Newton's Laws of Motion Review
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Part A: Mass, Inertia, Weight, and Newton's First Law of Motion
1. Which of the following statements are true of inertia? List all that apply.
- Inertia is a force.
- Inertia is a force which keeps stationary objects at rest and moving objects in motion at constant velocity.
- Inertia is a force which brings all objects to a rest position.
- All objects have inertia.
- A more massive object has more inertia than a less massive object.
- Fast-moving objects have more inertia than slow-moving objects.
- An object would not have any inertia in a gravity-free environment (if there is such a place).
- Inertia is the tendency of all objects to resist motion and ultimately stop.
- In a gravity-free environment (should there be one), a person with a lot of inertia would have the same ability to make a turn as a person with a small amount of inertia.
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Answer: DE
a. False - Inertia is not a force.
b. False - Inertia is NOT a force.
c. False - Inertia is NOT a force. Inertia is simply the tendency of an objects to resist a change in whatever state of motion that it currently has. Put another way, inertia is the tendency of an object to "keep on doing what it is doing." Mass is a measure of an object's inertia. The more mass which an object has, the more that it sluggish towards change.
d. True - Bet money on this one. Any object with mass has inertia. (Any object without mass is not an object, but something else like a wave.)
e. True - Mass is a measure of an object's inertia. Objects with greater mass have a greater inertia; objects with less mass have less inertia.
f. False - The speed of an object has no impact upon the amount of inertia that it has. Inertia has to do with mass alone.
g. False - Inertia (or mass) has nothing to do with gravity or lack of gravity. In a location where g is close to 0 m/s/s, an object loses its weight. Yet it still maintains the same amount of inertia as usual. It still has the same tendency to resist changes in its state of motion.
h. False - Inertia is NOT the tendency to resist motion, but rather to resist changes in the state of motion. For instance, its the tendency of a moving object to keep moving at a constant velocity (or a stationary object to resist changes from its state of rest).
i. False - Once more (refer to g), inertia is unaffected by alterations in the gravitational environment. An alteration in the g value effects the weight of an object but not the mass or inertia of the object.
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2. Which of the following statements are true of the quantity mass? List all that apply.
- The mass of an object is dependent upon the value of the acceleration of gravity.
- The standard metric unit of mass is the kilogram.
- Mass depends on how much stuff is present in an object.
- The mass of an object is variable and dependent upon its location.
- An object would have more mass on Mount Everest than the same object in the middle of Lake Michigan.
- People in Weight Watcher's are really concerned about their mass (they're mass watchers).
- The mass of an object can be measured in pounds.
- If all other variables are equal, then an object with a greater mass would have a more difficult time accelerating.
- If all other variables are equal, then it would require less exerted force to stop a less massive object than to stop a more massive object.
- The mass of an object is mathematically related to the weight of the object.
Answer: BCFHIJ
a. False - Mass is independent of the gravitational environment that an object is in and dependent solely upon the number of atoms in the object and the type of atoms (Carbon: ~12 g/mol; Hydrogen: ~1 g/mol ; Oxygen: ~16 g/mol). Because of this, mass is said to be invariable (unless of course, an object loses some of its atoms) - a constant quantity which is independent of the acceleration of gravity and therefore independent of location. (Weight on the other hand depends upon the gravitational environment.)
b. True - Know this one. Kilograms is for mass and Newtons is for force.
c. True - This is kind of a simple definition of mass but it does do the job (provided stuff means atoms or material).
d. False - See explanation to #2d.
e. False - An object has the same mass on Mount Everest as it does at sea level (or near sea level); only the weight of the object would be slightly different in these two locations.
f. True - Weight Watcher's participants only use a measurement of their weight as a reflection of how many atoms of flesh that they have burned from their bodies. Their real interest is in losing mass for reasons related to health, appearance, etc.
g. False - Pounds is a unit of force commonly used in the British system of measurement. It is not a metric unit and it is not a unit of mass. Kilogram is the standard metric unit of mass and slug is the British unit.
h. True - Weight and force of gravity are synonymous terms. You should quickly become comfortable with the terms mass, weight and force of gravity; it will save you many headaches as we continue through the course.
i. True - A less massive object has less inertia and as such would offer less resistance to changes in their velocity. For this reason, a less massive object requires less force to bring from a state of motion to a state of rest.
j. True - The weight of an object is the mass of the object multiplied by the acceleration of gravity of the object. Mass and weight are mathematically related by the equation: Weight (or Fgrav) = m•g
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3. Which of the following statements are true of the quantity weight? List all that apply.
