Chapter 4: Newton's Laws

Question 1

What is the equation for total force?

Answer 1

∑F = ma

Question 2

What does ∑F mean in the total force equation?

Answer 2

Sum of the total force

Question 3

What does m mean in the total force equation?

Answer 3

Mass

Question 4

What does a mean in the total force equation?

Answer 4

Acceleration

Question 5

How do you show direction in 2D versus 1D?

Answer 5

In 1D it is down through +/- signs while in 2D it’s done through arrows above the letters F/a to signify direction

Question 6

Define normal force

Answer 6

A contact force bewteen surface and the other surface touching it. A single upward force pushes on them (like a book on a table).

Question 7

What does W mean in the equation w=mg

Answer 7

Weight

Question 8

What does mg mean in the equation W=mg

Answer 8

The mass of an object with gravitaional pull

Question 9

What is g’s value? (On Earth)

Answer 9

9.81m/s^2

Question 10

What does T mean? (not t, T)

Answer 10

T means tension while t means time

Question 11

What are the 4 rules regarding Normal force (N)?

Answer 11

1) Is the push on theo bject due to the compression of the surface below
2) The strength of the normal force depends on the other forced in the problem
3) Direction is perpendicular (“normal”) to the surface
4) Normal force drops to zero as the object is lifted from the surface

Question 12

What are the 6 steps in solcing Newton Second Law problems?

Answer 12

1. Read the question, make sure you understand it
2. Draw a free body diagram (FBD)
3. Resolve forces into “x and y” / “north and east” / perpendicular directions
4. Apply ∑Fx=max and ∑Fy=may
5. Algebra! Find the unknowns
6. Double check work, take a step back, and ask yourself “did I answer the question?”

Question 13

T/F: If an object is moving at a constant velocity, there must be a net force acting on it

Answer 13

False; according to Newton’s first law, objects maintain the same velocity when there is no net force.

Question 14

If an asteroid and an unmanned spaceship were to collide. And the asteroid is much larger than the spaceship. Which exerts more force?

A) Spaceship
B) Asteroid
C) Neither

Answer 14

C

C) Neither. Newton’s 3rd law states that when object A exerts force on object B, then object B exerts the same force as Object A but the opposite direction. Basically their forces are the same

Question 15

If an asteroid and an unmanned spaceship were to collide. And the asteroid is much larger than the spaceship. Which experiences more acceleration?

A) Spaceship
B) Asteroid
C) Neither

Answer 15

A

A) Spaceship. Acceleration is calculated by Force / mass. Since they both have the same force, it is their mass that differs their acceleration, and the spaceship experiences more acceleration than the asteroid.

Question 16

A car is driving in a circle at constant speed…

True or false: According to newton’s first law, the net force on the car must be zero

Answer 16

False. The car has changing velocity because the direction is changing, so there must be a nonzero net force

Question 17

In the absense of a net force, an object cannot be…

A) accelerating
B) experiencing opposite but equal forces
C) moving with an acceleration of zero
D) in motion with a constant velocity
E) at rest

Answer 17

A

A) Accelrating

Question 18

When a net force is acting on an object, the object…

A) is accelerating
B) is at rest or in motion with constant velocity
C) has zero speed
D) is at rest
E) is in motion with a constant velocity

Answer 18

A

A) is accelerating

Question 19

Lucy boards a crowded bus as it sits in the station. There are no seats, so she stands in the center aisle beside a support pole.

While the bus is speeding up, what is the direction of the total force (if any) on Lucy?

A) The total force is 0
B) Forward
C) Backward

Answer 19

B

B) Forward. Even though Lucy has to steady herself from falling backwards this is not because the force is pushing her backwards but the force of the move is moving forward

Question 20

Lucy boards a crowded bus as it sits in the station. There are no seats, so she stands in the center aisle beside a support pole.

As the bus drives down a straight road at a constant speed, Lucy has no trouble keeping her balance. During this time, what is the direction of the total force (if any) on Lucy?

A) Forward
B) Backward
C) The total force is zero

Answer 20

C

C) The total force is zero. Since Lucy is traveling at a constant speed in a straight line her net force is zero.

