Chapter 2Forces and Motion

Section 1: Gravity and Motion

In Ancient Times, around 400 BC, a philosopher named Aristotle, thought that the rate objects fell depended on their mass.

Example: he thought a baseball would fall faster than a marble

In the late 1500’s a young Italian scientist named Galileo Galilei questioned this idea.

He thought that the mass of an object did not matter.

To prove this, he dropped two different cannonballs off of the Leaning Tower of Pisa in Italy

Objects fall to the ground at the same rate because the acceleration due to gravity is the same for all objects!!!.

Acceleration depends on both force and mass

A heavier object experiences a greater gravitational force than a lighter object does

But a heavier object is also harder to accelerate because it has more mass

The extra mass of the heavier object exactly balances the additional gravitational force so they fall at the same rate

Acceleration is the rate at which velocity changes over time

All objects accelerate toward Earth at a rate of 9.8 m/s2.

So for every second an object falls, the object’s downward velocity increases by 9.8m/s

You can calculate the change in velocity (∆v) of a falling object by using the following equation:

∆v = g × t

In this equation, g is the acceleration due to gravity on Earth (9.8 m/s2)

t is the time the object takes to fall (in seconds)

The change in velocity is the difference between the final velocity and the starting velocity

Calculating Velocity of Falling Objects:

A stone at rest is dropped from a cliff, and the stone hits the ground after a time of 3 seconds. What is the stone’s velocity when it hit the ground?

∆v = g × t = 9.8 m/s2 × 3 s = 29.4 m/s

To rearrange the equation to find time, divide by the acceleration due to gravity:

t = ∆v g

Your turn:

A penny at rest is dropped from the top of a tall stairwell. What is the penny’s velocity after it has fallen for 2 seconds?

The same penny hits the ground in 4.5 seconds. What is the penny’s velocity as it hits the ground?

A marble at rest is dropped from a tall building. The marble hits the ground with a velocity of 98 m/s. How long was the marble in the air?

An acorn at rest falls from an oak tree. The acorn hits the ground with a velocity of 14.7 m/s. How long did it take the acorn to land?

Air resistance: the force that opposes the motion of objects through air

Amount depends on size, shape, and speed of object

As speed increases, air resistance increases until it is equal to the downward force of gravity

Terminal Velocity: the constant velocity of a falling object when the force of air resistance is equal in magnitude and opposite in direction to the force of gravity

http://www.youtube.com/watch?v=1ukf2vntU44

Free Fall: the motion of a body of when only the force of gravity is acting on the body

Can only occur if there is NO AIR!!!!!

This is only in space and in a vacuum.

Astronauts are not weightless, but they are in Free Fall due to the lack of air

Orbiting: when an object is traveling around another object in space. (See figure 7 on page 40)

Centripetal Force: The unbalanced force that causes objects to move in a circular path

Gravity provides the centripetal force that keeps objects in orbithttp://www.youtube.com/watch?v=yyDRI

6iQ9Fw

Projectile Motion: the curved path that an object follows when thrown, launched, or otherwise projected near the surface of Earth

Has Two components:1. Horizontal motion – parallel to the

ground2. Vertical motion – perpendicular to the

ground

These components are independent of one another, so they have no effect on each other

When the two motions are combined, they form a curved path

Examples of projectile motion:

Frog leaping

Water sprayed by a sprinkler

Arrow shot by an archer

Section 2: Newton’s Laws of Motion

Newton’s First Law of Motion An object at rest remains at rest, and an object in motion remains in motion as a constant speed and in a straight line unless acted upon by an outside force

An object at rest is not moving. These objects will not move until a push or pull is exerted on them.

A moving object stops eventually because of the opposing force of friction.

Inertia: the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction until an outside force acts on the object

Newton’s First Law is sometimes called the Law of Inertia.

Mass is a measure of inertia

Newton’s Second Law of Motion The acceleration of an object depends on the mass of the object and the amount of force applied

Acceleration depends on Mass: the acceleration of an object decreases as its mass increases and vice versa

Acceleration Depends on Force: acceleration increases as the force of the object increases and vice versa; acceleration of an object is always in the same direction as the force applied

Newton’s second Law Mathematically:

a = F/m

Or

F = ma

Practice Problems:

What is the acceleration of a 3 kg mass if a force of 14.4 N is used to move the mass? (Note: 1 N is equal to 1 kg · m/s2)

a = F/m Replace F and m with the values

given in the problem, and solve a = 14.4/3 = 4.8 m/s2

You try!!

What is the acceleration of a 7 kg mass if a force of 68.6 N is used to move it toward Earth?

What force is necessary to accelerate a 1,250 kg car at a rate of 40 m/s2?

Zookeepers carry a stretcher that holds a sleeping lion. The total mass of the lion and the stretcher is 175 kg. The lion’s forward acceleration is 2 m/s2. What is the force necessary to produce this acceleration?

Newton’s Third Law of Motion: Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

Simply stated, all forces act in pairs; they are action and reaction forces.

Example: You sit on a chair. Your weight pushing down on the chair is an action force. The reaction force is the force exerted by the chair that pushes up on your body. The force is equal to your weight.

These forces do not always equal though or nothing would ever move!!

When the action and reaction forces are unbalanced, there is movement.

Section 3: Momentum

Momentum: a quantity defined as the product of the mass and velocity of an object

The more momentum an object has the harder it is to stop the object or change its direction

Calculating momentum (p):

p = mv

m = the mass of the object in kilograms

v = the object’s velocity in meters per second

units of momentum will be kg∙m/s

http://www.pbs.org/opb/circus/classroom/circus-physics/activity-guide-linear-momentum/

Practice Problems: What is the momentum of an ostrich with a mass

of 120 kg that runs with a velocity of 16 m/s north?

Write the equation: p = mv

Replace the m and v with the values given in the problem and solve:

p = 120 x 16

p = 1,920 kg· m/s north

You try!!

What is the momentum of a 6 kg bowling ball that is moving at 10 m/s down the alley toward the pins?

An 85 kg man is jogging with a velocity of 2.6 m/s to the north. Nearby, a 65 kg person is skateboarding and is traveling with a velocity of 3 m/s north. Which person has a greater momentum? Show your calculations.

Like velocity, momentum has a direction and its direction is always the same as the direction of the object’s velocity

The Law of Conservation of Momentum: states that any time objects collide, the total amount of momentum stays the same

is true for any collision if no other forces act on the colliding objects

law applies whether the objects stick together or bounce off each other after they collide

Objects sticking together:

after objects stick together they move together as one object (like a dog catching a ball)

the mass of the combined objects is equal to the masses of the two objects added together

When mass changes, velocity must change also

Objects Bouncing off Each other:

Momentum is usually transferred from one object to another

The transfer causes the objects to move in different directions at different speeds; however the total momentum of all the objects will remain the same before and after the collision

When action and reaction forces are equal and opposite, momentum is neither gained nor lost.