# Cat Falls Off a Building

## Presentation on theme: "Cat Falls Off a Building"— Presentation transcript:

Cat Falls Off a Building
Why is it that a cat that falls from the top of a 50 story building will hit the ground no faster than if it fell from the 20th story? The cat reaches terminal velocity in a 20 story fall, so falling the extra distance doesn’t affect the speed. The low terminal velocities of small creatures enables them to fall without harm from heights that would kill larger creatures. Falling is favored by their higher ratio of surface area/mass. Humans boost this ratio by using parachutes.

Newton’s 3rd Law Drop a sheet of tissue paper in front of the heavyweight boxing champion of the world and challenge him to hit it in midair with a force of only 50 pounds (222 N). Sorry, the champ can't do it. In fact, his best punch couldn't even come close. Why is this? We'll see in this chapter that the tissue has insufficient inertia for a 50-pound interaction with the champ's fist.

Forces and Interactions
So far we have treated force in its simplest sense—as a push or pull. In a broader sense, a force is not a thing in itself but makes up an interaction between one thing and another. If you push on a wall with your fingers, more is happening than you pushing on the wall. The wall is also pushing on you. How else can you explain the bending of your fingers? Your fingers and the wall push on each other. There is a pair of forces involved: your push on the wall and the wall's push back on you. These forces are equal in magnitude and opposite in direction and comprise a single interaction. In fact, you can't push on the wall unless the wall pushes back.

Boxer Consider a boxer's fist hitting a massive punching bag.
Fist hits the bag (and dents it) while the bag hits back on the fist (and stops its motion). In hitting the bag there is an interaction with the bag that involves a pair of forces. The force pair can be quite large. But what of hitting a piece of tissue paper, as discussed earlier? The boxer's fist can only exert as much force on the tissue paper as the tissue paper can exert on the fist. Furthermore, the fist can't exert any force at all unless what is being hit exerts the same amount of force back. An interaction requires a pair of forces acting on two objects.

In the interaction between the hammer and the stake, the hammer exerts a force against the stake, but is itself brought to a halt in the process. Such observations led Newton to his third law of motion.

Forces and Interactions
The impact forces between the blue and yellow balls move the yellow ball and stop the blue ball.

Which exerts the force and which receives the force?
Isaac Newton's answer to this was that neither force has to be identified as “exerter” or “receiver”; he concluded that both objects must be treated equally. For example, when you pull the cart, the cart simultaneously pulls on you. This pair of forces, your pull on the cart and the cart's pull on you, makes up the single interaction between you and the cart.

Action and reaction forces
Action and reaction forces. Note that when action is “A exerts force on B,” the reaction is then simply “B exerts force on A.”

Newton’s 3rd Law Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. Newton's third law is often stated thus: “To every action there is always opposed an equal reaction.” In any interaction there is an action and reaction pair of forces that are equal in magnitude and opposite in direction. Neither force exists without the other—forces come in pairs, one action and the other reaction. The action and reaction pair of forces makes up one interaction between two things.

You interact with the floor when you walk on it
You interact with the floor when you walk on it. Your push against the floor is coupled to the floor's push against you. The pair of forces occurs simultaneously. Likewise, the tires of a car push against the road while the road pushes back on the tires—the tires and road push against each other. In swimming you interact with the water that you push backward, while the water pushes you forward—you and the water push against each other. In each case there is a pair of forces, one action and the other reaction, that make up one interaction. The reaction forces are what account for our motion in these cases. These forces depend on friction; a person or car on ice, for example, may not be able to exert the action force to produce the needed reaction force. Which force we call action and which we call reaction doesn't matter. The point is that neither exists without the other.

Defining a System An interesting question often arises; since action and reaction forces are equal and opposite, why don't they cancel to zero? To answer this question we must consider the system involved. Consider the force pair between the apple and orange.

When the apple pulls on the orange, the orange accelerates
When the apple pulls on the orange, the orange accelerates. At the same time, the orange pulls on the apple. Do the forces cancel to zero?

When the orange is the system (within the dashed line) an external force provided by the apple acts on it. Action and reaction forces do not cancel and the system accelerates.

When both the orange and apple compose the system (both within the dashed line) no external force acts on it. Action and reaction are within the system and do cancel to zero. Zero net force means no acceleration of the system.

If, however, we consider the system to enclose both the orange and apple, the force pair is internal to the orange-apple system. Then the forces do cancel each other. The apple and orange move closer together but the system's “center of gravity” is in the same place before and after the pulling. There is no net force and therefore no net acceleration. Similarly, the many force pairs between molecules in a golf ball may hold the ball together into a cohesive solid, but they play no role at all in accelerating the ball. A force external to the ball is needed to accelerate the ball.

So a force external to both the apple and orange is needed to produce acceleration of both (like friction of the floor on the apple's feet). In general, when Body A inside a system interacts with Body B outside the system, each can experience a net force. Action and reaction forces don't cancel. You can't cancel a force acting on Body A with a force acting on Body B. Forces cancel only when they act on the same body, or on the same system. Action and reaction forces always act on different bodies. When action and reaction forces are internal to a system, they cancel each other and produce no acceleration of the system.

Check Yourself If this is confusing, it may be well to note that Newton had difficulties with the third law himself. 1. On a cold rainy day your car battery is dead and you must push the car to move it and get it started. Why can't you move the car by remaining comfortably inside and pushing against the dashboard? 2. Why does a book sitting on a table never accelerate “spontaneously” in response to the trillions of inter-atomic forces acting within it? 3. Does a speeding missile possess force? 4. We know that the Earth pulls on the moon. Does it follow that the moon also pulls on the Earth? 5. Can you identify the action and reaction forces in the case of an object falling in a vacuum?

