4.1-Describing Motion: Examples from Daily Life

Speed

The rate at which an object moves. Its units are distance divided by time, such as m/s or km/hr

Speed of a car

tells us how far it will go in a certain amount of time

• ex: 100 km per hour is a speed, and it tells us that the car will cover a distance of 100 km if it is driven at this speed for an hour

Velocity

the combination of speed and direction of motion; it can be stated as a speed in a particular direction, such as 100 km/hr due north

Velocity of cars

of the car tells us both its speed and its direction

• ex: 100 km/hr going due north describes a velocity

Acceleration

the rate at which an object’s velocity changes. its standard units are meters per second squared (m/s²)

Acceleration of a car

has an acceleration if its velocity is changing in any way, whether in speed or direction or both

While we normally think of acceleration as an increase in speed…

in science we also say that you are accelerating when you slow down or turn

Slowing

represent a negative acceleration, causing your velocity to decrease

Turning

means a change in direction-which therefore mens a change in velocity-so turning is a form of acceleration even if your speed remains constant

You can often feel the effects of what?

acceleration

• ex: as you speed up in a car, you feel yourself being pushed back into your seat. as you slow down, you feel yourself being pulled forward. as you drive around a curve, you feel yourself being pushed away from the direction of your turn.

• in contrast you don’t feel such effects when moving at a constant velocity-why you don’t feel any sensation of motion when you’re traveling in an airplane on a smooth flight

1 of most important types of acceleration…

is the acceleration caused by gravity

Galileo’s experiment

Supposedly dropped weights from the leaning tower of Pisa, Galileo demonstrated that gravity accelerates all objects by the same amount, regardless of their mass

• The feather floats gently to the ground, while a rock plummets. However, air resistance causes this difference in acceleration

  • If you dropped a feather at the rock on the moon, where there is no air, both would fall at exactly the same rate

Acceleration of gravity

acceleration of a falling object (on earth-designated by g, is 9.8 m/s²)

Acceleration of Gravity on Earth

• causes falling objects to fall faster by 9.8 meters per second or about 10 m/s, with each passing second

  • ex: drop a rock from a tall building. the moment you let it go, its speed is 0 m/s. after 1 second, the rock will be falling downward at about 10 m/s. after 2 seconds, it will be falling at about 20 m/s. in the absence of air resistance, its speed will continue to increase by about 10 m/s each second until it hits the ground

• the acceleration of gravity is about 10 meters per second per second, or 10 meters per second squared (10 m/s²)

The concepts of speed, velocity, and acceleration…

Describe how an individual object moves

Most of the interesting phenomena we see in the universe…

Result from interactions between objects

Momentum

the product of an object’s mass and velocity: momentum = mass x velocity

• The only way to change an objects momentum is to apply a force to it

Force

Anything that can cause a change in momentum

Momentum example: effects of collisions

• Stopped in your car at a red light when a bug flying out of velocity of 30 km/hr due south slams into your windshield

  • Nothing much will happen to your car

• 2 ton truck runs the red light and hits you head on with the same velocity as the bug

• The truck will cause far more damage. We can understand why by considering the momentum and force in each collision

• Before the collisions, the trucks much greater mass means it has far more momentum than the bug, even though both the truck and the bugs are moving with the same velocity

• During the collisions, the bug in the truck need to transfer some of their momentum to your car

• Bug has very little momentum to give to your car, so it does not exert much of a force

• The truck and parts enough of its momentum to cause a dramatic and sudden change in your cars momentum

• you feel the sudden change in momentum as a force, and it can do great damage to you and your car

The mere presence of a force…

doesn’t always cause a change in momentum

• ex: a moving car is always affected by forces of resistance and friction with the road-Forces that will slow your car if you take your foot off the gas pedal. However, you can maintain a constant velocity, and hence constant momentum, if you step on the gas pedal hard enough to overcome the side effects of these forces

Forces of some kind…

Always present, such as the force of gravity or the electromagnetic forces acting between atoms

Net force

The overall force to which an object responds; the net force is equal to the rate of change in an objects momentum, or equivalently to the objects mass X acceleration

• (overall force) acting on an object represents the combined effect of all the individual forces put together

• Change in momentum occurs only when the net force is not zero

There is no net force on your car when you are…

Driving at constant velocity, because the force generated by the engine to turn the wheels precisely offsets the forces of air resistance and road friction

• Change in momentum occurs only when the net force is not zero

Change in an objects momentum means what?

