Chapter 4Chapter 4Newton’s Laws: Newton’s Laws: Explaining MotionExplaining Motion

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The concepts of force,

mass, and weight

play critical roles.

Newton’s Laws of Motion

A Brief History

Where do our ideas and theories about motion come from?

What roles were played by Aristotle, Galileo, and Newton?

How did Newton’s theory come about?What does it tell us about motion?Can we trust our intuition?

Will the chair continue to move when the person stops pushing?

Aristotle’s View

A force is needed to keep an object moving.Air rushing around a thrown object continues to push the object forward.

Galileo’s Contribution

Galileo challenged Aristotle’s ideas that had been widely accepted for many centuries.

He argued that the natural tendency of a moving object is to continue moving.No force is needed to keep an object

moving.This goes against what we seem to

experience.

Newton’s ContributionNewton built on Galileo’s

work, expanding it.He developed a

comprehensive theory of motion that replaced Aristotle’s ideas.

Newton’s theory is still widely used to explain ordinary motions.

Newton’s First and Second Laws

How do forces affect the motion of an object?

What exactly do we mean by force? Is there a difference between, say, force, energy, momentum, impulse?

What do Newton’s first and second laws of motion tell us, and how are they related to one another?

Newton’s First Law of Motion

An object remains at rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposed force.

Newton’s Second Law of Motion

The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object.The acceleration is the same direction as that of the imposed force.

Newton’s Second Law of Motion

Note that a force is proportional to an object’s acceleration, not its velocity. We need some precise definitions of some commonly used terms:

This resistance to a change in motion is called inertia.The mass of an object is a quantity that tells us how much resistance (inertia) the object has to a change in its motion.

F ma

units : 1 newton = 1 N = 1 kgm s2

It is the total force or net force that determines an object’s acceleration. If there is more than one vector acting on an object, the forces are added together as vectors, taking into account their directions.

Fstring 10 N (to the right)

ftable 2 N (to the left)

Fnet 10 N 2 N

8 N (to the right)

a Fnet

m8 N

5 kg

1.6 m s2 (to the right)

Two equal-magnitude horizontal forces act on a box. Is the

object accelerated horizontally?a) Yes.b) No.c) You can’t tell from

this diagram.

b) Since the two forces are equal in size, and are in opposite directions, they cancel each other out and there is no acceleration.

Is it possible that the box is moving, since the forces are equal in size but opposite in

direction?a) Yes, it is possible for the

object to be moving.b) No, it is impossible for the

object to be moving.

a) Even though there is no acceleration, it is possible but not guaranteed that the object is moving with a constant speed.

Two equal forces act on an object in the directions shown.

If these are the only forces involved, will the object be

accelerated?a) Yes.b) No.c) It is impossible to determine

from this figure.

a) The vector sum of the two forces results in a force directed toward the upper right corner. The object will be accelerated toward the upper right corner.

Two forces act in opposite directions on a box. What is the

mass of the box if its acceleration is 4.0 m/s2?

a) 5 kgb) 7.5 kgc) 12.5 kgd) 80 kge) 120 kg

a) The net force is 50 N - 30 N = 20 N, directed to the right. From F=ma, the mass is given by:

m = F/a = (20 N) / (4 m/s2) = 5 kg.

A 4-kg block is acted on by three horizontal forces. What is the net

horizontal force acting on the block?

a) 10 Nb) 20 Nc) 25 Nd) 30 Ne) 40 N

b) The net horizontal force is:5 N + 25 N - 10 N = 20 N directed to the right.

A 4-kg block is acted on by three horizontal forces. What is the horizontal acceleration of the

block?a) 4 m/s2

b) 80 m/s2

c) 15 m/s2

d) 5 m/s2

e) 16 m/s2

d) From F=ma, the acceleration is given by:

a = F/m = (20 N) / (4 kg) = 5 m/s2

directed to the right.

Mass and Weight

What exactly is mass? Is there a difference between mass and

weight? If something is weightless in space,

does it still have mass?

Mass, Weight, and Inertia

A much larger force is required to produce the same acceleration for the larger mass.Inertia is an object’s resistance to a change in its motion.Mass is a measure of an object’s inertia.The units of mass are kilograms (kg).

Mass, Weight, and Inertia

An object’s weight is the gravitational force acting on the object.Weight is a force, measured in units of newtons (N).In the absence of gravity, an object has no weight but still has the same mass.

Mass, Weight, and Inertia

Objects of different mass experience the same gravitational acceleration on Earth: g = 9.8 m/s2

By Newton’s 2nd Law, F = ma, the weight is W = mg.Different gravitational forces (weights) act on falling objects of different masses, but the objects have the same acceleration.

A ball hangs from a string attached to the ceiling. What is the net force acting on the ball?a) The net force is

downward. b) The net force is upward. c) The net force is zero.

c) Since the ball is hanging from the ceiling at rest, it is not accelerating so the net force is zero. There are two forces acting on the ball: tension from the string and force due to gravitation. They cancel each other.