Horse and Cart Problem

Action and Reaction on Different Masses
As strange as it may first seem, a falling object pulls upward on the Earth as much as the Earth pulls downward on it. The downward pull on the object seems normal because the acceleration of 10 meters per second each second is quite noticeable. The same amount of force acting upward on the huge mass of the Earth, however, produces acceleration so small that it cannot be noticed or measured.

The Earth is pulled up by the boulder with just as much force as the boulder is pulled downward by the Earth.

We can see that the Earth accelerates slightly in response to a falling object by considering the exaggerated examples of two planetary bodies. The forces between bodies A and B are equal in magnitude and oppositely directed in each case. If acceleration of planet A is unnoticeable in a, then it is more noticeable in b where the difference between the masses is less extreme. In c, where both bodies have equal mass, acceleration of object A is as evident as it is for B. Continuing, we see the acceleration of A becomes even more evident in d and even more so in e. So strictly speaking, when you step off the curb, the street comes up ever so slightly to meet you.

Which falls toward the other, A or B? Do the accelerations of each relate to their relative masses?

Interaction Between Rifle and Bullet
The role of different masses is evident in a fired rifle The force exerted against the recoiling rifle is just as great as the force that drives the bullet. Why then, does the bullet accelerate more than the rifle?

If we extend the idea of a rifle recoiling or “kicking” from the bullet it fires, we can understand rocket propulsion. Consider a machine gun recoiling each time a bullet is fired. If the machine gun is fastened so it is free to slide on a vertical wire , it accelerates upward as bullets are fired downward. A rocket accelerates the same way. It continually “recoils” from the ejected exhaust gas. Each molecule of exhaust gas is like a tiny bullet shot from the rocket .

The rocket recoils from the
“molecular bullets” it fires and climbs upward

A common misconception is that a rocket is propelled by the impact of exhaust gases against the atmosphere. In fact, in the early 1900s before the advent of rockets, many people thought that sending a rocket to the moon was impossible because of the absence of an atmosphere for the rocket to push against. But this is like saying a gun wouldn't kick unless the bullet had air to push against. Not true! Both the rocket and recoiling gun accelerate not because of any pushes on the air, but because of the reaction forces by the “bullets” they fire—air or no air. A rocket works better, in fact, above the atmosphere where there is no air resistance to oppose its motion.

Newton's 3rd Law

Newton’s 3rd Law is Everywhere
A fish pushes the water backward with its fins, and the water pushes the fish forward. The wind pushes against the branches of a tree, and the branches push back on the wind and we have whistling sounds. Forces are interactions between different things. Every contact requires at least a two-ness; there is no way that an object can exert a force on nothing. Forces, whether large shoves or slight nudges, always occur in pairs, each of which is opposite to the other. Thus, we cannot touch without being touched.

Newton’s 1st Law An object at rest tends to remain at rest; an object in motion tends to remain in motion at constant speed along a straight-line path. This tendency of objects to resist change in motion is called inertia. Mass is a measure of inertia. Objects will undergo changes in motion only in the presence of a net force.

Newton’s 2nd Law When a net force acts on an object, the object will accelerate. The acceleration is directly proportional to the net force and inversely proportional to the mass. Symbolically, a = F/m. Acceleration is always in the direction of the net force. When objects fall in a vacuum, the net force is simply the weight, and the acceleration is g (the symbol g denotes that acceleration is due to gravity alone). When objects fall in air, the net force is equal to the weight minus the force of air resistance, and the acceleration is less than g. If and when the force of air resistance equals the weight of a falling object, acceleration terminates, and the object falls at constant speed (called terminal speed).

Newton’s 3rd Law Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. Forces come in pairs, one action and the other reaction, both of which comprise the interaction between one object and the other. Action and reaction always act on different objects. Neither force exists without the other.

Problems How much in newtons does a 20 Kg bag weigh?
A 350,000 Kg airplane in takeoff uses 25,000 N thrust of each one of its four engines. What is the acceleration of the plane during take-off ? An unbalanced force of 35 N gives an object an acceleration of 5 m/s . What force would be needed to give it an acceleration of 1 m/s ?

A certain unbalanced force gives a 10 Kg object an acceleration of 2 m/s . What acceleration would the same force give a 20 Kg object? A net force of 2N acts on a 3 Kg object, initially at rest, for 2 seconds. What is the distance the object moves during that time? A 20 Kg block of cement is pulled upward (not sideways) with a force 300 N. What is the acceleration of the block?

What is the Pressure on a table when a 12 N book with a
What is the Pressure on a table when a 12 N book with a .06 meters squared cover lies flat on it? Two people have a tug of war on low-friction ice, One person has 3 times the mass of the other. Compared to the lighter person, how many times as fast does the heavier person accelerate? What engine thrust (in newtons) is required for a rocket of mass 30 Kg to leave the launching pad?

Quiz 1 1. If a man has a mass of 60 Kg, calculate his weight in Newtons. 2. Calculate in Newtons the weight of a 3 Kg melon. What is its weight in pounds?

Quiz 2 Calculate the acceleration of a
400,000 Kg jumbo jet just before takeoff when the thrust for each of its 4 engines is 35,000 N. a. Calculate the acceleration if you push with a 40 N horizontal force on a 2 Kg block on a horizontal friction-free air table. b. What acceleration occurs if the friction force is 20 N?