unit 6, lesson 5 - newton's laws of motion

NEWTON’S LAWS OF MOTION

Unit 6, Lesson 6.5

Lesson Outline

Law 1: Law of Inertia Law 2: F = ma Law 3: Law of Interaction Momentum and Impulse (Introduction only)

Credits to the owner. Some slides are derived from this site:education.jlab.org/jsat/powerpoint/newtons_laws_of_motion.ppt

Mechanics is the branch of Physics dealing with the study of motion. 

It has two areas:

• Kinematics – describing motion

• Dynamics – what causes changes in motion?

So far, we have already studied Kinematics, that is, we have described motion in terms of the speed, acceleration, time, and distance travelled by a certain body by applying different formulas.

After describing the motion of an object, we will now look into what caused the motion, in a branch called dynamics.

What causes something to move?

What causes change in motion?

This can be answered by studying Newton’s 3 Laws of Motion

Newton’s Laws of Motion (Summary)

• 1st Law – An object at rest will stay at rest, and an object in motion will stay in motion at constant velocity, unless acted upon by an unbalanced force.

• 2nd Law – Force equals mass times acceleration.

• 3rd Law – For every action there is an equal and opposite reaction.

1st LawLAW OF INERTIA

1st LawLAW OF INERTIAInertia is a resistance to a change in its state of motion (speed, direction, or state of rest).

Inertia is an ability to resist any change in its state of motion.

1st LawLAW OF INERTIAIn layman’s term:Objects tend to "keep on doing what they're doing”.

A moving object will continue moving and a nonmoving object will remain not moving (at rest)…

UNLESS a FORCE is applied!

1st LawLAW OF INERTIAWhich leads us to a formal statement:

LAW NO. 1:A body at rest will remain at rest and a body in motion will remain in motion unless acted upon by an outside unbalanced force.

1st LawLAW OF INERTIA

WHY UNBALANCED FORCE?

Unbalanced forces do not cancel out (in terms of vectors via tip-to-tail method):

The resultant is a vector, thus, there is a motion going to that direction.

1st LawLAW OF INERTIA

IN BALANCED FORCES…

Vectors cancel out

The resultant is zero, thus, there is no motion.

1st LawLAW OF INERTIA

CAN ALL FORCES CAUSE CHANGE IN MOTION?No. To be able to cause a change in motion, the force exerted must be greater than the inertia of the object.

Example:

You cannot move your house by pushing it because you do not have enough energy to do so!. You need to exert tremendous amount of force to surpass its inertia, which will of course, if possible, destroy your house!

1st LawLAW OF INERTIA

CAN FORCES CAUSE MOTION?

No! It is a big misconception even among physics students that forces cause motion. Force causes a change in motion, not motion. Instead, the correct though is that, force causes acceleration, not motion.

1st LawLAW OF INERTIA

CAN FORCES CAUSE MOTION?Forces are not the cause of motion, but forces cause "a change" in motion. I mean, if something has a straight line motion with a velocity of 3 m/s and a second later it has a velocity of 5 m/s, Newton's Laws would say a force interacted with that something, changing its motion status, but Newton's Law would not explain why that something had a straight line motion with a velocity of 3 m/s at the beginning.

• Unless acted upon by an unbalanced force, this golf ball would sit on the tee forever.

1st LawLAW OF INERTIA

Why then, do we observe everyday objects in motion slowing down and becoming motionless seemingly without an outside force?It’s a force we sometimes

cannot see – friction.

Slide a book across a table and watch it slide to a rest position. The book comes to a rest because of the presence of a force - that force being the force of friction - which brings the book to a rest position.

In the absence of a force of friction, the book would continue in motion with the same speed and direction - forever! (Or at least to the end of the table top.)

Newtons’s 1st Law and You

Don’t let this be you. Wear seat belts.

Because of inertia, objects (including you) resist changes in their motion. When the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 m/hour.

2nd LawF = ma

UnitsForce – Newtons (N)

Mass – kg

Acceleration – m/s2

2nd LawF = ma

If mass remains constant, doubling the acceleration, doubles the force. If force remains constant, doubling the mass, halves the acceleration.

Newton’s 2nd Law proves that different masses accelerate to the earth at the same rate, but with different forces.• We know that objects

with different masses accelerate to the ground at the same rate (9.8 m/s2).

• However, because of the 2nd Law we know that they don’t hit the ground with the same force.

F = ma98 N = 10 kg x 9.8 m/s2

F = ma9.8 N = 1 kg x 9.8 m/s2

The problem solving part has already been tackled previously.

F=ma

a=F/m

M=F/a

2nd LawF = ma

3rd LawLAW OF INTERACTION or

LAW OF ACTION AND REACTION

3rd LawLAW OF INTERACTION

LAW NO. 3:For every action, there is an equal and opposite reaction.

3rd LawLAW OF INTERACTION

Mathematically:action = –reaction

The negative (–) sign indicates opposite reaction.

Graphically:

3rd LawLAW OF INTERACTION

Therefore, if you punch a wall with a strong force, it also punches you back with the same force you exerted. That’s why it hurts.

Flying gracefully through the air, birds depend on Newton’s third law of motion. As the birds push down on the air with their wings, the air pushes their wings up and gives them lift.

