Chapter 5 - Newton's Laws of Motion

Dynamics

-the study of the causes of motion

A force

-a push or a pull

What are two quantities that characterize forces?

-magnitude and direction

As such, what is a force?

-a vector

Mass (in Newtonian terms)

-a measure of how difficult it is to change the velocity of an object

Mass (in everyday terms)

-the quantity of matter in an object

To tighten the metal head of a hammer, you drop the hammer down onto a table. Should you drop the hammer with the handle end down, or drop the hammer with the head end down?

-you should drop the hammer with the handle end down

Why?

-if you drop the hammer with the handle end down, the head continues downward until a force acts on it to bring it to rest. the force that acts on it is supplied by the handle, which results in the head being wedged more tightly into the handle. Since the

What forces are depicted in a free-body diagram?

-only those forces acting on an object are shown (none of the forces exerted by the object are included)

What two main classes do external forces acting on an object fall into?

-forces at the point of contact with another object
-forces exerted by an external agent, such as gravity

What is a normal force?

-the component of the contact force exerted on an object

In what direction does the normal force act?

-perpendicular to the surface of contact (such as the floor or a wall)

Describe the acceleration experienced by two forces that are in contact with each other when a force is applied

-acceleration is assumed to be the same

Two boxes, one heavy and one light, rest on a smooth level floor. You push with a force on either the small or large box. Is the contact force between the two: the same; larger when you push on the large box; or larger when you push on the small box?

-larger when you push on the small box

Why?

-we assume the same acceleration
-F1 = m1a, F2 = m2a
-since the mass of the large box is greater than the small box, it follows that the force of contact is larger when you push on the small box - therefore, you require a greater force to cause the larger

If the mass of the larger box is twice that of the smaller box, what will the comparative sizes of the contact forces be when force is alternately applied to the two boxes?

-the contact force applied on the larger box will be double the value of the contact force applied to the smaller box
-this follows because the large box has twice the mass of the small box

If more than one force acts on an object, in what direction is its acceleration?

-in the direction of the vector sum of its forces

If a question states that acceleration must be purely vertical (either accelerate straight up or down), what does this say about the x or y components of acceleration?

-x component must be zero (so the horizontal components of applied forces cancel)
-y component can be positive or negative

If a question states that acceleration must be purely horizontal (either accelerate straight up or down), what does this say about the x or y components of acceleration?

-x component can be positive or negative
-y component must be zero (so the vertical components of applied forces cancel)

What is the weight of an object on the Earth's surface?

-the gravitational force exerted on it by Earth

What is weight equal to (in terms of mass and gravity)?

-(mass)(gravity)
-mg

Describe the difference between weight and mass

-weight is a gravitational force measured in newtons
-mass is a measure of the inertia of an object, measured in kilograns

If you were to travel to the moon, would your mass or weight change?

-your mass would stay the same, but your weight would

Why would your weight change?

-because the gravitational force on the Earth's surface is greater than the gravitational force on the Moon's surface

As a result, would your weight be larger or smaller on the moon?

-it would be smaller

Is weight a force?

-yes it is

Therefore, is it a vector quantity?

-yes it is

Therefore, what does it have?

-magnitude and a direction

What is its magnitude?

-mg

What is its direction?

-the direction of gravitational acceleration

What two forces act on you when you are in an elevator that is moving with an upward acceleration? In what directions?

-your weight, acting downward
-the normal force exerted on your feet by the floor of the elevator, acting upward

When an object is at rest or moving with constant velocity within an elevator, what is its apparent weight be equal to?

-it will be equal to its actual weight

If that object is moving with positive acceleration, will its apparent weight be greater or less than its actual weight?

-greater than its actual weight
-(a person feels heavier than normal when riding in an elevator with upward acceleration)

If that object is moving with negative acceleration, will its apparent weight be greater or less than its actual weight?

-less than its actual weight
-(a person feels lighter than normal when riding in an elevator with downward acceleration)

Why is the normal force called "normal"?

-because it is perpendicular to the surface
-(in mathematical terms, normal simply means perpendicular)

What is the origin of the normal force?

-the interaction between atoms in a solid that act to maintain its shape

What is the reaction of a normal force to the introduction of greater weight?

-the normal force becomes greater as the weight be comes greater

Is the normal force greater, less than, or equal to the weight of the object?

-can be greater than, less than, or equal to

In what type of scenario would the normal force be less than the weight of an object?

-if there is an upward force (such as a pulling force) that supports part of the object's weight

In what type of scenario would the normal force be more than the weight of an object?

-if there is a downward force (such as a pulling force) on the object

What is the direction of the normal force when surfaces are horizontal?

-vertical

What is the direction of the normal force when surfaces are inclined?

-still perpendicular to the surface (at a right angle), even through the surface is no longer verticle

When choosing a coordinate system for an inclined surface, what is it generally best to do?

-to have the x and y axes of the system parallel and perpendicular to the surface, respectively

If the surface is inclined by an angle theta, what angle is the weight at with respect to the negative y axis?

-the weight is at the SAME ANGLE THETA with respect to the negative y axis

As a result, what is the x component of the weight equal to?

-Wx = mg sin THETA

As a result, what is the y component of the weight equal to?

-Wy = -mg cos THETA

When a surface is inclined at an angle between 0 and 90 degrees, is the acceleration of an object more or less than the acceleration of gravity?

-less than the acceleration of gravity

Why?

-because only a component of the object's weight is causing the acceleration

What is the effect on acceleration if the mass of an object on an inclined surface is doubled?

-the is no effect on acceleration

Why?

-because as in free fall, the acceleration produced by gravity is independent of mass

What is the normal force that an object experiences at an angle of 0 degrees (if the only other force acting on the object is gravity)?