Question 21

Lucy boards a crowded bus as it sits in the station. There are no seats, so she stands in the center aisle beside a support pole.

The bus comes to a sudden stop at a red light and Lucy grips the pole tightly to avoid falling over forward. During this time, what is the direction of the total force (if any) on Lucy?

A) Backward
B) The total force is zero
C) Forward

Answer 21

A

A) Backward. This is because Lucy’s inertia keeps her moving forward. She did not have a force pushing her backward.

Question 22

Define acceleration

Answer 22

the rate at which an object’s velocity changes over a period of time

Question 23

Define carrier particle

Answer 23

a fundamental particle of nature that is surrounded by a characteristic force field; photons are carrier particles of the electromagnetic force

Question 24

Define dynamics

Answer 24

the study of how forces affect the motion of objects and systems

Question 25

Define external force

Answer 25

a force acting on an object or system that originates outside of the object or system

Question 26

Define force

Answer 26

a push or pull on an object with a specific magnitude and direction; can be represented by vectors; can be expressed as a multiple of a standard force

Question 27

Define force field

Answer 27

a region in which a test particle will experience a force

Question 28

Define free-body diagram

Answer 28

a sketch showing all of the external forces acting on an object or system; the system is represented by a dot, and the forces are represented by vectors extending outward from the dot

Question 29

Define free-fall

Answer 29

a situation in which the only force acting on an object is the force due to gravity

Question 30

Define friction

Answer 30

a force past each other of objects that are touching; examples include rough surfaces and air resistance

Question 31

Define inertia

Answer 31

the tendency of an object to remain at rest or remain in motion

Question 32

Define inertial frame of reference

Answer 32

a coordinate system that is not accelerating; all forces acting in an inertial frame of reference are real forces, as opposed to fictitious forces that are observed due to an accelerating frame of reference

Question 33

Define mass

Answer 33

the quantity of matter in a substance; measured in kilograms

Question 34

Define net external force

Answer 34

the vector sum of all external forces acting on an object or system; causes a mass to accelerate

Question 35

Define Newton’s first law of motion (Law of inertia)

Answer 35

a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force

Question 36

Define Newton’s second law of motion

Answer 36

forceFneton an object with massmis proportional to and in the same direction as the acceleration of the object,a, and inversely proportional to the mass; defined mathematically asa=Fnetm

Question 37

Define Newton’s third law of motion

Answer 37

whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that the first body exerts

Question 38

Define normal force

Answer 38

the force that a surface applies to an object to support the weight of the object; acts perpendicular to the surface on which the object rests

Question 39

Define system

Answer 39

defined by the boundaries of an object or collection of objects being observed; all forces originating from outside of the system are considered external forces

Question 40

Define tension

Answer 40

the pulling force that acts along a medium, especially a stretched flexible connector, such as a rope or cable; when a rope supports the weight of an object, the force on the object due to the rope is called a tension force

Question 41

Define thrust

Answer 41

a reaction force that pushes a body forward in response to a backward force; rockets, airplanes, and cars are pushed forward by a thrust reaction force

Question 42

Define weight

Answer 42

the forcew due to gravity acting on an object of massm; defined mathematically as:w=mg, wheregis the magnitude and direction of the acceleration due to gravity

Question 43

Dynamics is the study of…

Answer 43

How forces affect the motion of objects

Question 44

What are the 2 ways Newton’s second law are wrriten in equation form?

Answer 44

F = ma
A = Fm

Question 45

If the only force acting on an object is due to gravity the object…

Answer 45

Is in free fall

Question 46

When objects rest on an inclined plane that makes an angleθwith the horizontal surface, the weight of the object can be resolved into components that act perpendicular (w⊥) and parallel (w∥)to the surface of the plane. These components can be calculated using:

Answer 46

w∥=wsin(θ)=mgsin(θ)

w⊥=wcos(θ)=mgcos(θ)

Question 47

How is tension calculated?

Answer 47

T = mg

Question 48

To solve problems involving Newton’s laws of motions, what are the 4 steps used?

