Apr 21, 2023

Chapter 4 Newton’s Second Law

of Motion

How does an object move when a force acts on it?

What is Weight?

• Weight-The force of gravity acting on an object

• Since F=MA and weight is a force– F=Mg where g=the acceleration due to

gravity =10 m/s/s on earth (different on different planets)

Apr 21, 2023

Friction and Air Resistance

Friction and air resistance are forces opposing motion.

Apr 21, 2023

FrictionOrigin of friction is molecular interaction between

solid surfaces.

Friction is complicated.

Friction depends on support force (also called the normal force) and on properties of the surface.

Basic properties of friction first established by Leonardo da Vinci.

Friction

• Depends on the roughness of the surfaces that are moving over each other and the normal force between the objects– Coefficient of friction () is a dimensionless

ratio that relates the roughness of the surfaces

– Normal force=support force. We will only be dealing with flat surfaces so Fn=weight=m*g

Apr 21, 2023

Free Body Diagram

Apr 21, 2023

• A free body diagram outlines all of the forces that act on an object– Fa=Applied force– Ff=Friction force– Fn=Normal Force– Fg=Weight

What does each force mean?• Fa=Applied force. The outside force that is

being exerted on the object in order to make it move.

• Ff=Friction force. The retarding force that opposes the motion of the object.

• Fg=Weight. Force of gravity on the object.• Fn=Normal Force. The upward support

force the surface exerts on the moving object.

Apr 21, 2023

Equations

• Fn=m*g (weight)

• Ff=*Fn (friction force)• Fnet=Fa-Ff

• Fnet=M*A

Apr 21, 2023

Apr 21, 2023

Air Resistance (Drag)Origin of drag is molecules of gas (or liquid) striking

a moving object.

Drag force depends on:

•Size (area) of the object•Speed of the object

Larger the size or speed, larger the drag.

Also depends on shape of object, density of gas or liquid, etc.

Apr 21, 2023

Air Resistance on a Falling Object

Gravity force on an object (i.e., weight) is constant but air resistance depends on an object’s speed.

As a falling object gains speed, the resistance force gets larger so the net force decreases.

Net force is sum of:Weight (downward)Resistance (upward)

Apr 21, 2023

Demo: Drop the Sheet

A flat sheet of paper falls slowly because of air resistance.

What happens if we place it on top of a book, blocking the air from reaching it?

AirResistance

Weight

Apr 21, 2023

Check Yourself

Golf ball has more mass than a ping-pong ball. Force of gravity is greater on: golf ball, ping-pong ball, or the same?

The two balls are the same size; when speeds are equal, drag force is greater on which ball?

Which ball falls faster (which has greater acceleration)?

GolfBall

PingpongBall

Drag

Weight

Apr 21, 2023

Terminal SpeedSpeed of falling objects increases until drag force

balances weight.

When forces balance, zero acceleration so constant velocity.

Speed for which air resistance balances weight called terminal speed.

High terminal speed(better open the chute!)

Low terminal speed(large area of chute)

Apr 21, 2023

Demo: Drop the CatCats seem to have an uncanny ability to survive

falls from high places. For example, cats have been known to survive falls of up to 32 stories. By contrast, dogs rarely survive falls of more than six stories. Humans usually die when they fall from such heights.

From: www.animalhealthcare.ca

In a study of cats that had fallen from up to 32 stories, an interesting finding emerged: while the rate of injury in cats seemed to increase linearly depending on the length of the fall, after seven stories, the rate of injury seemed to level off! In other words, the survival rate and severity of injuries were no more severe in a cat that fell seven stories than in one that fell 32 and in some cases, injuries were even less!

Apr 21, 2023

Demo: Drop the Cat (cont.)After further study, the reasons for this discrepancy

became clear. When a person falls from a building, maximum speed or "terminal velocity" (120 mph) is reached after 32 stories. Cats, on the other hand, achieve terminal velocity at 60 mph after falling only five stories!

Until a cat reaches terminal velocity, it will experience acceleration and tend to reflexively extend its limbs, making it more susceptible to injuries. However, when a cat reaches terminal velocity, its vestibular system (i.e. the organs of balance) become less stimulated, causing the cat to relax. It will then orient its limbs more horizontally (splay-legged), thereby increasing air drag in much the same way a parachute does. In this posture, the force of impact also appears to become more evenly distributed.