Mechanics

A clothesline hangs between two poles. No matter how tightly the line is stretched, it sags a little at the center. Explain why.

An egg is released from rest from the roof of a building and falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a student on the ground, who uses coordinates with origin at the ground. Do the values the two students assign to the following quantities match each other: initial gravitational potential energy, final gravitational potential energy, change in gravitational potential energy, and kinetic energy of the egg just before it strikes the ground? Explain.

A physics teacher had a bowling ball suspended from a very long rope attached to the high ceiling of a large lecture hall.To illustrate his faith in conservation of energy, he would back up to one side of the stage, pull the ball far to one side until the taut rope brought it just to the end of his nose, and then release it. The massive ball would swing in a mighty arc across the stage and then return to stop momentarily just in front of the nose of the stationary, unflinching teacher. However, one day after the demonstration he looked up just in time to see a student at the other side of the stage push the ball away from his nose as he tried to duplicate the demonstration. Tell the rest of the story, and explain the reason for the potentially tragic outcome.

In one day, a 75 kg mountain climber ascends from the 1500m level on a vertical cliff to the top at 2400m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1350m. What is her change in gravitational potential energy (a) on the first day and (b) on the second day?

The maximum height a typical human can jump from a crouched start is about 60 cm . By how much does the gravitational potential energy increase for a 72 kg person in such a jump? Where does this energy come from?

A 90.0 kg mail bag hangs by a vertical rope 3.5 m long. A postal worker then displaces the bag to a position 2.0 m sideways from its original position, always keeping the rope taut. (a) What horizontal force is necessary to hold the bag in the new position? (b) As the bag is moved to this position, how much work is done (i) by the rope and (ii) by the worker?

The food calorie, equal to $\mathbf{4186} \mathbf{J}$, is a measure of how much energy is released when the body metabolizes food. A certain fruit-and-cereal bar contains 140 food calories. (a) If a $\mathbf{65} \mathbf{kg}$ hiker eats one bar, how high a mountain must he climb to “work off” the calories, assuming that all the food energy goes into increasing gravitational potential energy? (b) If, as is typical. Only $\mathbf{20}\mathbf{\%}$ of the food calories go into mechanical energy, what would be the answer to part (a)? (Note: In this and all other problems, we are assuming that $\mathbf{100}\mathbf{\%}$of the food calories that are eaten are absorbed and used by the body. This is not true. A person’s “metabolic efficiency” is the percentage of calories eaten that are actually used: the body eliminates the rest. Metabolic efficiency varies considerably from person to person.)

Is it possible for a friction force to increase the mechanical energy of a system? If so, give examples.

In physical terms, explain why friction is a nonconservative force. Does it store energy for future use?

A box slides down a ramp and work is done on the box by the forces of gravity and friction. Can the work of each of these forces be expressed in terms of the change in a potential­energy function? For each force explain why or why not.

A woman bounces on a trampoline, going a little higher with each bounce. Explain how she increases the total mechanical energy.

Fractured Physics. People often call their electric bill a power bill, yet the quantity on which the bill is based is expressed in kilowatt-hours. What are people really being billed for?

(a) A book is lifted upward a vertical distance of 0.800 m. During this displacement, does the gravitational force acting on the book do positive work or negative work? Does the gravitational potential energy of the book increase or decrease? (b) A can of beans is released from rest and falls downward a vertical distance of 2.00 m. During this displacement, does the gravitational force acting on the can do positive work or negative work? Does the gravitational potential energy of the can increase or decrease?