Newton's Laws of Motion
1. Which of the following statements are true of inertia? List all that apply.
1. Which of the following statements are true of inertia? List all that apply.
a. Inertia is a force.
b. Inertia is a force which keeps stationary objects at rest and moving objects in motion at constant velocity.
c. Inertia is a force which brings all objects to a rest position.
d. All objects have inertia.
e. A more massive object has more inertia than a less massive object.
f. Fast-moving objects have more inertia than slow-moving objects.
g. An object would not have any inertia in a gravity-free environment (if there is such a place).
h. Inertia is the tendency of all objects to resist motion and ultimately stop.
i. 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.
| 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 |
a. The weight of an object is dependent upon the value of the acceleration of gravity.
b. Weight refers to a force experienced by an object.
c. The weight of an object would be less on the Moon than on the Earth.
d. A person could reduce their weight significantly by taking an airplane ride to the top of Mount Everest.
e. Two objects of the same mass can weigh differently.
f. To gain weight, one must put on more mass.
g. The weight of an object can be measured in kilograms.
h. The weight of an object is equal to the force of gravity acting upon the object.
i. 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. |
3. 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. |
EXERCISE
Question 1
Sophia, whose mass is 52 kg, experience a net force of 1800 N at the bottom of a roller coaster loop during her school’s physics field trip to the local amusement park. Determine Sophia’s acceleration at this location.
F =1800 N F = ma
m = 52 kg 1800 = 52a
a = ? a = 1800/52
a = 34.6 m/s/s
Question 2
Kelli and Jarvis are members of the stage crew for the Variety Show. Between acts, they must quickly move a Baby Grand Piano on to the stage. After the curtain closes, they exert a sudden forward force of 524 N to budge the piano from rest and get it up to speed. The 158 kg piano experienced 418 N of friction.
a) What is the piano’s acceleration during the phase of motion?
b) If Kelli and Jarvis maintain this forward force for 1.44 seconds, then what speed will the piano have?
a. F = 524 – 418
= 106 N
m = 158 kg
a = ?
F = ma
106 = 158 a
a = 106/158
a = 0.671 m/s
b. Speed = (0.671)(1.44)
= 0.966 m/s/s
Question 3
A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s/s. Determine the mass of the encyclopedia.
F = 15 N
a = 5 m/s/s
m = ?? F = ma
15 = m (5)
m = 15/5
m = 3 kg
Momentum and Collisions
1. Which of the following are true about the relationship between momentum end energy?
a. Momentum is a form of energy.
b. If an object has momentum, then it must also have mechanical energy.
c. If an object does not have momentum, then it definitely does not have mechanical energy either.
d. Object A has more momentum than object B. Therefore, object A will also have more kinetic energy.
e. Two objects of varying mass have the same momentum. The least massive of the two objects will have the greatest kinetic energy.
| Answer: BE a. FALSE - No. Momentum is momentum and energy is energy. Momentum is NOT a form of energy; it is simply a quantity which proves to be useful in the analysis of situations involving forces and impulses. b. TRUE - If an object has momentum, then it is moving. If it is moving, then it has kinetic energy. And if an object has kinetic energy, then it definitely has mechanical energy. c. FALSE - If an object does NOT have momentum, then it definitely does NOT have kinetic energy. However, it could have some potential energy and thus have mechanical energy. d. FALSE - Consider Object A with a mass of 10 kg and a velocity of 3 m/s. And consider Object B with a mass of 2 kg and a velocity of 10 m/s. Object A clearly has more momentum. However, Object B has the greatest kinetic energy. The kinetic energy of A is 45 J and the kinetic energy of B is 100 J. e. TRUE - When comparing the momentum of two objects to each other, one must consider both mass and velocity; both are of equal importance when determining the momentum value of an object. When comparing the kinetic energy of two objects, the velocity of an object is of double importance. So if two objects of different mass have the same momentum, then the object with the least mass has a greater velocity. This greater velocity will tip the scales in favor of the least massive object when a kinetic energy comparison is made. |
| 2. Three boxes, X, Y, and Z, are at rest on a table as shown in the diagram at the right. The weight of each box is indicated in the diagram. The net or unbalanced force acting on box Y is _____. | | |||||
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| Answer: E If an object is at rest, then all the forces acting upon the object must be zero. The net force on any one of the boxes is 0 Newtons. Subsequently, in each case, the support force (which we have called the "normal force throughout this course) acting upwards on any of the boxes must be equal to the force of gravity on that box (i.e., the weight) plus the amount of load exerted from above (which would be equivalent to the weight of the other boxes located above the box). So for box Y, the support force acting upward would be equal to 9 N while the net force is still 0 Newtons. And for box Z, the support force is 19 N, sufficient to balance the 10-N gravitational force plus the 9-N of force resulting from the other two boxes bearing down on it. |
3. In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach together) and roll together with a speed of _____________. Ignore resistive forces.
| a. 0.5 m/s | b. 0.33 m/s | c. 0.67 m/s | d. 1.0 m/s | e. none of these |
| Answer: A Use 1 kg as the mass of the carts (or any number you wish) and then set the expression for initial total momentum equal to the expression for the final total momentum: (1 kg)*(2) + (1 kg) *(-1) = (1 kg) *v + (1 kg) *v Now solve for v using the proper algebraic steps. (2 kg•m/s) - (1 kg•m/s) = (2 kg) v 1 kg•m/s = (2 kg)v (1 kg•m/s) / (2 kg) = v 0.5 m/s = v |
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