the situations described below.
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a. First Law (inertia)
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b. Second Law (F = m•a)
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c. Third Law (action-reaction)
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16. A helicopter must have two sets of blades in order to fly with stability.
17. If you were in an elevator and the cable broke, jumping up just before the elevator hit the ground would not save you. Sorry.
18. You usually jerk a paper towel from a roll in order to tear it instead of pulling it smoothly.
19. A student desk changes the amount of force it puts on other objects throughout a school day.
20. Heavy objects are not easier to move around in a horizontal fashion on the Moon than on the Earth.
21. The stronger, heavier team in a tug-of-war does not create a larger tension in the rope than the weaker, lighter team.
Answers: See answers and explanations below.
16. C - As the helicopter blades spin and push air in one direction, the air pushes the blades in the opposite direction; the result is that the helicopter can begin to rotate about the axis of the blade. To counteract this rotation, a second set of blades is required.
17. A - An object moving downwards will continue to move downwards unless acted upon by an unbalanced force. If you make an effort to supply such a force in an attempt to suddenly alter the direction of your motion, then you are creating a greater velocity change than if you merely hit the ground and stopped. If this greater velocity change occurred suddenly (in the same amount of time as the stopping of you and the elevator), then you would experience a greater acceleration, a greater net force, and a greater ouch mark than if you had merely hit the ground and stopped.
18. A - The paper towel is at rest and resists changes in its at rest state. So if you apply a sudden force to one of the paper towel sheets, the great mass of the remainder of the roll will resist a change in its at rest state and the roll will easily break at the perforation.
19. C - As a student sits in the seat, they are applying a downward force upon the seat. The reaction force is that the seat applies an upward force upon the person. A weightier person will apply more downward force than a lighter person. Thus, the seat will constantly be changing the amount of reaction force throughout the day as students of different weight sit in it.
20. A - All objects have inertia or a tendency to resist changes in their state of motion. This inertia is dependent solely upon mass and is subsequently not altered by changes in the gravitational environment. To move an object horizontally, one must apply a force; this force will be resisted by the mass or inertia of the object. On the moon, the object offers the same amount of inertia as on Earth; it is just as difficult (or easy) to move around.
21. C - A rope encounters tension when pulled on at both ends. The tension in the rope is everywhere the same. If team A were to pull at the left end, then the left end would pull back with the same amount of force upon team A. This force is the same everywhere in the rope, including at the end where team B is pulling. Thus team B is pulling back on the rope with the same force as team A. So if the forces are the same at each end, then how can a team ever win a tug-of-war. The way a stronger team wins a tug-of-war is with their legs. They push upon the ground with a greater force than the other team. This force upon the ground results in a force back upon the team in order for them to pull the rope and the other team backwards across the line.
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For the next several questions, consider the velocity-time plot below for the motion of an object along a horizontal surface. The motion is divided into several time intervals, each labeled with a letter.
22. During which time interval(s), if any, are there no forces acting upon the object? List all that apply.
23. During which time interval(s), if any, are the forces acting upon the object balanced? List all that apply.
24. During which time interval(s), if any, is there a net force acting upon the object? List all that apply.
25. During which time interval(s), if any, is the net force acting upon the object directed toward the right? List all that apply.
26. During which time interval(s), if any, is the net force acting upon the object directed toward the left? List all that apply.
Answers: See answers and explanations below.
22. None - If an object is on a surface, one can be guaranteed of at least two forces - gravity and normal force.
23. BDFH - If the forces are balanced, then an object is moving with a constant velocity. This is represented by a horizontal line on a velocity-time plot.
24. ACEG - If an object has a net force upon it, then it is accelerating. Acceleration is represented by a sloped line on a velocity-time plot.
25. AE - If the net force is directed to the right, then the acceleration is to the right (in the + direction). This is represented by a line with a + slope (i.e., upward slope).
26. CG - If the net force is directed to the left, then the acceleration is to the left (in the - direction). This is represented by a line with a - slope (i.e., downward slope).
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For the next several questions, consider the dot diagram below for the motion of an object along a horizontal surface. The motion is divided into several time intervals, each labeled with a letter.
27. During which time interval(s), if any, are there no forces acting upon the object? List all that apply.
28. During which time interval(s), if any, are the forces acting upon the object balanced? List all that apply.
29. During which time interval(s), if any, is there a net force acting upon the object? List all that apply.
30. During which time interval(s), if any, is the net force acting upon the object directed toward the right? List all that apply.
31. During which time interval(s), if any, is the net force acting upon the object directed toward the left? List all that apply.
Answers: See answers and explanations below.
27. None - If an object is on a surface, one can be guaranteed of at least two forces - gravity and normal force.
28. ACEGI - If the forces are balanced, then an object is moving with a constant velocity or at rest. This is represented by a section of a dot diagram where the dots are equally spaced apart (moving with a constant velocity) or not even spaced apart at all (at rest).
29. BDFH - If an object has a net force upon it, then it is accelerating. Acceleration is represented by a section of a dot diagram in which the spacing between consecutive dots is either increasing or decreasing.
30. BF - If the net force is directed to the right, then the acceleration is to the right (in the + direction). This is represented by a dot diagram in which the dots are increasing their separation distance as the object moves from left to right.
31. DH - If the net force is directed to the left, then the acceleration is to the left (in the - direction). This is represented by a dot diagram in which the dots are decreasing their separation distance as the object moves from left to right.
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For the next several questions, consider the trajectory diagram shown below for a projectile thrown at an angle to the horizontal. The vector arrows represent the horizontal and vertical components of the projectile's velocity. Several points in the trajectory are labeled with a letter. Use the trajectory diagram to answer the next several questions. (Consider air resistance to be negligible.)
32. At which point(s), if any, are there no forces acting upon the object? List all that apply.
33. At which point(s), if any, are the forces acting upon the object balanced? List all that apply.
34. At which point(s), if any, is there a net force acting upon the object? List all that apply.
35. At which point(s), if any, is the net force acting upon the object directed toward the right? List all that apply.
36. At which point(s), if any, is the net force acting upon the object directed upward? List all that apply.
Answers: See answers and explanations below
32. None
33. None
34. ABCDEFG
35. None
36. None
This object is a projectile as can be seen by its constant horizontal velocity and a changing vertical velocity (besides that, the problem states that this is a projectile). A projectile is an object upon which the only force is gravity. Gravity acts downward to accelerate an object downward. This force is an unbalanced force or net force. It causes a vertical rising object to slow down and a falling object to speed up.
The presence of a horizontal velocity does not demand a horizontal force, only a balance of horizontal forces. Having no forces horizontally would cause the projectile to move at a constant horizontal speed once it is launched. Similarly an upward force is not needed on this projectile. When launched, an upward velocity is imparted to it; this velocity is steadily decreased as the object is acted upon by the downward force of gravity. An upward force would only be required for an object which is speeding up as it rises upward.
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