What do you remember from Physics 53?

Review

Newton’s Law of Universal Gravitation

Every particle in universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles.

F = G m1m2/r2

Question

1. The Moon falls around the Earth than straight into it. If tangential velocity were zero, how would the Moon move?

2. According to the equation for gravitational force, what happens to the force between two bodies if the mass of one of bodies is doubled? If both masses are doubled?

The Universal Gravitational Constant G

F = Gm1m2/d2

G = 6.67 10-11 Nm2/kg

Questions

1. If there is an attractive force between all objects, why do we not feel gravitating toward massive buildings in out vicinity?

2. Consider an apple at the top of the tree that is pulled by Earth’s gravity with a force of 1 N. If the tree were twice as tall, would the force of gravity be only ¼ as strong? Defend your answer.

Question

In what sense is drifting in space far away from all celestial bodies like stepping off the table?

Momentum

When we combine the ideas of inertia and motion we are dealing with momentum

By momentum we mean inertia in motion. More specifically momentum is defined as the product of the mass of an object and its velocity, that is:

momentum = mass x velocity

When direction is not important

momentum = mass x speed.

Impulse

Impulse = Force x Time interval

Assume that your friend jumps from the roof of the garage and lands on the ground. How will the impulses the ground exerts on your friend compare if the landing is on grass or on concrete?

Conservation of Momentum

To change a momentum we must apply some impulse…

In other words, the force or impulse must be exerted on the object or any system of objects by something external to the object.

Questions

1. A high-speed bus and an innocent bug have a head-on collision. The sudden change of momentum for the bug spatters it all over the windshield. Is the change in momentum of the bus greater, less or the same as the change in momentum experienced by the unfortunate bug?

2. The Starship Enterprise is being in space by a Klingon warship moving at the same speed. What happens to the speed of the Klingon ship when it fires a projectile at the Enterprise? What to the speed happens of the Enterprise when it returns the fire?

1. How does the padding (or air pockets) in the soles of running shoes reduce the forces on your legs? Explain your answer in terms of impulse and momentum.

2. Two identical objects moving at the same speed collide head-on. If the two objects stick together after the collision, will they move to the right, left not at all?

1. An astronaut training at the Craters of the Moon in Idaho jumps off platform in full space gear and hits the surface at 5 m/s. If later, on the Moon, the astronaut jumps from the landing vehicle and hits the surface at the same speed, will the impulse be larger, smaller, or the same as that on Earth? Why?

2. An object of mass m and an object of mass 3m, both moving at the same speed, collide head-on. If the two objects stick together after the collision, will they be moving to the left, to the right or not at all?

Some times a star “dies” in an enormous explosion know as a supernova. What happens to the total momentum of such a star?

Work

For the simplest case, where the force is constant and the motion takes place in a straight line in the direction of the force we define the work done on an object by applied force as a product of the force and the distance through which the object is moved. In shorter form

Work = force x distance

Conceptual Question

Does Earth do work on Moon?

Important: Definition of work involves both a force and a distance.

Units of Work

1 J = 1 N m

Power

Power = work done/time interval

Units of Power

1 W = 1J/s

Mechanical Energy

We can define energy as “the ability

to do work”.

Conservation of Kinetic Energy

Question

Are the collisions of billiard balls perfectly elastic?

Important: The change in potential energy between any two points does not depend on the choice of reference level.

Important: The changes in gravitational potential energy depend only on the change in vertical height and not on the path taken.

PE of Elastic Spring

Important: Potential energy belongs to a system, and not to a single object alone!!!! The potential energy is a property of a system as a whole.

Mechanical Energy and its Conservation

If no frictional (or other dissipative) forces are involved, the total mechanical energy of a system neither increases nor decreases in any process. It stays constant – it is conserved.

Conceptual Example: Speeds on Two Water Slides

Two water slides at a pool are shaped differently, but have the same length and start at the same height h. Two riders, Paul and Kathleen, start from rest at the same time on different slides.

(a) Which rider, Paul or Kathleen, is traveling faster at the bottom?

(b) Which rider makes it to the bottom first?

1. In tryouts of the national bobsled team, each competing team pushes a sled along a level, smooth surface for 5 meters. One team brings a sled that is much lighter than the others. Assuming that this team pushes with the same force as the others, compare the kinetic energy of the light sled to that of the others after 5 meters . Compare the momentum of the light sled to that of the others after 5 meters.

2. Suppose the rules were changed in previous question so that the teams pushed for a fixed time of 5 seconds rather that a fixed distance of 5 meters. Compare the momentum of the light sled to that of the others after 5 seconds. Compare the kinetic energy of the sled to that of the others after 5 seconds.

1. Does a car consume more fuel when its air conditioner is turned on? When its lights are on? When its radio is on while it is sitting on the parking lot?

2. Rows of wind-powered generators are used in various windy locations to generate electric power. Does the power generated affect the speed of the wind? That is, would locations behind the “windmills” have more wind if the windmills weren’t there?

1. Mountain highways often have emergency ramps for truckers whose brakes fail. Why are these covered with soft dirt or sand rather that paved?

2. A physics textbook is launched up a rough inline with a kinetic energy of 200 J. When the book comes momentarily to rest near the top of incline, it has gained 180J of gravitational potential energy. How much kinetic energy will it have when it returns to the launch point?

1. When you get your power bill, you are charged for the number of kilowatt-hours that you have used. Is kilowatt-hour a unit of power or a unit of energy?

2. Athletes will sometimes run along the beach to increase the effect of their workouts. Why is running on soft sand so tiring?

3. Which of the following is not a unit of energy: joule, Newton-meter, kilowatt-hour, watt?

Rotational Motion

Question

On a rotating platform, if you sit halfway between the rotating axis and the outer edge and have a rotational speed of 20 RPM and tangential speed of 2 m/s, what will be the rotational and tangential speeds of your friend, who sits on the outer edge?

Questions

1. Consider balancing a hammer upright on the tip of your finger. If the head of hammer is heavy and the handle long, would it be easier to balance with the end of the handle on your finger so that the head is at the top, or the other way around with the head at your fingertip and the end of the handle on the top?

2. Consider a pair of meter sticks standing nearly upright against the wall. If you release them, they’ll rotate to the floor in the same time. But what if one has a massive hunk of clay stuck to its top end? Will it rotate to the floor in a longer or shorter time?

1. A figure skater is spinning with her arms held straight out. Which has greater rotational speed, her shoulders or her fingertips? Why?

2. You are looking down on a merry-go-round and observe the it is rotating clockwise. What is the direction of the merry-go-round rotational velocity? If the merry-go-round is slowing down, what is the direction of its rotational acceleration?

3. What is the direction of rotational velocity of Earth?

1. Earth rotational speed is slowing due to tidal influences of the Sun and Moon. What is the direction of Earth’s rotational acceleration?

2. Two flywheels have the same mass but one of them is much thinner than the other so that its radius is twice that of the other one. If both flywheels are spinning about their axes at the same rate, which one would be harder to stop? Why?

Torque

Balancing a Seesaw

Newton’s first Law for Rotation

The angular velocity of an object remain constant unless acted on by an unbalanced torque.

Newton’s Second Law for Rotation

= I

Conceptual Example: Who’s fastest?

Several objects roll without slipping down an inline of vertical height H, all starting from rest at the same moment. The objects are: thin hoop, a marble, a solid cylinder an empty soup can. In addition a greased box slides down without friction. In what order do they reach the bottom of the incline?

Angular Momentum and its Conservation