1. Dynamics: Newton’s Laws of Motion
Chapter 4
Dynamics: Newton’s Laws of Motion

3. Force
A force is a push or pull. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. A change in velocity means there is a non-zero acceleration.
The magnitude of a force can be measured using a spring scale.

4. Newton’s First Law of Motion
Newton’s first law is often called the law of inertia.
Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.

5. Force
Not all forces result in motion. For example you can push against a wall and the wall does not move.

6. Newton’s First Law of Motion
Inertial reference frames:
An inertial reference frame is one in which Newton’s first law is valid.
This excludes rotating and accelerating frames.

7. Mass
Mass is the measure of inertia of an object. In the SI system, mass is measured in kilograms.
Mass is not weight:
Mass is a property of an object. Weight is the force exerted on that object by gravity.
If you go to the moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same.

8. Newton’s First Law of Motion
Every object remains in the same state of rest or motion at constant velocity unless acted on by a net external force
Bicycle Does 100mph! - YouTube

9. Objects in motion remain in motion in a straight line (unless acted upon by an outside force).
                                                                      
                           
A lot of inertia!
Very little inertia
Since the train is so huge, it is difficult to stop it once it is moving. It is difficult to change its speed. In fact, a large net force is required to change its speed.
Since the soccer ball is so small, it is very easy to stop it once it is moving. A small net force is required to change its speed.

10. Newton’s First Law: Equilibrium
Equilibrium the net force on an object is zero
                                                                                        

11. Balanced forces

12. Object
Mass
electron rest mass
x kg
proton
x kg
neutron rest mass
x kg
smallest virus
9.5 x kg
typical red blood cell
9 x kg
typical rain drop
2 x 10-6 kg
mosquito
5 x 10-5 kg
dime (U.S.)
2.268 x 10-3 kg
ping-pong ball
2.5 x 10-3 kg
quarter (U.S.)
5.750 x 10-3 kg
golf ball
4.6 x 10-2 kg
tennis ball
5.7 x 10-2 kg
baseball
1.45 x 10-1 kg
volley ball
2.55 x 10-1 kg
soccer ball
4.25 x 10-1 kg
basketball
6.25 x 10-1 kg
baseball bat
8.5 x 10-1 to 1.02 kg

13. Object
Mass
bowling ball
7.2 kg
wheel and tire (small car)
13 kg
average woman
58 kg
average man
70 kg
polar bear (male)
5.9 x 102 kg
typical automobile
1.5 x 103 kg
elephant
3.8 x 103 kg
blue whale (large)
1.4 x 105 kg
747 (empty)
1.6 x 105 kg
JFK class aircraft carrier
7.3 x 107 kg
living matter on Earth
3.6 x 1014 kg
Moon
7.354 x 1022 kg
Earth
x 1024 kg
Sun
1.99 x 1030 kg
Milky Way galaxy
4 x 1041 kg
universe
1 x 1053 kg

14. Question Why is mass more fundamental than weight?
Mass is a measure of inertia, which quantifies the amount of matter. Weight is the force of gravity, i.e. weight depends on the local gravitational acceleration.
How To Draw A Tablecloth Off From Under A Dinner Service - YouTube

15. If the car were to abruptly stop and the seat belts were not being worn, then the passengers in motion would continue in motion. Assuming a negligible amount of friction between the passengers and the seats, the passengers would likely be propelled from the car and be hurled into the air. Once they leave the car, the passengers becomes projectiles and continue in projectile-like motion.
Now perhaps you will be convince of the need to wear your seat belt. Remember it's the law - the law of inertia
Invisible Forces: Ned Kahn | Science, The Arts | Video | PBS LearningMedia

16. Newton’s Second Law of Motion
Newton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass.

17. Force and Net Force
Force is a push or pull that accelerates an object.
The net force is the vector sum of all forces acting on an object. Be sure to use vector addition rules when adding forces.

18. Newton’s 2nd Law
                                a = F / m
                                a  / 2= F / 2m
                                 a / 3 = F / 3m
Note Newton’s second law quantifies the first law: it takes more force to accelerate more massive objects and it shows the linear relationship between acceleration and net force.