Two masses connected by a string are placed on a fixed frictionless pulley. If m2 is larger than m1, will the two

masses accelerate?a) Yes. b) No. c) You can’t tell

from this diagram.

a) Mass m2, being heavier, will fall and mass m1, tied to mass m2 with a string, will rise. Both will increase speed with time and have the same magnitude of acceleration.

Newton’s Third Law

Where do forces come from? If we push on an object like a chair, does the

chair also push back on us? If objects do push back, who experiences the

greater push, us or the chair? Does our answer change if we are pushing

against a wall? How does Newton’s third law of motion help

us to define force, and how is it applied?

Newton’s Third Law(“action/reaction”)

For every action (force),

there is an equal but opposite reaction

(force).

It is important to identify the forces acting on an object.

The forces acting on the book are W (gravitational force from Earth) and N (normal force from table).Normal force refers to the perpendicular force a surface exerts on an object.

It is important to identify the forces acting on an object. It is also important to identify the action-reaction pairs.

The reaction force to the Earth’s attractive force W on the book, is an equal attractive force -W the book exerts on the Earth.

It is important to identify the forces acting on an object. It is also important to identify the action-reaction pairs.

The reaction force to the table’s normal force N exerted upward on the book, is an equal force -N the book exerts downward on the table.

An uncompressed spring and the same spring supporting a book. The compressed spring exerts an upward force on the book.

Third-Law Action/Reaction Pair

If the cart pulls back on the mule equal and opposite to the mule’s pull on the cart,

how does the cart ever move?

Third-Law Action/Reaction Pair

The car pushes against the road, and the road, in turn, pushes against the car.

Applications of Newton’s Laws

How can Newton’s laws be applied in different situations such as pushing a chair, sky diving, throwing a ball, and pulling two connected carts across the floor?

What forces are involved in moving a chair?

The weight W (gravitational force from Earth) The upward force N (normal force from floor).The push P (normal force from hand of person)The frictional force f exerted by the floor

Does a sky diver continue to accelerate?

Air resistance R is a force directed upward, that opposes the gravitational force W R increases as the sky diver’s velocity increasesWhen R has increased to the magnitude of W, the net force is zero so the acceleration is zeroThe velocity is then at its maximum value, the terminal velocity

What happens when a ball is thrown?

Three forces act on a thrown ball:The initial push P

Only acts at the beginning; once the ball leaves the hand, P is no longer acting on the ball.

The weight W Is a constant (does not change) throughout the trajectory

The air resistance RIs always directed against the motionIs proportional to the speed

What happens when objects are connected?

Two connected carts being accelerated by a force F applied by a string:Both carts must have the same acceleration a which is equal to the net horizontal force divided by the total massEach cart will have a net force equal to its mass times the acceleration

What happens when objects are connected?

The interaction between the two carts illustrates Newton’s third law:m1 exerts a pull of 16 N to the right on m2

m2 exerts an equal and opposite pull of 16 N to the left on m1

Two blocks with the same mass are connected by a string and are pulled across a frictionless surface by a constant force.

Will the two blocks move with constant velocity?

a) Yes, both blocks move with constant velocity.

b) No, both blocks move with constant acceleration.

c) The two blocks will have different velocities and/or

accelerations.

b) The front block will accelerate due to the constant force F. The rear block is also pulled by a constant force due to the connecting string, so it will accelerate with the same acceleration as the front block. The constant force implies a constant acceleration. Constant acceleration results in constantly increasing velocity.

Will the tension in the connecting string be greater than, less than, or equal to

the force F?

a) Greater than.b) Less than.c) Equal to.

b) The tension in the connecting string is less than F. Both bodies have the same acceleration. The force F accelerates a total mass, 2m. The force in the connecting string accelerates a mass, m, so it is half of F.

Two blocks tied together by a string are being pulled across the table by a horizontal

force. The blocks have frictional forces exerted on them by the table as shown.

What is the net force acting on the entire two-block system?

a) 16 Nb) 36 Nc) 38 Nd) 44 Ne) 46 N

a) The net horizontal force is:30 N - 6 N - 8 N = 16 N directed to the right.

What is the acceleration of this system?

a) 2.00 m/s2 b) 2.67 m/s2

c) 5.00 m/s2

d) 7.50 m/s2

The total mass is:2 kg + 4 kg = 6 kg

b) The acceleration of the system is:Total force ÷ total mass =16 N ÷ 6 kg = 2.67 m/s2 directed to the right.

What force is exerted on the 2-kg block by the connecting string?

a) 16 Nb) 5.3 Nc) 2.7 Nd) 12.7 Ne) 11.3 N

The net horizontal force on the 2-kg block is:Fnet = ma = 2 kg x 2.67 m/s2 = 5.3 N

e) So the force due to the string is:Fstring = Fnet + 6 N = 11.3 N

directed to the right.

What is the acceleration of the 4-kg block?

a) 5.33 m/s2

b) 2.67 m/s2

c) 1.33 m/s2

d) 0 m/s2

e) 16 m/s2

The net horizontal force on the 4-kg block is:Fnet = 30 N - 8 N - 11.3 N = 10.7 N

b) The acceleration of the 4-kg block is:a = F ÷ m = 10.7 N ÷ 4 kg = 2.67 m/s2

directed to the right.