- The weight of an object is dependent upon the value of the acceleration of gravity.
- Weight refers to a force experienced by an object.
- The weight of an object would be less on the Moon than on the Earth.
- A person could reduce their weight significantly by taking an airplane ride to the top of Mount Everest.
- Two objects of the same mass can weigh differently.
- To gain weight, one must put on more mass.
- The weight of an object can be measured in kilograms.
- The weight of an object is equal to the force of gravity acting upon the object.
- When a chemistry student places a beaker on a balance and determines it to be 84.3 grams, they have weighed the beaker.
Answer: ABCH and possibly EF
a. True - The weight of an object is equal to the force of gravity acting upon the object. It is computed by multiplying the object's mass by the acceleration of gravity (g) at the given location of the object. If the location of the object is changed, say from the Earth to the moon, then the acceleration of gravity is changed and so is the weight. It is in this sense that the weight of an object is dependent upon the acceleration of gravity.
b. True - This statement is true in the sense that the weight of an object refers to a force - it is the force of gravity.
c. True - The weight of an object depends upon the mass of the object and the acceleration of gravity value for the location where it is at. The acceleration of gravity on the moon is 1/6-th the value of g on Earth. As such, the weight of an object on the moon would be 6 times less than that on Earth.
d. False - A trip from sea level to the top of Mount Everest would result in only small alterations in the value of g and as such only small alterations in a person's weight. Such a trip might cause a person to lose a pound or two.
e. Mostly True - Two objects of the same mass can weigh differently if they are located in different locations. For instance, person A and person B can both have a mass of 60 kg. But if person A is on the Earth, he will weigh ~600 N, whereas person B would weight ~100 N on the moon.
f. Kinda True (Mostly False) - Weight is the product of mass and the acceleration of gravity (g). To gain weight, one must either increase their mass or increase the acceleration of gravity for the environment where they are located. So the statement is true if one disregards the word MUST which is found in the statement.
g. False - By definition, a free-falling object is an object upon which the only force is gravity. Such an object is accelerating at a rate of 9.8 m/s/s (on Earth) and as such cannot be experiencing a balance of forces.
h. True - This statement is the precise definition of weight. Weight is the force of gravity.
i. False - This student has determined the mass of the beaker, not the weight. As such, he/she has massed the beaker, not weighed it.
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4. Which of the following statements are true of an object that experiences balanced forces (or unbalanced forces)? List all that apply.
- If a person is moving to the right, then the forces acting upon it are NOT balanced.
- A balance of forces is demonstrated by an object which is slowing to a stop.
- It would take an unbalanced force to keep an object in motion.
- If an object is moving with a constant speed in a circle, then the forces acting upon the object are balanced.
- If an object is accelerating at a constant rate of acceleration, then the forces acting upon the object are balanced.
- It is NOT possible for just three forces to be acting upon an object and they still balance each other.
- A free-falling object experiences a balance of forces.
- Balanced forces cause stationary objects to remain at rest and moving objects to come to rest.
- Unbalanced forces cause objects to move.
Answer: None of these are true, though one might make a strong argument for I.
a. False - An object which is moving to the right could have unbalanced forces, but only if it is accelerating. The presence of unbalanced forces must always be associated with acceleration, not mere motion. In this case, an object moving to the right could have a balance of forces if it is moving with a constant velocity.
b. False - An object would never slow to a stop unless the forces acting upon it were unbalanced. In fact, an object which slows down must have a unbalanced force directed in the direction opposite their motion.
c. False - An unbalanced force is only required to accelerate an object. A balance of forces is required to keep an object moving at a constant velocity. For instance, a car moving to the right at constant velocity encounters as much rightward force as leftward force.
d. False - An object which moves in a circle has a changing direction. As such, there is an acceleration and this acceleration requires that there be an unbalanced force present on the object.
e. False - Any object that accelerates has a changing velocity. An object that accelerates at a constant rate has a velocity that changes by the same amount each second. For instance, a free-falling object changes its velocity by -9.8 m/s ever second. It is said to have a constant acceleration of -9.8 m/s2. A free-falling object, or any object with an acceleration (whether constant or non-constant) must be experiencing an unbalanced force.