19. Newton’s 1st and 2nd Laws

20. Newton’s Second Law of Motion
Force is a vector, so is true along each coordinate axis.
The unit of force in the SI system is the Newton (N).
Note that the pound is a unit of force, not of mass, and can therefore be equated to Newtons but not to kilograms.

21. A sailboat is being blown across the sea at a constant velocity
A sailboat is being blown across the sea at a constant velocity. What is the direction of the net force on the boat?
A) Left  B) Right  C) Net force is zero
D) Down  E) Up 

22. Solving Problems with Newton’s Laws – Free-Body Diagrams
When a cord or rope pulls on an object, it is said to be under tension, and the force it exerts is called a tension force.

23. Free Body Diagrams
A free body diagram is a pictorial representation often used by physicists and engineers to analyze the forces acting on a body of interest. A free body diagram shows all forces of all types acting on this body. Drawing such a diagram can aid in solving for the unknown in a problem.
The sketch of the free body need include only as much detail as necessary. Often a simple outline is sufficient. Depending on the analysis to be performed and the model being employed, just a single point may be the most appropriate

26. Adding vectors

27. On two different occasions during a high school soccer game, the ball was kicked simultaneously by players on opposing teams. In which case (Case 1 or Case 2) does the ball undergo the greatest acceleration? Explain your answer
Case 2 results in the greatest acceleration. Even though the individual forces are greater in Case 1, the net force is greatest in Case 2. Acceleration depends on the net force; it is not dependent on the size of the individual forces.

28. What are the Forces? A = 50N, B = 200N C = 1100N D = 20N, E= 300N
F = H, G=50N

29. In both cases an applied force of 100 N accelerates the 100-N block
In both cases an applied force of 100 N accelerates the 100-N block. In which case is the acceleration greater?

30. Forces When a box sits on the table what forces are at work?
The normal force is the force the table exerts on the box in this case the weight of the box. To make the net force be zero
(b) The normal force is directed upward with a force equal to the weight of the book + 40N.

31. Consider the situation below in which a force is directed at an angle to the horizontal. In such a situation, the applied force can be resolved into two components. These two components can be considered to replace the applied force at an angle. By doing so, the situation simplifies into a familiar situation in which all the forces are directed horizontally and vertically.

32. N > mg
N = mg
N < mg

34. Air Resistance Air resistance is the result of
collisions of the object's leading
surface with air molecules. The air
Resistance encountered by the
object is dependent on a variety of
factors. To keep the topic simple,
the two most common factors
which have a direct effect upon
the amount of air resistance are
The speed of the object and the
cross sectional area of the object.
Increased speeds result in an
increased amount of air
resistance. Increased cross
sectional areas result in an
resistance.

35. Terminal Velocity as a function of mass
Two objects with the same surface area but different weights.
Air resistance equals the weight of the object at a lower speed, since air resistance increases with velocity so heavier objects have a greater terminal velocity

36. Terminal Velocity

37. Two smooth balls of exactly the same size, one made of wood and the other of iron, are dropped from a high building to the ground below. The ball to encounter the greater force of air resistance on the way down is the
  a) wooden ball
b) iron ball
c) both the same

39. If an elephant and a feather fall from a high tree, which one will encounter the greater force of air resistance while falling to the ground below?

40. A coffee filter floats gently downward, at some constant ("terminal") velocity v.
The net force on the coffee filter is
A: Upwards B: Downwards
C: Zero.

41. Equilibrium
If an object is at equilibrium, then the forces are balanced. Balanced is the key word which is used to describe equilibrium situations. Thus, the net force is zero and the acceleration is zero.

42. If an object is at rest and is in a state of equilibrium, then we would say that the object is at "static equilibrium."
Force A B C
Magnitude
3.4 N
9.2 N
9.8 N
Direction
161 deg.
70 deg.
270 deg

43. Example
Suppose the tension in both of the cables is measured to be 50 N and that the angle which each cable makes with the horizontal is known to be 30 degrees. What is the weight of the sign?
Weight = 2*25 N = 50N

44. Solving Problems with Newton’s Laws – Free-Body Diagrams
Draw a sketch.
For one object, draw a free-body diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each one.
Resolve vectors into components.
Apply Newton’s second law to each component.
Solve.

