Motion, Force, and Gravity

Speed describes how fast a body moves:

measured in feet/second, miles per hour, meter/second, etc.

Instantaneous speed describes the speed at any instant.

Average speed describes the speed over some time period.

On a graph of distance versus time, we have found that the speed is the slope.

Look at Fig. 5.1 in text.

Note instantaneous and average speed.

In order to describe speed and direction, we have to be sure of our frame of reference. We describe position, velocity, etc. in a reference frame. Remember the train shooting the ball up.

All motion is relative to something. We don't think there is an absolute frame of reference.

Scalar: a scalar quantity describes magnitude only.

Vector: a vector quantity describes both direction and magnitude.

Describe where I am with respect to you. It doesn't suffice to say 3 m. That would be on a circle of radius 3 m. You also have to give the direction. You could say 3 m south, or 3 m toward the computer. We often find vectors necessary to describe motion.

We call a description of where something is located a position vector.

Look at Fig. 5.4 in text for good examples of position vectors.

Now let's define more precisely speed and velocity.

speed: only magnitude

velocity: magnitude and

direction.

 

 

Two cars moving with the same speed do not necessarily have the same velocity. One could be traveling north and the other south.

Look at Fig. 5.3 in text.

We use boldface to indicate vectors or arrows over the quantity.

acceleration is the rate of change of velocity.

note that v and a are vectors!

Look at Fig. 5.6.

Acceleration can be due to a change in speed or a change in direction.

Circular motion at constant speed is called centripetal acceleration.

Galileo is generally known as the father of physics.

He was the first to express many of our current ideas, for example inertia.

Inertia is the property of a body that causes it to remain at rest or in motion unless acted upon by an outside force. Galileo actually did experiments to show that bodies behaved this way.

Newton's 1^st Law

A body remains at rest or continues in uniform motion except when compelled to change its motion by forces acting upon it.

Also called the law of inertia.

We did experiments to clarify this law. What were they?

New concept:

momentum, p

p = mv

The momentum of a body is its mass times its velocity. It is a vector. Its direction is the same as the velocity.

SI units are kg m/s.

Consider the momentum of a ping pong ball and of a golf ball moving at the same speed. They both hit you. What happens?

What is a force?

A force is a push or pull. We used springs to express them.

A force is a vector.

There are four fundamental forces:

gravitational

electromagnetic

strong (nuclear)

weak (beta decay)

We must distinguish between external and internal forces.

External (or outside) forces are agents of change. Examples of internal forces are the electromagnetic ones holding the body together, both inside the atoms and between the atoms.

Most of the forces with which we are familiar are electromagnetic.

Newton's 2^nd Law

Force is defined as the rate of change of momentum.

The force and are vectors in the same direction.

The instantaneous force occurs over a very small D t.

The SI unit of force is the newton.

1 N = 1 kg m/s²

If we always use SI units, then the answer will always be in SI units. If we use velocity in cm/s, the answer will not be in N.

How is force related to acceleration?

Now if the mass m is constant, we have

This is the familiar form of Newton's 2^nd law that is valid when the mass is constant.

For a constant mass, the resulting acceleration is directly proportional to the external force.

Note again that if we use m and a in SI units (kg and m/s²), the resulting force will be in newtons.

Look at the examples.

Newton's 3^rd Law.

Whenever one body exerts a force on a second body, the second body exerts a force of equal magnitude and opposite direction on the first body.

"For every action, there is a equal and opposite reaction."

Think about examples:

Pushing on a wall.

Book resting on a table.

Holding a bag of groceries.

Spanking a child.

Driving a car into a tree.

Launching the space shuttle.

A book falling to floor.

Conservation of Linear Momentum.

In the absence of a net external force, the linear momentum of a body, or of a system of bodies, is always conserved.

Look at the definition of force:

If F = 0, then D p = 0, and momentum is constant (or conserved).

Look at Fig. 5.10 for examples of conservation of linear momentum. Playing billiards is a good example.

We will not study angular momentum.

Gravitation

Newton and Galileo both believed that in the absence of air resistance, all bodies falling to Earth have the same acceleration.

We call the acceleration with which a body falls to Earth, the acceleration of gravity and use the symbol g to denote it. It is fairly constant over the surface of the Earth, but decreases with altitude as we shall see.

F = ma = mg

The direction of g is towards the center of Earth.

Look at Fig. 5.14 in text.

When the air resistance F_air equals the force of gravity F_gravity, the body reaches its terminal speed or velocity. The total force is then zero, and there is no more acceleration, so the speed is constant. Air resistance tends to be proportional to speed.

Weight = F_g = mg

Direction is towards center of Earth.

If our mass is 100 kg, what is our weight?

F = mg = (100 kg)(10 m/s²)

= 1000 N

Projectile motion is always a parabola, because there is only a vertical force. The vertical speed changes due to gravity, but the horizontal speed is constant.

Newton's Law of Universal Gravitation

There exists an attractive interaction between any two material bodies in the universe, and the magnitude of the force on each body is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between their centers.

Newton figured out that the same force that causes an apple to fall to the ground from a tree is the same force that keeps the moon in its orbit. He worked out what the relationship must be.

where G is a constant, and m₁ and m₂ are the two masses, and r is the distance between the two bodies. The direction of the force is along the line between the masses. The force is attractive.

Kepler's Laws of Planetary Motion

Kepler's 1^st law:

each planet moves around the sun in an orbit that is an ellipse, with the sun at one focus of the ellipse.

Kepler's 2^nd Law:

the line joining a planet and the sun sweeps out equal areas of space in equal intervals of time.

Kepler's 3^rd Law:

the squares of the periods are proportional to the cubes of the average radii.

Look at Figs. 5.17, 5.18.

Look at Fig. 5.21.

Consider tides.