f. False - Consider an object which weighs 1000 N (a 1000 N downward force) which is being pulled on by two people, each exerting 500 N of upward force. Such an object has three forces acting upon it and the three forces together balance each other.
g. False - A free-falling object is an object upon which the only force is gravity. As such, there is an unbalanced force acting upon it; this unbalanced force explains its acceleration.
h. False - Balanced forces cause stationary objects to stay at rest. However balanced forces would never cause moving objects to stop; an unbalanced force would be required to stop a moving object.
i. False - Unbalanced forces do more than cause objects to move; unbalanced forces cause objects to accelerate. Though one could make a strong argument that an object that is accelerating must also be moving (albeit with a changing velocity). In this sense, this statement is true.
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5. Consider Newton's first law of motion to determine which of the following statements are true? List all that apply.
- Newton's first law of motion is applicable to both moving and nonmoving objects.
- If a football is moving upwards and rightwards towards the peak of its trajectory, then there are both rightwards and upwards forces acting upon it.
- It would take an unbalanced force to keep an object in motion.
- If an object is at rest, then there are no forces acting upon the object.
- It would take an unbalanced force to keep an object in motion at a constant velocity.
- It is the natural tendency of all objects to eventually come to a rest position.
- A pendulum bob is set into its usual back-and-forth periodic motion. After some time (perhaps 10 minutes), the pendulum bob comes to a rest position. This is best explained by the idea of inertia - all objects eventually resist motion.
- If a 3-kg rock is thrown at a speed of 2 m/s in a gravity-free environment (presuming one could be found), then an unbalanced force of 6 N would be required to keep the rock moving at a constant speed.
- It would take an unbalanced force to cause an object to accelerate from rest.
Answer: AI
a. True - Absolutely true. Like all true scientific laws, they govern all objects. In the case of Newton's first law of motion: An object that is nonmoving remains at rest (unless acted upon by an unbalanced force); and a moving object will continue in its motion at a constant velocity (unless acted upon by an unbalanced force).
b. False - A football which is moving upwards and rightwards towards its peak, then it has both an upward and a rightward velocity; it does not however have an upward and a rightward force. In fact, if acting as a projectile, it has no horizontal force and maintains a constant horizontal velocity; similarly, it would have a downward force of gravity and a slowing down motion as it rises. If the football were not a projectile, then the horizontal force would be leftward (air resistance opposing its motion) and the vertical force would be gravity and air resistance, both directed downward.
c. False - An unbalanced force would accelerate an object. If directed against its motion, then it would actually slow it down rather than keep is motion going. A balance of forces is all that is required to keep an object going at a constant velocity. An unbalanced force directed in the direction of motion would be required to keep an object going with an increasing speed.
d. False - If an object is at rest, then there are no unbalanced forces acting upon it. There is a force of gravity and at least one other upward force capable of balancing the force of gravity.
e. False - This is dead wrong. It would take a balance of forces to keep an object in motion at constant velocity. An unbalanced force would cause some form of acceleration.
f. False - If you answered TRUE, then Galileo and Newton just rolled over in their grave. It is the natural tendency of all objects to maintain their velocity and to resist changes in whatever state of motion that they have. This is the law of inertia.
g. False - All objects resist changes in their state of motion. In the absence of unbalanced forces, they maintain their velocity (whether zero or nonzero). The pendulum changes its state of motion due to an unbalanced force - the force of air resistance.
h. False - For an object to maintain a constant velocity, 0 Newtons of net force (i.e., a balance of forces) is required.
i. True - Unbalanced forces cause stationary objects to accelerate from rest. In the absence of an unbalanced force, a stationary object would remain at rest.
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Part B: Force, Acceleration and Newton's Second Law of Motion
6. Which of the following statements are true of the concept of force? List all that apply.
- A force is a push or pull exerted upon an object which results from the interaction of that object with its environment.
- Bubba approaches Billie and gives him a swift shove. Timid little Billie keeps his hands in his pocket during this interaction. Subsequently, while Bubba places a force upon Billie, Billie does not place a force upon Bubba.
- A quarterback throws a football down field. Once thrown, the force from the quarterback persists upon the ball to cause it to continue on its upward trajectory towards its peak.