45. Newton’s Third Law of Motion
Any time a force is exerted on an object, that force is caused by another object.
Newton’s third law:
Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first object.

46. Newton’s Third Law of Motion
A key to the correct application of the third law is that the forces are exerted on different objects. Make sure you don’t use them as if they were acting on the same object.

47. Newton’s Third Law of Motion
Rocket propulsion can also be explained using Newton’s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket.
Note that the rocket does not need anything to “push” against. That is why rocket propulsion works in outer space.

48. Newton’s Third Law of Motion
Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source.
This need not be done indefinitely, but is a good idea until you get used to dealing with these forces.

49. Newton’s Third Law
When an object exerts a force on a second object, the second object exerts an equal but opposite force on the first object.
These forces are called action and reaction, note both forces occur simultaneously.

50. More Action-Reaction Forces
Note the rocket pushes on the gases it expels when the fuel is burned. This is why rocket propulsion can work in space, which does not provide anything to push against

51. Consider the apple at rest on the table
Consider the apple at rest on the table. If we call the gravitational force exerted on the apple action, what is the reaction force according to Newton's 3rd law?
The gravitational force the apple exerts on Earth

52. Identifying Action Reaction Pairs

53. Question
While driving down the road, a firefly strikes the windshield of a bus and makes a quite obvious mess in front of the face of the driver. This is a clear case of Newton's third law of motion. The firefly hit the bus and the bus hits the firefly. Which of the two forces is greater: the force on the firefly or the force on the bus?
The forces are equal and opposite

54. Arnold Strongman and Suzie Small pull on opposite ends of a rope in a tug of war. The greatest force exerted on the rope is by a) Arnold b) Suzie c) ... both the same

55. Does the scale read 100 N, 200 N, or zero?

56. Question
Since action-reaction forces are equal and opposite why don’t they cancel and result in a net force of zero?

57. Answer
The action force is the force object 1 exerts on object 2. The reaction force is the force object 2 exerts on object 1. So although they are equal in magnitude and opposite in direction they are acting on different objects. Therefore the net force on either one of the objects is not zero for a given action-reaction pair of forces.
Newton's Third Law of Motion: Astronauts in Outer Space | Science | Classroom Resources | PBS Learning Media

58. Weight – the Force of Gravity; and the Normal Force
Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight is:

59. Weight – the Force of Gravity; and the Normal Force
An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there?
The force exerted perpendicular to a surface is
called the normal force. It is exactly as large as needed to balance the force from the object (if the required force gets too big, something breaks!)

60. Weight – the Force of Gravity; and the Normal Force
The Normal force is not the action-reaction pair to the gravitational force known as weight. The reason is that it is also acting on the object. Action-reaction pairs act on different objects.
Note, if you are standing on a bathroom scale, the scale reading gives the value of the normal force acting on you from the scale. If you are standing on a scale which is on the horizontal ground, then this normal force is just equal to your weight. However,  if the floor is inclined, or if the scale happens to be in an elevator which is accelerating, then the scale reading will not be equal to your weight!  In this case, the scale reading that is, the normal force is sometimes called the apparent weight.

61. Wt = 120 lb
Wt > 120 lb
Wt < 120 lb

62. Wt = 120 lb
Wt > 120 lb
Wt < 120 lb

63. Wt = 120 lb
Wt > 120 lb
Wt < 120 lb

64. An Atwood's machine is a pulley with two masses connected by a string as shown. HERE, The mass of A is twice the mass of B. How does the force exerted on the mass B by the string (T) compare with the weight of body B? (Assume a frictionless, massless pulley)
A: T = mB g. B: T < mB g.
C: T > mB g. D: not enough information

65. How does the force exerted on the cart by the string (T) compare with the weight of body B?
(Assume all surfaces are frictionless)
A: T = mB g. B: T < mB g C: T > mB g.

