Physics chapter 4

What was aristotle’s view of the cause of motion?

• A force had to act for an object to move and that the velocity of the object was proportional to the strength of the force

• A heavy object would fall more quickly toward the earth than a lighter object, because there was a larger force pulling the object to the Earth.

What moves through the air more rapidly a rock or water?

A rock because water provides greater resistance to motion than air.

What keeps a ball moving?

• the force that was used on the ball initially has the after effect until gravity pulls the object downward 

• Once a ball or rock is thrown, the force that initially propels the object no longer acts once the ball leaves the hand. 

How did Galileo change Aristotle’s views?

• He developed new ideas like the tendency of a moving object continues to move: No force is required to maintain the motion. 

What is Galileo’s mathematical description of motion?

D = ½ at²

What did Newton accomplish?

• He proposed a theory of the causes of motion that could explain the motion of any object - the motion of ordinary objects such as a ball or chair as well as the motion of the moon and planets. 

If we push a chair across the floor, what causes the chair to move or stop moving?

• Newton's first and second law of motion

• His first two laws of motion address these questions and, in the process, provide part of the definition of force. 

• The first law tells us what happens in the absence of a force, and the second describes effects of applying force to an object

What is Newton’s first law of motion?

• An object remains at rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposed force. 

• In other words, unless there is a force acting on the object, its velocity will not change.

• if it is initially at rest, it will remain at rest; if it is moving, it will continue to do so with constant velocity. 

• The first law is contained in the second law

What is constant velocity

• The direction or magnitude of the of the velocity changes 

• When an object is at rest its velocity is zero and that value remains constant in the absence of an external force. 

is a force needed to keep an object in motion?

No unless it is heavy like a chair

What is frictional force

the existence of resistance

The resistance the floor plays on an object

if you push a chair will it go far?

• a chair will not move much farther after you stop pushing it because the frictional forces of the floor acting on the chair cause velocity to quickly decrease to zero.

how is a force related to acceleration?

Newton’s second law of motion

What is Newton’s second aw of motion?

• The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is in the same direction as that of the imposed force. 

What is the equation for Newton’s second law of motion?

a = Fnet/m 

a - acceleration 

Fnet- the total net force acting on the object

m - mass of the object 

• Since the acceleration is directly proportional to the imposed force, if we double the force acting on the object, we double the acceleration acting on the object 

• the same force acting on an object with a larger mass, will produce a smaller acceleration. Like a chair 

What are the quantities acceleration is determined by?

• the net force acting on the object 

• the mass of the object 

What is mass?

• the quantity that tells us how much resistance an object has to change in its motion

• the measure of an object's inertia, the property that causes it to resist a change in its motion.

• The standard unit for mass is kg

What is inertia

Resistance to a change in motion

How do we solve for Fnet

• multiplying both sides of the second law equation by the mass

Fnet = (m)(a)  

How do forces add?

• Our version of the second law implies that the imposed force is the total or net force acting on the object.

• if there is more than one force acting on an object, as there often is, we must add these forces as vectors, taking into account their directions 

Do forces oppose each other?

• Yes if a force is being pulled to the right and a frictional force is acting upon the object then the forces must be subtracted from one another. 

• The direction cannot be ignores

How is the first and second law related

• The first law is contained in the second law but newton found it very important to state the first law as a separate law as to counter the long-standing beliefs about motion

• The relationship between the two laws can be demonstrated by asking what happens, according to the second law, when the net force acting on an object is zero. 

• If the acceleration is zero the velocity must be constant 

• The first law tells us that if the net force is zero the object moves with constant velocity (or remains at rest)

What is the difference between frictional force and inertia?

• Frictional force is a resistive force that occurs when two surfaces are in constant motion or attempt to move relative to each other.

Ex. When you push a box across the floor the frictional force between the box and floor resist your push 

• Inertia is a property of matter that describes its resistance to change in its state of motion (rest or uniform motion) 

• not a force, not a property, does not have direction or magnitude

Ex.  According to Newton’s first law of motion, your internal organs (like your stomach) resist change. When the coaster drops quickly, the rest of your body moves with it, but your internal organs lag slightly behind due to inertia. This relative motion created the sensation of your stomach “floating” or “dropping” 

Is your weight the same as your mass or is there a difference in the meaning of these two terms

• Weight is a familiar term often used interchangeably with mass in everyday language. 

• Mass is the amount of matter in the object.

• Weight is the gravitational force acting on an object 

How can masses be compared?

• mass is defined as the property of matter that determines how much an object resists a change in its motion. 

• The greater the mass, the greater the inertia, or resistance to change, and the smaller the acceleration provided by a given force. 

Do objects with different masses stop the same way

• If we try to stop a blowing ball and a ping pong ball each having the same velocities; a much greater force is required to stop the bowling ball than the ping pong ball because of its mass. 

• The force required is proportional to the mass. 

• If we use the same forces to accelerate different masses, the different accelerations could be used to compare the masses involved. 

How do we define weight?

• The more common method of comparing masses is to “weigh” the objects on a balance or a scale. 

• The gravitational force acting on an object is the weight of the object. 

• The unit for weight is W 

how is weight compared to mass?

• Objects of different mass experience the same gravitational acceleration near the Earth's surface (g = 9.8 m/s^2)

• The natural acceleration is caused by the gravitational force exerted by the Earth which equals the weight of the object. 

• The force (weight) is equal to the mass times the acceleration.

W = mg 

W - weight 

m - mass 

g - acceleration (9.8 m/s^2) 

How many newtons are in 1 lb?