3rd LawLAW OF INTERACTION

MOMENTUM AND IMPULSE

• Mass in motion

Mathematically:p = mvWhere p is the momentum, from the Latin petere meaning pressure.

m is mass (kg)

v is velocity (m/s)

MOMENTUM

The higher the momentum, the harder it is for the object to stop.

MOMENTUM

From the formulap=mvWe can see the following relationships:

1. Mass is directly proportional to momentum

2. Velocity is directly proportional to momentum

MOMENTUM

Therefore:

-The greater the mass, the greater the momentum (Converse is also true)

-The faster the velocity, the greater the momentum (Converse is also true)

MOMENTUM

It makes sense because its indeed hard to stop a heavy train from moving compared to stopping a rolling ball.

MOMENTUM

Problem Solving:

A fat man weighing 80 kg is running at 4 m/s, while a thin man weighing 40 kg is running at 10 m/s. Who has a larger momentum?

MOMENTUM

Problem Solving:

A fat man weighing 80 kg is running at 4 m/s, while a thin man weighing 40 kg is running at 10 m/s. Who has a larger momentum?

MOMENTUM

Fat man:

p = mv

= (80 kg)(4 m/s) = 320 kg m/sThin man:

p = mv

= (40 kg)(10 m/s) = 400 kg m/s

Problem Solving:

A fat man weighing 80 kg is running at 4 m/s, while a thin man weighing 40 kg is running at 10 m/s. Who has a larger momentum?

MOMENTUM

Fat man: 320 kg m/sThin man: 400 kg m/sTherefore, the thin man has the larger momentum!Note that even the fat man is far heavier than the thin man, the thin man’s momentum is greater because it is running at a high velocity. Therefore, it is harder to stop the thin man.

• Something that changes the momentum of an object

To change the momentum, you have to apply a force for a period of time, which gives us the formula for impulse (on the next slide)

IMPULSE

Mathematically:I = Ft or

I = mv = m(vf – vi)I is impulse (Ns) m is mass

F is force (N) v is change in velocity:

T is time (s) final velocity – initial velocity

IMPULSE

1. Which of Newton's Laws is demonstrated by a ball rolling to a wall then stopping? (1 pt)

2. It is the tendency of an object to continue doing what it is currently doing. (1 pt)

3. Calculate the force of a moving body of mass 45 kg accelerating at 3 m/s2. (3 pts)

4. Refer to the experiment on p. 223-224. Answer no. 1. (4 pts)

5. Answer no. 2 (6 pts)

6. Answer no. 4 (4 pts)

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts

7. Solve:From the data given by LRT System Line 1, the maximum speed allowed for these trains is 22.22 m/s. If the mass of a train is 40,000 kg moving to the west:

a) Calculate the momentum of the train at its maximum speed. (3 pts)

b) Calculate the momentum of the train at 15 m/s. (3 pts)

c) Find the impulse if the train slowed down from its maximum speed to 15 m/s. (5 pts)

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts

ANSWERS

1. Which of Newton's Laws is demonstrated by a ball rolling to a wall then stopping? (1 pt)

FIRST LAW: LAW OF INERTIA2. It is the tendency of an object to continue doing what it is

currently doing. (1 pt)

INERTIA3. Calculate the force of a moving body of mass 45 kg

accelerating at 3 m/s2. (3 pts)

F= ma = (45 kg)(3 m/s2) = 135 N

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts

For nos. 4-6, answers may vary but must be rational.

4. Refer to the experiment on p. 223-224. Answer no. 1. (4 pts)

The air from the balloon rushes out (action) and propels the car forward (reaction). (Law of Action and Reaction)5. Answer no. 2 (6 pts)

Law of Inertia = the unbalanced force from the air coming out of the balloon caused the car to moveSecond Law = The greater the mass placed on the car, the slower it moves.Third Law = same to answer in no. 4

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts

6. Answer no. 4 (4 pts)

The greater the mass, the greater the momentum, that is, the harder for the object to cease motion.

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts

7. From the data given by LRT System Line 1, the maximum speed allowed for these trains is 22.22 m/s. If the mass of a train is 40,000 kg moving to the west:

a) Calculate the momentum of the train at its maximum speed. (3 pts)

p=(40,000 kg)(22.22 m/s)

p=888,800 kg m/s, west

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts

7. From the data given by LRT System Line 1, the maximum speed allowed for these trains is 22.22 m/s. If the mass of a train is 40,000 kg moving to the west:

b) Calculate the momentum of the train at 15 m/s. (3 pts)

p=(40,000 kg)(15 m/s)

p=600,000 kg m/s, west

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts

7. From the data given by LRT System Line 1, the maximum speed allowed for these trains is 22.22 m/s. If the mass of a train is 40,000 kg moving to the west:

c) Find the impulse if the train slowed down from its maximum speed to 15 m/s. (5 pts)

I = m(vf – vi)

I = (40,000 kg)(15 m/s – 22.22 m/s)

I = -288,800 Ns, west or 288,800 Ns, east

ASSIGNMENT: 1 whole sheet of paper (submit tomorrow)= 30 pts