66. Two blocks, with masses M2>M1, are connected by ropes
Two blocks, with masses M2>M1, are connected by ropes. You pull to the right on a second rope, with external force "T1". The blocks sit on a frictionless surface.
How do the magnitudes of the tensions in the rope compare?
A: T2 > T1 B: T2 < T1 C: T2 = T1

67. An object is being lowered on a cord at a constant speed.
How does the tension T in the cord compare to the weight mg of the object?
T = mg
T > mg
T < mg

68. Applications Involving Friction, Inclines
On a microscopic scale, most surfaces are rough. The exact details are not yet known, but the force can be modeled in a simple way.
For kinetic – sliding – friction, we write:
is the coefficient of kinetic friction, and is different for every pair of surfaces.

69. Applications Involving Friction, Inclines

70. Applications Involving Friction, Inclines
Static friction is the frictional force between two surfaces that are not moving along each other. Static friction keeps objects on inclines from sliding, and keeps objects from moving when a force is first applied.

71. Applications Involving Friction, Inclines
The static frictional force increases as the applied force increases, until it reaches its maximum. Then the object starts to move, and the kinetic frictional force takes over.

72. A mass, m, is pushed with a horizontal force, F, on a horizontal surface. The coefficient of static friction is μs. The block does not move. The magnitude of the static friction force on the mass is
a. μsmg
b. μsF
c. F
d. mg

73. What can you say about the net force (total force) on the glider?
A glider is gliding along an air track at constant speed. There is no friction or air resistance.
What can you say about the net force (total force) on the glider?
A) The net force is zero.
B) The net force is non-zero and is in the direction of motion.
C) The net force is non-zero and is in the direction opposite the motion.
D) The net force is non-zero and is perpendicular to the motion.
v = constant

74. A glider on a level air track is coasting along at constant velocity
A glider on a level air track is coasting along at constant velocity. Which of the following free-body diagrams correctly indicates all the forces on the glider? Assume that there is no air resistance or friction.
v = constant A B C D
E) None of these

75. Which statement below must be true?
A mass m is pulled along a rough table at constant velocity with an external force Fext at some angle above the horizontal. The magnitudes of the forces on the free-body diagram have not been drawn carefully, but the directions of the forces are correct.
Which statement below must be true?
Ffric > Fext , N > mg.
Ffric < Fext , N < mg.
Ffric > Fext , N < mg.
Ffric < Fext , N > mg.
None of these.

76. Applications Involving Friction, Inclines
An object sliding down an incline has three forces acting on it: the normal force, gravity, and the frictional force.
The normal force is always perpendicular to the surface.
The friction force is parallel to it.
The gravitational force points down.
If the object is at rest, the forces are the same except that we use the static frictional force, and the sum of the forces is zero.

77. Friction: Inclined Plane

78. Inclined Planes
An object placed on a tilted surface will often slide down the surface. The rate at which the object slides down the surface is dependent upon how tilted the surface is; the greater the tilt of the surface, the faster the rate at which the object will slide down it. In physics, a tilted surface is called an inclined plane. Objects are known to accelerate down inclined planes because of an unbalanced force. To understand this type of motion, it is important to analyze the forces acting upon an object on an inclined plane.

79. Inclined planes
The first peculiarity of inclined plane problems is that the normal force is not directed vertically.
The force of gravity will be resolved into two components of force - one directed parallel to the inclined surface and the other directed perpendicular to the inclined surface.

80. Inclined planes
The perpendicular component of the force of gravity is directed opposite the normal force and as such balances the normal force. The parallel component of the force of gravity is not balanced by any other force.
In the absence of friction and other forces the acceleration of an object on an incline is the value of the parallel component (m*g*sinθ) divided by the mass (m).

81. Friction and Inclined Planes
In the presence of friction or other forces the situation is slightly more complicated. Consider the diagram shown at the right. The perpendicular component of force still balances the normal force since objects do not accelerate perpendicular to the incline. Yet the frictional force must also be considered when determining the net force.

82. This problem (and all inclined plane problems) can be simplified through a useful trick known as "tilting the head." An inclined plane problem is in every way like any other net force problem with the sole exception that the surface has been tilted. Thus, you transform the problem back into the form with which you are more comfortable. Once the force of gravity has been resolved into its two components and the inclined plane has been tilted, the problem should look very familiar. Merely ignore the force of gravity (since it has been replaced by its two components) and solve for the net force and acceleration.

