According to Newton’s 2 nd Law

According to Newton’s 2nd Law

If the force is held constant

If the mass is held constant

If the acceleration is held constant

the relationship between mass and acceleration is direct/inverse.

the relationship between force and acceleration is direct/inverse.

the relationship between mass and force is

direct/inverse.

In this situation . . .

Mass• Amount of matter in an

object

• Is always constant at any place and time

• Is measured in kilograms• Is measured using a balance• Is an intrinsic property of an

object and is independent of any external factor

Weight

• Force which a given mass feels due to the gravity at its place

• Depends on gravity at the place

• Is measured in Newtons• Is measured using a scale• Depends on:

– Mass of the object– Mass of the object that is

attracting it

To calculate weight: When you know the mass use ΣF = ma If standing on the Earth (no friction force),

acceleration due to gravity is 9.8 m/sec/sec

Mass = 65.0 kg

Weight on earth?

Weight on the moon?

Weight on Jupiter?

Free Fall

Falling without air resistance Gravity is the only force acting upon the object

causing the object to change it’s velocity Acceleration (change in velocity) due to

gravity on earth is 9.8 m/sec/sec for all objects That means . . . When an object is in free fall it

will be increasing its velocity 9.8 m/sec every second

∑F=ma

Free Fall on the Moon

a = 9.8 m/sec/sec

Free Fall neglecting friction – which object – the elephant or the feather-

will hit the ground first The elephant and the feather each have the same

force of gravity The elephant has the greatest acceleration

(change in velocity) On earth, all objects (whether an elephant or a

feather) have the same force of gravity The elephant and the feather have the same

acceleration (change in velocity) due to gravity

True or false:

Free fall cont.

In the absence of air resistance, the elephant and the feather land at the same time.

The force of gravity experienced by an object is dependent upon the mass of that object.

RULE: all objects (regardless of their mass)experience the same acceleration

(change in velocity) when in astate of free fall

Free FallDraw a velocity vs. time graph Draw an acceleration vs. time

graph

-9.8 m/s/s

a

tt

v

Slope = -9.8 m/s/s

Acceleration of fall is less when air resistance (drag) acts

Air resistance is the result of collisions of the object's leading surface with air molecules.

Fluid friction (air drag) depends on two things: surface area & speed

The greater the surface area, the greater the friction

As an object falls, the friction increases as the speed increases

∑F=ma

Falling with Air Resistance

Falling with air resistanceSame size, different massΣF = maΣF & m are directly relatedbigger mass = bigger weight

ΣF on each ball decreasesΣF and a are directly relatedsmaller ΣF = smaller a

a (change in velocity) = 9.8 m/sec/sec

ΣF is smaller than before so a is smaller

Balls are still speeding up but not as much as they were before

Because a is not zero the balls are still speeding up, friction gets bigger

Because a = 0 ball no longer speeds up; ball will travel at that speed the rest of the way down (terminal velocity)

ΣF = 0a = 0

Ball will continue to speed up but not as much as it was before

Because a is not zero the balls are speeding up, friction increases

Terminal VelocityDraw a velocity vs. time graph Draw an acceleration vs. time

graph

a

tt

v

Lab 4 Air Resistance• Purpose: Does changing the mass of a falling object

affect the velocities observed on the motion graphs?• Method:• Materials: motion detector on ceiling; laptop; coffee

filters• Hypothesis:• Procedure:• Data: 5 different velocity vs. time graphs• Analysis: analyze motion on graphs and label with

descriptions of motion (ie where is the terminal velocity)

• Conclusion:

Which object - the elephant or the feather - will hit the ground first?

The elephant encounters a smaller force of air resistance than the feather and therefore falls faster.

The elephant has a greater acceleration (change in velocity) due to gravity than the feather and therefore falls faster.

Both elephant and feather have the same force of gravity, yet the feather experiences a greater air resistance.

The feather has a smaller force of gravity so friction equals the force of gravity sooner causing a net force of zero (no acceleration); whereas the elephant has a net force that is not zero and will continue to speed up.

True or false:

What is the acceleration for A? What is the acceleration for B? What is the acceleration for C? What is the acceleration for D?

Which encounters the greater force of air resistance—a falling elephant or a falling

feather?

Two smooth balls exactly the same size, one made of wood and the other made of iron, are dropped from a high building to the ground below. The ball to encounter the greatest force of air resistance on the way down is the:

a) wooden ballb) iron ballc) ... both the same

As she falls faster and faster through the air, her acceleration (change in velocity)

a) increasesb) decreasesc) remains the same

What will be the acceleration (change in velocity) of a rock thrown straight upward at the moment it reaches the tippity-top of its trajectory (no air)?

Chapter 3 Review1. On a long alley a bowling ball slows down as it rolls. Is

any horizontal force acting on the ball? How do you know?

2. What is the net force on a 1-N apple when you hold it at rest above your head? What is the net force on it after you release it?

3. A bear that weighs 4000 N grasps a vertical tree and slides down at constant velocity. What is the friction force that acts on the bear?

4. Two basketballs are dropped from a high building through the air. One ball is hollow and the other filled with rocks. Explain in detail the fall of the two balls.

Review6. Upon which will air resistance be greater; a sheet of falling paper or

the same paper wadded into a ball if they have both reached terminal velocity? (Careful!)

7. Aristotle claimed the speed of a falling object depends on its weight. We now know that objects in free fall, whatever their weights, undergo the same gain in speed. Why does weight not affect acceleration?

8. Why is it that a cat that accidentally falls from the top of a 50-story building hits the ground no faster than if it falls from the 20th story?

End of Chapter Exercises1. What is the net force on a bright red Mercedes convertible traveling

along a straight road at a steady speed of 100 km/h?

2. Your empty hand is not hurt when it bangs lightly against a wall. Why is it hurt if it does so while carrying a heavy load? Which of Newton's laws is most applicable here?

3. When a junked car is crushed into a compact cube, does its mass change? Its weight? Its volume? Explain.

4. If it takes 1 N to push horizontally on your book to make it slide at constant velocity, how much force of friction acts on the book?

5. A parachutist, after opening the chute, finds herself gently floating downward, no longer gaining speed. She feels the upward pull of the harness, while gravity pulls her down. Which of these two forces is greater? Or are they equal in magnitude?

1. Why will a sheet of paper fall slower than one that is wadded into a ball?

2. How does the force of gravity on a raindrop compare with the air drag it encounters when it falls at constant velocity?

3. How does the gravitational force on a falling body compare with the air resistance it encounters before it reaches terminal velocity? After?