Newton’s Second Law

Chapter 4Net Force causing acceleration

FrictionAir resistance

Student Learning Outcomes

• Understand when Newton’s law of inertia applies and when it does not

• Understand what happens to objects when there is a net force (Newton’s 2nd law)

• Calculate accelerations from the net force• Understand a conceptual model of friction– Calculate acceleration when friction acts

• Understand a conceptual model of air resistance– Calculate acceleration when falling with air resistance

What can happen to an object when the net force on it equals zero? Select all that apply.

0

0

0

0

0

Give examples in this room where the net force = 0.

1. Speed up2. Slow down3. Change direction of motion4. Stay at rest5. Move in a line with constant speed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

What can happen to an object when the net force on it is NOT zero? Select all that apply.

0

0

0

0

0

Give a one word answer to the question, “What happens to an object when the net force on it is NOT zero?”

1. Speed up2. Slow down3. Change direction of motion4. Stay at rest5. Move in a line with constant speed

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

Accelerations

• Newton’s second law:– Net force causes an object to accelerate.– An object’s acceleration depends on its mass– Equation: Fnet = mass * accelerate

• People often say F = ma, but the better version is Fnet = ma– Words: Net Force causes mass to accelerate– Same equation written another way:

accel = Fnet / mass• Describe this in words.

• Textbook pages 58-59, 63-65

Figure 4.2 – with extra labels, p. 59

Fnet/m = A

2Fnet/m= 2 * A

(2Fnet)/(2m)= Fnet / m= A

Figure 4.11 – with extra labels, p. 64

Fnet/m = A

Fnet/(2m) = ½ Fnet/m = ½ A

Fnet/(3m) = (1/3) Fnet/m = 1/3 A

Friction - what• When does friction occur?– When an object slides or attempts to slide across

another object.

• In which direction does friction push?– In a direction to oppose relative motion.• Note the word “relative” left out of your textbook!

• Sliding cart with scale– Start slowly, pull stronger. Maximum friction force?– Constant speed: how much friction force?

4 examples• 5-kg box sits on flat floor. Maximum friction force

is 100 N. Draw a picture for each of the 4 cases.– What is the net force in these cases?– What happens to the box?– Calculate acceleration.

1. You push to right with 70 N

2. You push to right with 100 N

3. You push to right with 110 N

4. You push to left with 120 N

Friction - why

• Why does friction occur?– 1) Rubbing and 2) microscopic bonds form

where the bumpy surfaces touch. Figure 4.3:

What does friction depend on?

• Students pick answers.• Surprising, NOT speed and NOT contact area– How do we know?– Except for “air resistance” (or friction inside any

gas/fluid )• In these cases, friction happens because object moves

air/fluid out of the way)

• How “rough” the two surfaces are• How much they’re squeezed together

3 Types of friction

• Sliding (kinetic) friction– When two surfaces ARE sliding across each other

• Static friction– When two surfaces are being pushed across each

other but neither has begun to slide– The surfaces WOULD slide if there were no friction.

• Rolling friction (not in your [or almost any other] textbook)– When one object rolls across a surface

Which kind of friction is weakest?

0

0

0

0 1. Static friction2. Sliding (kinetic) friction3. Rolling friction4. All 3 are the same

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

Which kind of friction is strongest?

0

0

0

0 1. Static friction2. Sliding (kinetic) friction3. Rolling friction4. All 3 are the same

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

Demonstrate with cart attached to balance.

Newton’s 3rd law causing unequal accelerations• Newton’s 3rd law told us– when two objects interact, both experience the same

force in opposite directions.

• Yet we “know” BIG truck “wins” and little car “loses” in a collision.

• Why? [Rhetorical]• On next slide, I’m going to color code car and truck.

In your notes, I suggest you somehow “color” code them too.

Unequal accelerations, continued• Ftruck on car = Fcar on truck (N’s 3rd law)

• Ftruck on car makes car accelerate – Ftruck on car = car mass * car acceleration (N’s 2nd law)

• Fcar on truck makes truck accelerate – Fcar on truck = truck mass * truck acceleration (N’s 2nd law)

• Summary – putting it all together:• Ftruck on car = Fcar on truck (N’s 3rd law)• car mass * car acceleration = truck mass * truck acceleration• Written more graphically: •

car mass * car acceleration = truck mass * truck acceleration

• And what do people feel?

Simple gravity• (More complicated version of gravity is our

next chapter, chap. 9 – we’ll come back to 6-8)• Near surface of a world, we can say:– All things accelerate equally

• On Earth: 10 m/s per sec (= 22 miles/hr per sec)• On Moon: about 1/6 , 3.7 miles/hr per sec)• The acceleration number is called “g”

– Force of gravity is called “weight” (symbol: w)– w = mass of object * g– Force depends on the mass of the thing falling and

the strength of the gravitational acceleration.

You have two balls of equal size and smoothness, and you can ignore air resistance. One is heavy, the other much lighter. You hold one in each hand at the same height above the ground. You release them at the same time. What will happen?

0

0

0 1. The heavier one will hit the ground first.2. They will hit the ground at the same time.3. The lighter one will hit the ground first.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Same objects. How does the acceleration of gravity compare? Be careful!

0

0

0 1. The heavier one has a larger gravitational acceleration.2. They have the same gravitational acceleration.3. The lighter one has a larger gravitational acceleration.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Same objects. How does the force of gravity compare? Be careful!

0

0

0 1. The heavier one has a stronger gravitational force.2. They have the same gravitational force.3. The lighter one has a stronger gravitational force.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

Falling with air resistance

• Air resistance depends on speed and “frontal” (contact) area.

• One model of air resistance:– Fair resistance = Area * speed * other things we ignore

• Coffee filter demo– Regular– Crumpled

• What forces act after you drop out of a very high-up helicopter?

What is speed at the instant you drop out of very high helicopter?

0

0

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. Zero2. 10 m/s3. Not enough information?

So how strong is air resistance?What forces act?What’s the net force?

What is acceleration at the instant you drop out of very high helicopter?

0

0

0

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. Zero2. 10 m/s3. 10 m/s per second4. Not enough information

If wait a long time, what happens to speed?

0

0

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. You always speed up2. You speed up, but then slow down3. You speed up to a certain speed

What is acceleration after waiting a long time, BUT before hitting ground?

0

0

0

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. More than g = 10 m/s per second2. g3. Less than g but more than zero4. zero

What is acceleration in middle, before achieving terminal speed?

0

0

0

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. More than g = 10 m/s per second2. G3. Less than g but more than zero4. zero

What’s happening to the acceleration?

Jumping out of planes

• People in the movies often jump out of planes without a parachute, usually after the bad guy takes the last parachute.

• What do the good guys do to survive?• Why does this work?– How does it affect terminal speed?

• What do parachutes do?– How does it affect terminal speed?

Which encounters a greater force of air resistance if dropped at same time?

0

0

0

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

1. Falling feather2. Falling elephant3. Same air resistance for both4. Not enough information

Student Learning Outcomes

• Understand when Newton’s law of inertia applies and when it does not

• Understand what happens to objects when there is a net force (Newton’s 2nd law)

• Calculate accelerations from the net force• Understand a conceptual model of friction– Calculate acceleration when friction acts

• Understand a conceptual model of air resistance– Calculate acceleration when falling with air resistance