- A sled slides down the hill and reaches the bottom where it gradually slows to a stop. Once on the level ground, the force of the hill persists upon the sled to allow it to continue its forward motion.
- Forces always cause objects to move.
- An object can experience two or more forces and not accelerate.
- A contact force results from the physical contact between two objects.
- A field force results from the action of two objects which are positioned some distance away.
- Spring and tension forces are examples of field forces.
- A force is a vector quantity; there is always a direction associated with it.
- Force can be measured in kilograms or Newtons depending upon the system of measurement (metric or otherwise).
Answer: AFGJ and sort of H.
a. True - This is a great definition of force.
b. False - According to Newton's third law, one cannot push on an object without being pushed back. The force on Billie is the result of an interaction of Bubba's hands with Billie's body. That force on Billie might cause Billie to go flying, but the reaction force offers resistance to the motion of Bubba's hands and slows them down. In general, forces will always (without exception) come in pairs.
c. False - The force of the quarterback on the football is a contact force which can only exist during the interaction (i.e., the contact) between the quarterback's hands and the football. Once thrown, the football continues its horizontal motion due to its own inertia and its vertical motion is effected by the force of gravity.
d. False - Be careful if you answered true to this one. If you did, perhaps you believe in the fatal misconception that a rightward force is required to sustain a rightward motion. The sleds motion to the right can be described as a leftward accelerated motion. Such a leftward acceleration demands that there is a leftward force (despite its rightward force). This leftward force slows the rightward-moving sled down. The hill cannot push on the sled unless the hill is in contact with the sled.
e. False - Forces, if unbalanced, can cause objects to accelerate (one form of moving; the other form is moving at a constant velocity). But by no means can one say that forces always cause objects to move. For instance, as you sit in your chair, the chair pushes up on your body but your body does not move.
f. True - Certainly! As you sit in your chair, the chair pushes up on your body but your body does not accelerate. This upward force (known as the normal force) is balanced by the downward force of gravity. Many objects experience a force yet do not accelerate.
g. True - There are two broad categories of forces - contact forces and field forces. Contact forces, by definition, are those which result from the physical contact of two forces.
h. True (mostly) - A field force is a force which can acts between two objects even when they are separated by a distance. Field forces have magnitudes which are dependent upon the distance of separation between the two interacting objects. For instance, the force of gravity between the Sun and the earth is a field force whose value depends upon the distance of separation between the center of the Earth and the center of the Sun. In this sense, the force of gravity is a force which acts when two objects are separated in space from each other. Yet field forces can also occur when the two objects are touching each other. In this sense, one can be skeptical of the wording of the statement.
i. False - Spring and tension are examples of contact forces. The spring or the rope/cable/wire are in contact with the object upon which it exerts its push or pull. The field forces are electric force, magnetic force, and gravity force.
j. True - Forces always have a direction associated with them. As such, force is a vector quantity - a quantity which is fully described by both a magnitude (size, value) and a direction.
k. False - Force is measured in Newtons in the metric system and in pounds in the British system. Kilograms is a unit of mass.
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7. Consider Newton's second law of motion to determine which of the following statements are true? List all that apply.
- If an object is accelerating to the right, the net force on the object must be directed towards the right.
- If an object is moving to the right and slowing down, then the net force on the object is directed towards the left.
- Accelerating objects are either slowing down or speeding up.
- The acceleration of an object is directly dependent upon its mass and inversely dependent upon its net force.
- An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 2, then the new acceleration would be 10 m/s/s.
- An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 3, then the new acceleration would be 11 m/s/s.
- An object has an acceleration of 8 m/s/s. If the mass of the object is increased by a factor of 2, then the new acceleration would be 16 m/s/s.
- An object has an acceleration of 8 m/s/s. If the mass of the object is increased by a factor of 4, then the new acceleration would be 2 m/s/s.
- An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 2 and the mass of the object is decreased by a factor of 2, then the two factors would offset each other and the acceleration would still be 8 m/s/s.
- An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 2 and the mass of the object is increased by a factor of 4, then the new acceleration would be 4 m/s/s.
- An object has an acceleration of 8 m/s/s. If the net force acting upon the object is decreased by a factor of 2 and the mass of the object is increased by a factor of 4, then the new acceleration would be 1 m/s/s.