Answer 48

1. Draw a sketch of the problem.
   2. Identify known and unknown quantities, and identify the system of interest. Draw a free-body diagram, which is a sketch showing all of the forces acting on an object. The object is represented by a dot, and the forces are represented by vectors extending in different directions from the dot. If vectors act in directions that are not horizontal or vertical, resolve the vectors into horizontal and vertical components and draw them on the free-body diagram.
   3. Write Newton’s second law in the horizontal and vertical directions and add the forces acting on the object. If the object does not accelerate in a particular direction (for example, thex -direction) thenFnetx=0. If the object does accelerate in that direction,Fnetx=ma.
   4. Check your answer. Is the answer reasonable? Are the units correct?

Question 49

T/F: The normal force of an object is always equal in magnitude to the weight of the object.

Answer 49

False

The normal force on an object is not always equal in magnitude to the weight of the object. If an object is accelerating, the normal force will be less than or greater than the weight of the object. Also, if the object is on an inclined plane, the normal force will always be less than the full weight of the object.

Question 50

During a circus performance, a 72-kg human cannonball is shot out of an 18 m long cannon. If the human cannonball spends 0.95s in the cannon, determine the average net force exerted on him in the barrel of the cannon.

Answer 50

Answer: 2, 870 N

Explanation:

Man in cannonball = 72kg. If we find the acceleration of the person then F = ma will determine the average force on the person.

Use equation for acceleration
X = 18m
A = find
Vo = 0 m/s
T = 0.95

X = vot + 1/2 at2
Since Vo is 0 cancel it out
X = 1/2 at2
Rearrange
A = 2x / t^2 = 2(18m) / (0.95)^2 = 39.9 m/s^2

Determine the average force on the person from N2
∑F = ma
∑F = (72kg)(39.9m/s^2)

∑F = 2,870 N

Question 51

At a time when mining asteroids has become feasible, astronauts have connected a line between their 3,500 kg space tug and a 6,200 kg asteroid. Using their ship’s engine, they pull on the asteroid with a force of 490N. Initially the tug and the asteroid are at rest, 450 m apart. How much time does it take for the ship and the asteroid to meet?

Answer 51

Answer: T = 64 seconds

Explanation:

Find the two acceleration: Note that magnitude of force on each is the same, 490 N
Aasteroid = F/masteroid -> 490N / 6,200 kg = 0.0790 m/s^2
Aship = F/mship -> -490N / 3,500kg = -0.140 m/s^2

Assess the variables for the asteroid and the ship
Asteroid
A = 0.0790 m/s^2
Vo = 0 m/s
T = same for ship
X = find
Ship
X (displacement): 450m
A = -0.140 m/s
Vo = 0 m/s
T = same as asteroid

Find the equations for both
Asteroid
X = Vot + 1/2 at^2
Vo = 0
X = 1/2 at^2
Ship
X = 1/2 at^2

The condition for the collision is Xasteorid = Xship
1/2 aasteroidt^2 = 1/2 ashipt^2 + 450m

Solve for t:
1/2 (aasteroid-aship)t^2 = 450m
t^2 = [2(450m)/aasertoid-aship)]
t^2 = 2(450m)/0.0790 m/s^2 - (-0.140 m/s^2)
t^2 = 4,109.6 s^2
Sqareroot both sides
T = 64 seconds

Question 52

Captain Jupiter is on course for a distant planet in his starship, with the rocket engines set to a steady 60% of full thrust. The ship is in deep space, with no nearby planets or starts to apply gravitational forces on it. Pick the most accurate statement

a. Looking out the porthole, the travelers see the distant stars moving by at the same rate all the time
b. Looking out the porthole, the travelers see the distant starts moving by more and more quickly

Answer 52

b. Looking out the porthole, the travelers see the distant starts moving by more and more quickly

Explanation: he engines are applying a force on the starship and there is no friction or any other force on it. So, there is a net force on the ship and therefore an acceleration: it gets faster and faster.

