Acceleration and Momentum - PowerPoint Presentation

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Acceleration and Momentum

Chapter 4

4-1 Accelerated Motion

Newton’s Second Law of Motion:

Definition:

A net force acting on an object causes the object to accelerate in the direction of the force.

The magnitude of acceleration is affected by the size of the force and the mass of the object.Equation**F = ma Where F = Force (Newton) [N] m= Mass (kilogram) [kg] a= acceleration [m/s2]

Example:

How much force is needed to accelerate a 70.0 kg rider and her 200.0 kg motorcycles at 4.0 m/s

2

?

Solution

F=ma = 270 x 4 = 1080. (2 significant figures) = 1100 N.

Practice Problems:

It takes a force of 3000.0 N to accelerate an empty 1000.0 kg carat 3.0 m/s

2

. If a 160.0 kg wrestler is inside the car, how much force will be needed to produce the same acceleration

?A 63.0 kg skater pushes off from a wall with a force of 300.0 N. What is the skater’s acceleration?

Falling Objects:

Near Earth’s surface, gravity causes all falling objects (no matter the size) to accelerate at 9.81 m/s2.

Since weight is calculated using gravity, we can rewrite the force equation to solve for weight…

**

FW = mg** Where FW = Force of weight m = mass g = acceleration of gravity

Acceleration due to gravity is the same for all objects.

Discounting all other forces, all objects accelerate at the same rate.

So

why don’t feathers fall at the same rate as billiard balls, despite what we’ve just learned?

Anything that moves in Earth’s atmosphere is affected by air resistance.

Air Resistance: The force air exerts on a moving object.It acts in the opposite direction of a falling object’s motion.

The larger the object, the greater the air resistance.

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youtu.be/ur40O6nQHsw

Terminal Velocity:

Air resistance will increase on a falling object until it balances the pull of gravity.At this point, the object will no longer be accelerating.This is called

t

erminal velocity

.Terminal Velocity: The highest velocity that will be reached by a falling object.

4-2: Projectile Motion and Circular Motion

Projectiles:

Thus far, we have been looking at objects that are moving in a straight line.

We need to recognize that most objects don’t move in straight lines…

Wheels spin, cars turn, and anything thrown/shot into the air eventually curves back toward Earth.Anything thrown or shot into the air is called a projectile.Shot arrows and basketballs, thrown baseballs, hit golf balls are all projectiles.Projectiles follow curved paths called parabolas.

What happens to an object after it is shot or thrown?

The forward motion is called horizontal motion.Once released, there are no accelerating forces, so horizontal motion remains constant.

Gravity begins to act on the projectile, creating

vertical motion

.Horizontal and vertical motion are completely independent of one another.If you were to throw a ball from shoulder height and another ball is just dropped from the same height, which travels farther horizontally?Which ball hits the ground first?

Moving in Circles:

When objects are moving in circular paths, they are accelerating.Remember, that acceleration is a change in speed, direction, or both.Centripetal Acceleration:

Acceleration toward the center of a curved or circular path.

Just think of what happens when you turn sharply on a bike.

Your body and the bike lean inward toward the center of the curved motion.For acceleration to occur, there must also be an unbalanced force acting in the direction of the center of the circle.Centripetal Force: A force that causes a moving object to move in a curved or circular path.It usually counters an object’s inertia.Car tires take advantage of this when turning sharply to avoid sliding or flipping.

Weightlessness in Orbit:

To be truly weightless, you have to be completely free of the effects of gravity.Astronauts are not truly weightless.Everything, including the shuttle, are falling toward the Earth as exactly the same rate, creating a sense of weightlessness.

4-4: Action and Reaction

Newton’s Third Law of Motion

:

“To every action, there is an equal and opposite reaction.”

**Important** Action-reaction forces always act on different objects. So even though the forces may be equal, they are not balanced.In swimming, the swimmer’s action force pushes on the water, while the water exerts a force of reaction on the person.Examples: Letting go of a balloon full of air, or getting kicked by a gun that is being fired.

Rocket Propulsion:

Acts the same way as a balloon full of air being released.The burning fuel produces hot gases that push against the rocket to escape out the bottom.

Momentum

:It is easier to stop a toy truck moving at 3 m/s than a real truck moving at the same speed.The real truck has more momentum.

Momentum

is a property a moving object has due to its mass and velocity

**Equation**p = m x v Where p = momentum m = mass v = velocityUnit: kg*m/s, and requires direction.

Example

Compare the momentums of a 5.0 x 101 kg dolphin swimming at 16.4 m/s and a 6300 kg elephant walking at 0.11 m/s.

Solution

Momentum of a dolphin:p = mv = 50 x 16.4 = 820 kg*m/s

Momentum of an elephant:

p

= mv = 6300 x 0.11 = 693 = 690 kg*m/s

Momentum doesn’t change unless its mass, velocity, or both, change.

Momentum can be transferred from one object to another.Example: When playing billiards, the cue ball is moving and carrying all of the momentum. When it strikes a resting billiard ball, the one at rest begins to move and the cue ball slows and loses momentum.

The Law of Conservation of Momentum

states that the total amount of momentum of a group of objects does not change unless outside forces act on the objects.If you were to measure the total momentum of the two billiard balls before and after the collision, it would be the same!

What causes the balls to eventually stop?