83. A box is sliding down a ramp. It is accelerating
A box is sliding down a ramp. It is accelerating. What would be the Free Body Diagram of the forces on the box?                                                     

84. Example
As an example consider the situation depicted in the diagram at the right. The free-body diagram shows the forces acting upon a 100-kg crate which is sliding down an inclined plane. The plane is inclined at an angle of 30 degrees. The coefficient of friction between the crate and the incline is 0.3. Determine the net force and acceleration of the crate.

85. Example
Begin the above problem by finding the force of gravity acting upon the crate and the components of this force parallel and perpendicular to the incline. The force of gravity is 980 N and the components of this force are:
849
490N
849N
Fparallel = 490 N (980 N • sin30 )
980
Fperpendicular = 849 N = (980 N • cos30 ).

86. Example Step 2
Now the normal force can be determined to be 849 N (it must balance the perpendicular component of the weight vector).
The force of friction can be determined from the value of the normal force and the coefficient of friction;
849
255
980
(Ffrict = μFnorm= 0.3 • 849 N).
Ffrict is 255 N

87. Answers
The net force is the vector sum of all the forces. The forces directed perpendicular to the incline balance; the forces directed parallel to the incline do not balance. The net force is
Fnet = 235 N (490 N N).
The acceleration is 2.35 m/s/s
(Fnet/m = 235 N/100 kg).
849
255
490N
849N
980

88. Hint a = 0, since speed is constant.
In the following diagram, a 100-kg box is sliding down a frictional surface at a constant speed of 0.2 m/s. Analyze the diagram and fill in the blanks.
Hint a = 0, since speed is constant.
849
Fgrav= 100kg*9.8m/s2 = 980N
490
F┴ = Fgrav*cos 30 = 849N
490N
F┴ = Fnorm = 849N
849N
F║ = Fgrav*sin30= 490N
Ffrict= F║ = 490N
980

89. What is the direction of the net force on the glider?
A glider is on a tilted air track and is sliding downhill at constant speed.
What is the direction of the net force on the glider? A B C
D) None of these, it’s zero. .

90. Problem Solving – A General Approach
Read the problem carefully; then read it again.
Draw a sketch, and then a free-body diagram.
Choose a convenient coordinate system.
List the known and unknown quantities; find relationships between the knowns and the unknowns.
Estimate the answer.
Solve the problem without putting in any numbers (algebraically); once you are satisfied, put the numbers in.
Keep track of dimensions.
Make sure your answer is reasonable.

92. Summary of Chapter 4
Newton’s first law: If the net force on an object is zero, it will remain either at rest or moving in a straight line at constant speed.
Newton’s second law:
Newton’s third law:
Weight is the gravitational force on an object.
The frictional force can be written:
(kinetic friction) or (static friction)
Free-body diagrams are essential for problem-solving

93. Aristotle on Motion All motion on the Earth is linear .
All motion in the heavens (outer space) is curved
The speed at which an object falls is directly related to the mass of an object .
Motion could be considered in two main factions: natural and violent.
Motion continues so long as there is only an applied motion to an object. Removing the motion stops the object

94. Galileo on Motion
According to Galileo, the motion of a falling object is independent of mass. Meaning two objects of unequal masses will fall to the ground when dropped from a set height in equal times
The reason why objects did not always fall in the same time was because of a retarding force called friction (air resistance).

95. The way Aristotle 'saw' objects to fall on the Earth
As we know, or will know in the next few sections, objects actually fall like this in a friction free environment (vacuum)

96. motion The way Aristotle thought projectiles moved
The way projectiles "really" move

97. Galileo

98. Galileo

99. Galileo
Back to the plane, if the angle of the second ramp were to decrease, the ball would 'try' reach a height original to the release height. Now this model assumes there is no opposing force - friction. I thought about this model some more and realized that if the angle of the second ramp was made to approach 0, the ball would keep rolling in a straight line in constant speed.
                                                            
The above depicts the thought experiment Galileo "thought of" (Now doesn't that make sense!)

100.                                                             
Note how the package slows down, and does not move at a constant (uniform) speed. The package is affected by the retarding force of friction

101. Aristotle vs. Galileo
Aristotle believed natural motion was straight up (smoke), straight down (drop a rock), or circular like the stars. For Aristotle, all other motion was “violent motion” and objects tended to return to the natural state of rest
Galileo predicted objects in motion would continue to move in a straight line at constant speed in the absence of any forces. It was the force of friction that made the object come to rest
Galileo was the first to systematically investigate how things move.

