### What were the two chapters we had to read for tonight?

Should we have a quiz?

# gravity and fluid dynamics

## the universal law of gravitation

In ancient times, Aristotle and others believed that stars, planets, and the Moon moved in divine circles, free from forces of Earth.

## the fact of the falling moon

We now know that the Moon falls around Earth in the sense that it falls beneath the straight line it would follow if no force acted on it.

The Moon maintains a tangential velocity, which ensures a nearly circular motion around and around Earth rather than into it. This path is similar to the paths of planets around the Sun.

## The universal law of gravitation

• Every body in the universe attracts every other body with a mutually attracting force.
• For two bodies, this force is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them,

## the universal law of gravitation

Newton discovered that gravity is universal.
In other words, every mass pulls on every other mass!

## the inverse square law

If the masses of two planets are each somehow doubled, the force of gravity between them

1. doubles.
3. reduces by half.
4. reduces by one quarter.

## THE INVERSE SQUARE LAW

If the masses of two planets are each somehow doubled, the force of gravity between them

1. doubles.
3. reduces by half.
4. reduces by one quarter.

## The Universal Gravitational Constant, G

G is the proportionality constant in Newton’s law of gravitation.

G has the same magnitude as the gravitational force between two 1-kg masses that are 1 meter apart:

## weight and weightlessness

Weight
is the force exerted against a supporting floor or weighing scale.
Weightlessness
is a condition wherein a support force is lacking—free fall, for example.

## projectile motion

A projectile is any object that moves through the air or through space under the influence of gravity.

Curved path of projectile (parabola)

Example:

A stone thrown horizontally curves downward due to gravity.

## projectile motion

Interactive Projectile Tutorial

Interactive Figure for answer!

## projectile altitude and range

For equal launching speeds, the same range is obtained from two different projection angles—a pair that add up to 90°.

## Fast-Moving Projectiles—Satellites

A satellite is any projectile moving fast enough to fall  continually around the Earth.

To become an Earth satellite, the projectile’s horizontal velocity must be great enough for its trajectory to match Earth’s curvature.

## FAST-MOVING PROJECTILES—SATELLITES

The Earth’s curvature drops a vertical distance of 5 meters for each 8000 m tangent to the surface. So to orbit Earth, a projectile must travel 8000 m in the time it takes to fall 5 m.

## satellites

As the ball leaves the girl’s hand, one second later it will have fallen
1. 10 meters.
2. 5 meters below the dashed line.
3. less than 5 meters below the straight-line path.
4. None of the above.

## circular satellite orbits

Hewitt video on giant bowling alleys.

Interactive Orbital Trajectories of Cannonballs

## escape speed (velocity)

Escape speed is the initial speed that an object must reach to escape gravitational influence of Earth
11.2 kilometers per second from Earth’s surface

What is a fluid?

## density

• Important property of materials (solids, liquids, gases)
• Measure of compactness of how much mass an object occupies
• “lightness” or “heaviness” of materials of the same size

## pressure

Why can a dull knife still cut through a piece of clay?
Pressure is the force per unit area that one object exerts on another

## pressure in a liquid

• Force per unit area that a liquid exerts on something
• Depth dependent and not volume dependent

Example: Swim twice as deep and the pressure due to the weight of water above you is twice as much. (For total pressure, add to this the atmospheric pressure acting on the water surface.)

Hewitt Video on pressure

## pressure in a liquid

Pressure in a liquid is independent of the shape of the container, and pressure at a particular depth is the same

## water tower

Why do towns have water towers?
(it might not be why you think!)

## boyancy in a liquid

Boyancy is the apparent loss of weight of a submerged object.

The amount of weight equals the weight of water displaced

## archimedes's principle

Archimedes's Principle states that an immersed body (completely or partially) is buoyed up by a force equal to the weight of the fluid it displaces.

The principle applies to liquids and gasses!

## archimedes's principle

Displacement rule: A completely submerged object always displaces a volume of liquid equal to its own volume.

## archimedes's principle

Flotation: A floating object displaces a weight of fluid equal to its own weight.  In other words, the more fluid that gets displaced, the greater the boyant force.

## check question

The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water

1. the buoyant force is greater.
2. a person feels less heavy.
3. a smaller volume of water is displaced.
4. None of the above.

## check question

The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water

1. the buoyant force is greater.
2. a person feels less heavy.
3. a smaller volume of water is displaced.
4. None of the above.

A floating person has the same buoyant force whatever the density of water. A person floats higher because a smaller volume of the denser salt water is displaced.

Even denser?  Mercury!

## Man sitting in Mercury

(do not try this at home)
(although you'd probably be fine)

## cHECK QUESTION

On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoam-filled preservers.

1. He apparently doesn’t know his physics.
2. He is correct.

## check question

On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoam-filled preservers.

1. He apparently doesn’t know his physics.
2. He is correct.

He’s correct, but what he doesn’t tell you is you’ll drown! Your life preserver will submerge and displace more water than those of your friends who float at the surface. Although the buoyant force on you will be greater, the net force downward is greater still!

## pressure in a gas

Double the density of air by:

1. Doubling the amount of air
2. Decreasing the volume by half

## boyle's law

• States that pressure X volume is a constant for a given mass of confined gas regardless of changes in pressure or volume (with temperature remaining unchanged)
• pressure X volume = constant means that P1V1 = P2V2

When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon

1. is 0.8 its former pressure.
2. remains the same if you squeeze it slowly.
3. is 1.25 times greater.
4. is 8 times greater.

## boyle's law

When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon

1. is 0.8 its former pressure.
2. remains the same if you squeeze it slowly.
3. is 1.25 times greater.
4. is 8 times greater.

Boyle’s law: P(1.0 V) = 1.25 P(0.8 V).

## pascal's principle

• Discovered by Blaise Pascal, a scientist and theologian in the 17th century
• States that a change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid
• Applies to all fluids—gasesand liquids

## pascal's principle

Application in a hydraulic press

## Buoyancy in a gas

• Archimedes’ principle applies to fluids—liquids and gases alike.
• Force of air on bottom of balloon is greater than force on top.
• Net horizontal forces cancel, but not vertical ones, which supplies the buoyant force.
• And this buoyant force equals the weight of displaced air!

## check question

Is there a buoyant force acting on your classmates at this moment? Defend your answer.

1. No. If there were, they would float upward.
2. Yes, but it is insignificant compared with their weights.
3. Only in water, but not in air.
4. None of these.

## check question

Is there a buoyant force acting on your classmates at this moment? Defend your answer.

1. No. If there were, they would float upward.
2. Yes, but it is insignificant compared with their weights.
3. Only in water, but not in air.
4. None of these.

## fluid flow

Continuous flow
• Volume of fluid that flows past any cross-section of a pipe in a given time is the same as that flowing past any other section of the pipe even if the pipe widens or narrows.
• Fluid speeds up when it flows from a wide to narrow pipe
• Motion of fluid follows imaginary streamlines

## Bernoulli’s Principle

• Discovered by Daniel Bernoulli, a 15th century Swiss scientist
• States that where the speed of a fluid increases, internal pressure in the fluid decreases
• Applies to a smooth, steady flow

By Chris Gregg

• 7,980