- An object has an acceleration of 8 m/s/s. If the net force acting upon the object is increased by a factor of 4 and the mass of the object is increased by a factor of 2, then the new acceleration would be 16 m/s/s.
- A 2-kg object accelerates from rest to a final velocity of 6 m/s in 3 seconds. The magnitude of the net force acting upon the object is 12 N.
- A 10-kg object slows down from 24 m/s to a final velocity of 9 m/s in 3 seconds. The magnitude of the net force acting upon the object is 80 N.
Answer: ABHJKL
a. True - The acceleration is directly related to the net force and the direction of the acceleration is always the same as the direction of the net force. When it comes to force, objects can be thought of as being in the middle of a tug-of-war between the individual forces. The force that wins the tug-of-war is the force which determines the direction of the acceleration. So if a rightward force wins over a leftward force, the acceleration will be to the right.
b. True - An object which is slowing down has an acceleration which is directed opposite the motion of the object. So an object which moves to the right and slows down experiences a leftward acceleration and therefore a leftward net force.
c. False - Acceleration involves a change in velocity and velocity is a vector with a magnitude (15 m/s, 22 m/s, etc.) and a direction (east, northeast, etc.). Accelerating objects are either changing the magnitude of the velocity by speeding up or slowing down or changing the direction of the velocity by turning.
d. False - Vice Versa. The acceleration of an object is inversely dependent upon the mass and directly dependent upon the net force.
e. False - Acceleration is directly dependent upon the net force. Whatever alteration is made in the net force, the same alteration must be made in the acceleration. So if the net force is increased by a factor of 2, then the acceleration is increased by a factor of 2 from 8 m/s/s to 16 m/s/s.
f. False - Whatever alteration is made in the net force, the same alteration must be made in the acceleration. So if the net force is increased by a factor of 3, then the acceleration is increased by a factor of 3 from 8 m/s/s to 24 m/s/s.
g. False - Acceleration is inversely dependent upon the mass. Whatever alteration is made in the mass, the inverse must be made of the acceleration. So if the mass is increased by a factor of 2, then the acceleration is decreased by a factor of 2 from 8 m/s/s to 4 m/s/s.
h. True - Acceleration is inversely dependent upon the mass. Whatever alteration is made in the mass, the inverse must be made of the acceleration. So if the mass is increased by a factor of 4, then the acceleration is decreased by a factor of 4 from 8 m/s/s to 2 m/s/s.
i. False - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is increased by a factor of 2, then the acceleration is increased by a factor of 2. If the mass is decreased by a factor of 2, then the acceleration is increased by a factor of 2. The overall result of the two changes is to increase acceleration by a factor of 4 from 8 m/s/s to 32 m/s/s.
j. True - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is increased by a factor of 2, then the acceleration is increased by a factor of 2. If the mass is decreased by a factor of 4, then the acceleration is decreased by a factor of 4. The overall result of the two changes is to decrease acceleration by a factor of 2 from 8 m/s/s to 4 m/s/s.
k. True - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is decreased by a factor of 2, then the acceleration is decreased by a factor of 2. If the mass is decreased by a factor of 4, then the acceleration is decreased by a factor of 4. The overall result of the two changes is to decrease acceleration by a factor of 8 from 8 m/s/s to 1 m/s/s.
l. True - Acceleration is inversely dependent upon the mass and directly dependent upon the net force. If the net force is increased by a factor of 4, then the acceleration is increased by a factor of 4. If the mass is increased by a factor of 2, then the acceleration is decreased by a factor of 2. The overall result of the two changes is to increase acceleration by a factor of 2 from 8 m/s/s to 16 m/s/s.
m. False - The net force is the product m•a. Acceleration (a) can be calculated as the velocity change per time. The velocity change is +6 m/s (from 0 m/s to 6 m/s), so the acceleration is (+6 m/s) / (3 s) = +2 m/s/s. Therefore the net force is (2 kg)•(+2 m/s/s) = +4 N. The + indicates information about the direction; the 4 N is the magnitude.
n. False - The net force is the product m•a. Acceleration (a) can be calculated as the velocity change per time. The velocity change is -15 m/s (from 24 m/s to 9 m/s), so the acceleration is (-15 m/s) / (3 s) = -5 m/s/s. Therefore the net force is (10 kg)•(-5 m/s/s) = -50 N. The - indicates information about the direction; the 50 N is the magnitude.
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