Question 53

Captain Jupiter is on course for a distant planet and his starship travels through the vacuum of space at constant velocity. Pick the most accurate statement:

a. To maintain a constant velocity, captain Jupiter sets the rock engines to a constant thrust of 60%

b. To maintain a constant velocity, the rocket engines need to be at zero thrust

Answer 53

b. To maintain a constant velocity, the rocket engines need to be at zero thrust

Explanation: When the engines are at zero thrust, the net force on the rocket is zero and the rocket will continue to move in a straight line at constant speed. This is from Newton’s First Law.

Question 54

Captain Jupiter has his starship on course for a distant world, with the rocket engines at 80% of full thrust. He decided to reduce the thrust to 50% gradually over a 20 minute period. Pick the most accurate statement:

a. During the 20 minutes, the starship speeds up

b. During the 20 minutes, the starship slows down

c. During the 20 minutes, the starship maintains a constant velocity

Answer 54

a. During the 20 minutes, the starship speeds up

Explanation: When the engines have nonzero thrust, there is a net force and the starship is accelerating. This acceleration is gradually decreasing, but still the starship is speeding up.

Question 55

If an object is moving, there must be a force on it

a. True
b. False

Answer 55

b. False

Explanation: If an object is moving and there is no force on it, there is nothing to speed it up or slow it down and it will just keep going at the same speed in the same direction. It is therefore incorrect to conclude that there must be a force on the object; there might be, but there does not have to be one.

Question 56

The force of Earth’s gravity pulls down on a snowflake as it floats gently toward the ground. What is the “equal and opposite force” during this interaction, according to Newton’s third law?

a. The force of the snowflake pushing down on the air
b. The force of the snowflake’s gravity pulling up on the Earth
c. The force of the air pushing up on the snowflake
d. There is no equal and opposite force in this case

Answer 56

b. The force of the snowflake’s gravity pulling up on the Earth

Explanation (Long): Newton’s third law says that whenever one object exerts a force on a second object, the second object simultaneously exerts a force back on the first object. This second force is equal in magnitude to the first force, but is in the opposite direction. Together, these two forces make up an interaction. Forces always come in pairs that are equal parts of a single interaction; neither force exists without theother.

Sometimes the two forces in an interaction are referred to as an “action” force and a “reaction” force. However, keep in mind that either force could be called the action force; the two forces are exactly simultaneous and neither one precedes theother.

There is a very simple way to identify interaction forces: if object A exerts a force on object B, then object B exerts a force on object A of the same magnitude, but in the opposite direction. For example, if your hand pushes on a wall, the wall pushes back on your hand. When you swim, you push on the water and the water pushes back on you. Note that the two forces in any interaction are always the samekindof force. If object A is exerting a gravitational force on object B, then object B must be exerting an equal and opposite gravitational force on objectA.

In this scenario, the Earth is exerting a downward gravitational force on a snowflake. According to Newton’s third law, the snowflake must therefore be exerting an upward gravitational force on theEarth.

Question 57

As Lucy pushes a box across the floor, she exerts a force on the box in the forward direction. What is the “equal and opposite force” in this interaction, according to Newton’s third law?

a. The force of the floor pushing backward on the box
b. The force on the box pushing forward on the floor
c. The force of Lucy pushing backward on the floor
d. The force of the box pushing backward on Lucy

Answer 57

d. The force of the box pushing backward on Lucy

Explanation:
Newton’s third law says that whenever one object exerts a force on a second object, the second object simultaneously exerts a force back on the first object. This second force is equal in magnitude to the first force, but is in the opposite direction. Together, these two forces make up an interaction. Forces always come in pairs that are equal parts of a single interaction; neither force exists without theother.

Sometimes the two forces in an interaction are referred to as an “action” force and a “reaction” force. However, keep in mind that either force could be called the action force; the two forces are exactly simultaneous and neither one precedes theother.

There is a very simple way to identify forces in an interaction: if Object A exerts a force on Object B, then Object B exerts a force on Object A of the same magnitude, but in the opposite direction. For example, if your hand pushes on a wall, the wall pushes back on your hand. When you swim, you push on the water and the water pushes back onyou.

In this scenario, Lucy is exerting a forward force on the box. According to Newton’s third law, the box must therefore be exerting an backward force on Lucy.