103. Which equation is true: T = mg B) T > mg C) T < mg
An object is being lowered on a cord at a speed which is increasing. There are two forces on the object, the weight, magnitude mg, and the tension, magnitude T, in the cord.
Which equation is true:
T = mg
B) T > mg
C) T < mg
Speed increasing

104. An object is being lowered on a cord at a constant speed.
How does the tension T in the cord compare to the weight mg of the object?
T = mg
T > mg
T < mg

105. An object is being lowered on a cord at a speed which is decreasing
An object is being lowered on a cord at a speed which is decreasing. There are two forces on the object, the weight, magnitude mg, and the tension, magnitude T, in the cord.
Which equation is true:
T = mg
T > mg
T < mg

106. Review
Lesson 6: Applications of Newton's Laws

107. A block of mass m on a rough table is pulled by a string as shown
A block of mass m on a rough table is pulled by a string as shown. The string exerts a horizontal force of magnitude FT . The coefficient of static friction between block and table is mS; the kinetic friction coefficient is mK. As with most surfaces, mS > mK .
True or False
If the block does not move, it must be true that the force of friction Ffric = msmg .
If the block does not move, it must be true that the string tension FT  msmg .

108. A hockey puck of mass 1 kg slides on the ice at a constant velocity of 10 m/s. Assuming that the acceleration of gravity is 10 m/s2 down, the coefficient of kinetic friction is:
A: K = 0 B: K = 0.1 C: K = 1

109. The 1 kg hockey puck slides on the ice at constant velocity of 10 m/s, but then hits a rough section of ice covered with sand. The puck slows to a stop with a uniform acceleration of –1 m/s2. Assuming that the acceleration of gravity is 10m/s2 down, the coefficient of kinetic friction is
A: K = 1 B: K = 0.1 C: K = 0

110. Which statement below must be true? mg > N N > mg N=mg
A mass m accelerates downward along a frictionless inclined plane. The magnitudes of the forces on the free-body diagram have not been drawn carefully, but the directions of the forces are correct.
Which statement below must be true?
mg > N
N > mg
N=mg

111. What is the correct equation for the y-direction? A) B) C) D) E)
A student chooses a tilted coordinate system for an object on an incline as shown, and then proceeds to write down Newton's 2nd Law in the form
What is the correct equation for the y-direction? A) B) C) D) E) q mg N x y a

112. A) a1 > a2 B) a1 = a2 C) a1 < a2
A mass slides down a rough inclined plane with some non-zero acceleration a1. The same mass is shoved up the same incline with a large, brief initial push. As the mass moves up the incline, its acceleration is a2. How do a1 and a2 compare?
A) a1 > a2 B) a1 = a2 C) a1 < a2

113. The sign below hangs outside the physics classroom, advertising the most important truth to be found inside. The sign is supported by a diagonal cable and a rigid horizontal bar. If the sign has a mass of 50 kg, then determine the tension in the diagonal cable which supports its weight.
The tension is 980 Newtons.

114. What is the direction of the acceleration? up B) down C) a=0
An object is being lowered on a cord at a speed which is increasing. There are two forces on the object, the weight, magnitude mg, and the tension, magnitude T, in the cord.
What is the direction of the acceleration? up
B) down
C) a=0
Speed increasing

115. TRUE or FALSE no air resistance:
The elephant and the feather each have the same force of gravity.
The elephant has more mass, yet both elephant and feather experience the same force of gravity.
The elephant experiences a greater force of gravity, yet both the elephant and the feather have the same mass. .

116. TRUE or FALSE with air resistance:
The elephant encounters a smaller force of air resistance than the feather and therefore falls faster.
The elephant has a greater acceleration of gravity than the feather and therefore falls faster.
Both elephant and feather have the same force of gravity, yet the acceleration of gravity is greatest for the elephant.
Both elephant and feather have the same force of gravity, yet the feather experiences a greater air resistance.

117. As she falls faster and faster through the air, her acceleration a) increases b) decreases c) remains the same