Changing its velocity, as long as it's mass remains constant

• A net force that is not zero therefore causes an object to accelerate

Whenever an object accelerates…

a net force must be causing the acceleration

• That's why you feel forces (pushing you forward, backward, or to the side) you accelerate in your car

How do planets accelerate?

Are always accelerating as they orbit the sun, because their direction of travel constantly changes as they go around their orbits. We can therefore conclude that some force must be causing this acceleration. Isaac newton identified this force as gravity

Ex: Ice Skater

• Think about an ice skater spinning in place

• He isn't going anywhere, so he has no overall velocity and hence no overall momentum

• The part of his body is moving in a circle as he spins, so these parts have momentum even though his overall momentum is zero

• There is a way to describe the total omentum from each part of his body as he spins, it's called angular momentum

angular Momentum

Momentum attributable to rotation or revolution. The angular momentum of an object moving in a circle of radius r is the product of its mass, velocity, and radius M x V x R

• “circling momentum/ turning momentum”

Any object that is either spinning or moving along a curved path…

Has angular momentum, which makes angular momentum very important in astronomy

• Has angular momentum due to its rotation (rotational angular momentum) and to its orbit around the sun (orbital angular momentum)

How does an objects angular momentum change?

Only when a special type of force is applied to it

• That force is called a torque

• ex: opening a door means making it rotate on its hinges, which means giving the door some angular momentum. Pushing directly on the hinges will have no effect on the door, even if you push with a very strong force. However, even a light force can make the door rotate if you push on the part of the door that is farthest from its hinges. The amount of torque depends not only on how much force is applied, but also on where it is applied

Torque

Twisting force that can cause be a change in an objects angular momentum

Ex of Torque: changing a tire

• Turning the bolts on a tire means making them rotate, which requires giving them some angular momentum

• A longer wrench allows you to push from further out than you can with the short wrench, so you can turn the bolts with less force

Mass

A measure of the amount of matter in an object (or body)

Weight

The net force that object applies to its surroundings; in the case of a stationary body on the surface of earth, it equals mass X acceleration of gravity

• your weight: Force that a scale measures when you stand on it; that is, weight depends both on your mass and on the forces (including gravity) acting on your mass

Ex of mass and weight: standing on a scale in an elevator

• Will be the same matter how the elevator moves, but your weight can vary

• When the elevator is stationary or moving at constant velocity, the scale reads your “normal” weight

• Elevator accelerates upward, the floor exerts a greater force than it does when you are at rest-you feel heavier, and the scale verifies your greater weight

• In the elevator accelerates downward, the floor and the scale exert a weaker force on you, so the scale registers less weight

• Scale shows a weight different from your “normal” weight only when the elevator is accelerating, not when it is going up or down at a constant speed

Your mass therefore depends…

Only on the amount of matter in your body and is the same anywhere, but your weight can vary because the forces acting on you can vary

• ex: this will be the same on the Moon as on earth, but you would weigh less on the moon because of its weaker gravity

What happens if the elevator cable brakes?

Elevator and you are suddenly in free-fall-without any resistance to slow you down

• Drops away at the same rate that you fall, allowing you to “float” freely above it, and the scale reads zero because you are no longer held to it. In other words your freefall has made you weightless

Free-fall

Condition in which an object is falling without resistance, objects or weightless when in free-fall

Weightless

Weight of zero, as occurs during free-fall

You are in free–fall whenever…

Nothing to prevent you from falling. For example, you are in free – fall when you jump off a chair or sprain from a diving board or trampoline

Why are astronauts weightless?

are weightless the entire time they orbit earth because they are in a constant state of free-fall

Ex to understand why astronauts are weightless

• Imagine a tower that reaches all the way to the space station orbit, about 350 km above earth

• You stepped off the tower, you would fall downward, remaining weight list until you hit the ground (or until air resistance had a noticeable effect on you)

• Imagine, that instead of stepping off the tower, you ran and jumped out of the tower

• You'd still fall to the ground, but because of your forward motion, you'd land a short distance away from the base of the tower

• the after you ran out of the tower, the farther you to go before landing

• You could somehow run fast enough – about 28,000 km/hour at the orbital altitude of the space station – very interesting thing would happen: downward as far as the life of the tower, and already have moved far enough around earth that you don't no longer be going down at all. Instead, I'd be just as high above earth as you've been all along, but a good portion of the way around the world -orbiting earth

How does the moon orbit earth?

Most people know that the moon orbits earth because of gravity, proving that there is gravity in space. In fact, at the altitude of the space station orbit, the acceleration of gravity is only about 10% less than it is on earth surface