4.45 Newtons

How many pounds equal 1 kilogram

2.2 pounds

How many kilograms are equal to 1 pound

.453 kilograms

What if a woman traveled to the moon would she weight the same as she did on earth?

• No, the gravitational acceleration of the moon is ⅙ of the Earth’s.

• Instead of the gravitational acceleration being 9.8 it would be 1.63.

Why is the gravitational acceleration independent of mass?

• We use the gravitational force to determine the acceleration.

• by Newton’s second law the acceleration can be found by dividing the force W = mg by the mass:

a = mg/m = g 

a - acceleration 

m- mass

g - gravitational acceleration (9.8) 

• mass cancels out the equation 

Are force and acceleration the same?

• no, they are not the same, although they are closely related. 

• a heavy object experiences a larger gravitational force (its weight) than a lighter object, but the two objects will have the same gravitational acceleration.

What is Newton’s third law of motion

• If object A exerts a force on object B, object B exerts a force on object A that is equal in magnitude but opposite in direction to the force exerted on B.

what is Newton’s third law in symbolic form

F2 = -F1 

• the minus sign indicates that two forces have opposite directions. 

• The force F2 is acting on you and partly determines your own motion, but has nothing to do with the motion of the chair. 

• Of the paired forces the only one that affects the motion of the chair is the one acting on the chair F1

What is the action/reaction principle

• for every action there is an equal but opposite reaction.

• forces act on two different objects, never the same object.

if you push on an object does it have a force back onto you?

• Yes, if you exert a force on a chair the chair is exerting a force back onto you.

How can we use the third law of to define forces?

• First, we identify other objects that interact with the object of interest 

• Consider a book lying on a table, what objects are interacting with the book?

• because the book is in direct contact with the table, the book must be net reacting with the table, but also with the earth because of its gravitational attraction.

• The downward pull of gravity that the earth exerts on the book is the book's weight W.

• The object interacting with the book to produce this force is the Earth itself. 

• The book and earth are attracted to each other through gravity with equal and opposite forces. 

• the earth pulls down on the book with the force W and the book pulls upward on the force -W

What is a normal force

• perpendicular to the surfaces of contact 

• if a second force is acting upon the book that is lying on the table it is the normal force which is an upward force exerted on the book by the table. 

• The book then exerts an equal but opposite force on the table directed downward -N. 

Can a mule accelerate a cart

• The cart is and acting force that is pulling on the mule

• The mule is the reacting force that is pulling the cart

• The harder the mule pulls on the cart the harder the cart pulls back

• The mule is able to move the cart because of the frictional force of the ground that the mule uses to pull the cart. 

• The frictional force the mule uses must be larger than the frictional force acting on the cart. 

What forces cause a car to accelerate

• The engine cannot push the car because it is part of the car.

• The engine drives either the rear or front axle of the car, which causes the tires to rotate. 

• The tires in turn push against the road surface through the force of friction between the tires and the road. 

• the road must then push against the tires with equal but oppositely directed force.

• The external force causes the car to accelerate. 

if a woman is standing on a scale in an elevator will it read her true weight?

• There are two forces acting on the woman: the earth pulling down on her from gravity and the scale pushing upward on her. 

• If the elevator is accelerating upward with an acceleration of a, the woman must also be accelerating upward at that rate. 

• The net force must also be upward which implied that the normal force is larger than the gravitational force. 

Fnet = N - W = ma

• The woman exerts a downward force on the scale equal to the normal force.

• The woman’s true weight has not changed, but the scale will read that it has increased by an amount equal to ma.

N = W + ma

What happens to the women’s weight if it is accelerate downward?

• The normal force will be less than her weight 

• The scale will be reading she weighs less than she does.

What id the cable of the elevator breaks?

• Both the woman and the elevator will accelerate downward 

• Because the woman’s weight is all that is required to give her the acceleration the normal force on her feet will be zero because she is accelerating on her own with no other acting forces 

• The scale reading will be zero and she will appear weightless. 

What forces are involved in a moving chair

• Four forces act on a chair from four separate interactions

1. the force of gravity (the weight) W, due to interaction with the Earth. 

2. The upward normal force exerted by the floor due to compression of the floor, N.

3. The force exerted by the hand pushing, P.

4. The frictional force exerted by the floor, F. 

• The normal force and frictional force both have to do with the interaction of the floor. 

• The weight and normal force acting on each other cancel one another out. 

• The sum of the vertical forces are 0. 

• The push of the hand and the frictional force do not cancel out and determine the horizontal force. 

• The push from the hand must be larger than the frictional force to make the chair move.

P-f 

• Once the chair is accelerated the strength of the push is reduced so that it is equal to the frictional force. 

• the net horizontal force then becomes 0.

• if the push is sustained then the chair moves across the floor with constant velocity. 

• When the hand is removed from the chair after a push its velocity quickly decelerated to zero under the influence of frictional force 

Does a skydiver accelerate

• The sky diver has an initial acceleration of (9.8) but as her velocity increases, the force of air resistance becomes significant and her acceleration decreases. 

What is terminal velocity

• When the net force is 0 and the skydiver keeps accelerating.

• From there on she moves downward with constant velocity. 

What happens when a ball is thrown? What forces are in act?

• the initial push (thrower)

• the downward pull of gravity

• And air resistance 

• When a ball is thrown the initial velocity does not matter after it is thrown

• The gravitational force and the air resistive force produce changes in the ball's velocity. 

• The gravitational force accelerates the ball downward and the air resistive force acts in a direction opposite to the velocity, gradually reducing the ball's velocity.