-mg!!

What is the normal force that an object experiences at an angle of 90 degrees (if the only other force acting on the object is gravity)?

-0!!

What is the acceleration that an object experiences at an angle of 0 degrees (if the only other force acting on the object is gravity)?

-0!!

What is the acceleration that an object experiences at an angle of 90 degrees (if the only other force acting on the object is gravity)?

-g!!

What exactly is the Normal Force equal to?

mg cos theta

What exactly is Acceleration equal to?

g sin theta

When you are in an elevator on a scale at rest, what is the relationship between the normal force and the force of gravity?

N = mg

When you are in an elevator on a scale as the elevator is moving upward, what is the relationship between the normal force and the force of gravity?

N > mg

How do you calculate the exact value of N in this instance?

N = may + mg
-->may will be positive in this instance

How would you feel in this elevator?

-heavier

What would the impact on the scale reading be?

-the scale reading would increase (as your apparent weight increases)

When you are in an elevator on a scale as the elevator is moving downward, what is the relationship between the normal force and the force of gravity?

N < mg

How do you calculate the exact value of N in this instance?

N = may + mg
-->may will be negative in this instance

How would you feel in this elevator?

-lighter

What would the impact on the scale reading be?

-the scale reading would decrease (as your apparent weight decreases)

What will the Normal Force be if the elevator cable breaks and you are in free fall?

-N will equal zero

How would you feel in this elevator?

-you would achieve a state of apparent weightlessness

If you are traveling (upward or downward) at constant velocity in an elevator, what will the relationship between the Normal Force and gravity be?

N = mg

Why?

-because acceleration is zero

Do astronauts in the space station experience true weightlessness?

-no they do not

Why not?

-because they still experience the force of gravity
-(this is what holds the space station in orbit around the Earth)

What is an orbit?

-a continuous free fall where you keep on missing the Earth

As such, what is the difference between the weightlessness that astronauts experience in the space station and that you might experience on the "drop zone.

-the only difference is that the apparent weightlessness of astronauts can be maintained indefinitely

Driving down the road, you hit the brakes suddenly. As a result, your body moves towards the front of the car. Explain using Newton's laws.

-the force exerted on the car by the brakes causes it to slow down, but your body continues to move forward with the same velocity (due to inertia) until the seat belt exerts a force on it to decrease its speed

As you sit quietly in a chair, are you at rest?

-no
-you are at rest relative to your surroundings, but you are in motion relative to other objects in the universe

Horse and cart problem: explain!

There are 2 action-reaction pairs:
1. horse exerts force on cart, cart exerts force on horse
2. horse exerts force on ground, ground exerts force on horse
-->since the only force acting on the cart is the horse, the cart moves forward

When will the horse move forward?

-if the ground pushes the horse (in reaction to the horse pushing the ground) harder than the cart pulls on the horse

The force exerted by gravity on a whole brick is greater than the force exerted by gravity on a half brick. Why then, doesn't a whole brick fall faster than a half brick?

-because a whole brick also has twice the mass as a half brick

Is it possible for an object to be in motion and yet have zero net force acting on it?

-yes, most definitely
-an object with zero net force acting on it has constant velocity

A small car collides with a large truck. Is the force experienced by the car greater than, less than, or equal to the force experienced by the truck?

-the two form an action-reaction pair
-as such, the force experienced by both of the vehicles is exactly the same

Is the acceleration experienced by the car greater than, less than, or equal to the acceleration experienced by the truck?

-the acceleration experienced by the car is greater than the acceleration experience by the truck
-the reason being is that both vehicles experience the same force; as such, since the mass of the small car is less, it experiences greater acceleration (acc

Riding an elevator moving upward with constant speed, you begin a game of darts. Do you have to aim your darts higher, lower, or the same as when you play darts on solid ground?

-no adjustment is necessary because you are moving with constant velocity
-if you throw an object in the elevator it falls with the same downward acceleration relative to you as it would if you were to throw it while standing on the surface of the Earth

When a nonzero net force is applied to an object, the object will: a. always move in the direction of the net force b. possibly move in the direction of the net force c. never move in the direction of the net force

-possibly move in the direction of the net force

When an object moves with constant speed, we can state that: a. there are no forces acting on the object b. there exist forces acting on the object but they sum to zero net force c. there may exist forces acting on the object that do not sum to zero net f

-there may exist forces acting on the object that do not sum to zero net force

Why?

-we cannot confirm that forces sum to zero net force
-the reason being is that if speed is constant, velocity can still change direction
-if velocity changes direction, then acceleration does not equal zero and Fnet does not equal zero

When a person is standing in an elevator, do the forces of gravity and the force from the floor constitute an action-reaction pair?

-no, never

Two boxes, one large and heavy and the other small and light, rest on a frictionless level floor. You push with a force of magnitude F on either the small or large box. Is the contact force between the two boxes the same in either case, larger when you pu

-larger when you push on the small box

A 2000 kg truck moving at 20 m/s rear-ends an 1000 kg car moving at 15 m/s. The force experienced by the car is how many times the force experienced by the truck?

-1 times

Why?

-the truck and the car form an action-reaction pair
-as a result, the force that they experience are equal in magnitude and opposite in direction

Two forces at an angle theta apart act on an object. Acceleration of the object will be greatest if theta equals what value?

-zero degrees

Why?

-if the forces point in the same direction, they will totally reinforce each other and the net force will be the largest

Two masses are connected with a massless stiff rope. When force of magnitude F is applied to mass M, mass m experience an acceleration of magnitude...?

F/(m+M)

Does mass m experience a net force of magnitude less than F, greater than F, or equal to F?

-less than F