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# College Physics 2017

## Educators

### Problem 1

Convert $3.50 \times 10^{3}$ cal to the equivalent number of (a) kilo-calories (also known as Calories, used to describe the energy content of food) and (b) joules.

Averell H.
Carnegie Mellon University

### Problem 2

A medium-sized banana provides about 105 Calories of energy. (a) Convert 105 Cal to joules. (b) Suppose that amount of energy is transformed into kinetic energy of a 1.00 -kg object initially at rest. Calculate the final speed of the object. (c) If that same amount of energy is added to 3.79 $\mathrm{kg}$ (about 1 gal) of water at $20.0^{\circ} \mathrm{C}$ , what is the water's final temperature?

Salamat A.

### Problem 3

A 75 -kg sprinter accelerates from rest to a speed of 11.0 $\mathrm{m} / \mathrm{s}$ in 5.0 s. (a) Calculate the mechanical work done by the sprinter during this time. (b) Calculate the average power
the sprinter must generate. (c) If the sprinter converts food energy to mechanical energy with an efficiency of $25 \%,$ at what average rate is he burning Calories? (d) What happens to the other 75$\%$ of the food energy being used?

Averell H.
Carnegie Mellon University

### Problem 4

A 55-kg student eats a 540 -Calorie (540 kcal) jelly doughnut for breakfast. (a) How many joules of energy are the equivalent of one jelly doughnut? (b) How many stairs must the student climb to perform an amount of mechanical work equivalent to the food energy in one jelly doughnut? Assume the height of a single stair is 15 $\mathrm{cm} .(\mathrm{c})$ loughnut? Assume only 25$\%$ efficient in converting chemical energy to mechanical energy, how many stairs must the woman climb to work off her breakfast?

Salamat A.

### Problem 5

A person's basal metabolic rate (BMR) is the rate at which energy is expended while resting in a neutrally temperate environment. A typical BMR is $7.00 \times 10^{6} \mathrm{J} / \mathrm{day}$ . Convert
this $\mathrm{BMR}$ to units of (a) watts and (b) kilocalories (or Calories) per hour. (c) Suppose a $1.00-\mathrm{kg}$ object's gravitation potential energy is increased at a rate equal to this typical BMR. Find the rate of change of the object's height in $\mathrm{m} / \mathrm{s}$ .

Averell H.
Carnegie Mellon University

### Problem 6

The temperature of a silver bar rises by $10.0^{\circ} \mathrm{C}$ when it absorbs 1.23 $\mathrm{kJ}$ of energy by heat. The mass of the bar is 525 $\mathrm{g}$ . Determine the specific heat of silver from these data.

Salamat A.

### Problem 7

The highest recorded waterfall in the world is found at Angel Falls in Venezuela. Its longest single waterfall has a height of 807 $\mathrm{m}$ . If water at the top of the falls is at $15.0^{\circ} \mathrm{C}$ , what is the maximum temperature of the water at the bottom of the falls?
ssume all the kinetic energy of the water as it reaches the bottom goes into raising the water's temperature.

Averell H.
Carnegie Mellon University

### Problem 8

An aluminum rod is 20.0 $\mathrm{cm}$ long at $20.0^{\circ} \mathrm{C}$ and has a mass of
0.350 $\mathrm{kg} .$ If $1.00 \times 10^{4} \mathrm{J}$ of energy is added to the rod by heat,
what is the change in length of the rod?

Salamat A.

### Problem 9

Lake Erie contains roughly $4.00 \times 10^{11} \mathrm{m}^{3}$ of water. (a) How much energy is required to raise the temperature of that volume of water from $11.0^{\circ} \mathrm{C}$ to $12.0^{\circ} \mathrm{C}$ (b) How many years would it take to supply this amount of energy by using the $1.00 \times 10^{4}$ -MW exhaust energy of an electric power plant?

Averell H.
Carnegie Mellon University

### Problem 10

A $3.00-\mathrm{g}$ copper coin at $25.0^{\circ} \mathrm{C}$ drops 50.0 $\mathrm{m}$ to the ground. (a) Assuming 60.0$\%$ of the change in gravitational potential energy of the coin-Earth system goes into increasing the internal energy of the coin, determine the coin's final temperature. (b) Does the result depend on the mass of the coin? Explain.

Salamat A.

### Problem 11

$\mathrm{A} 5.00-\mathrm{g}$ lead bullet traveling at $3.00 \times 10^{2} \mathrm{m} / \mathrm{s}$ is stopped by a large tree. If half the kinetic energy of the bullet is trans- formed into internal energy and remains with the bullet while the other half is transmitted to the tree, what is the increase in temperature of the bullet?

Averell H.
Carnegie Mellon University

### Problem 12

The apparatus shown in Figure P11.12 was used by Joule to measure the mechanical equivalent of
heat. Work is done on the water by a rotating paddle wheel, which is driven by two blocks falling at a
constant speed. The temperature of the stirred water increases due to the friction between the water and the paddles. If the energy lost in the bearings and through the walls is neglected, then the loss in potential energy associated with the blocks equals the work done by the paddle wheel on the water. If each block has a mass of 1.50 $\mathrm{kg}$ and the insulated tank is filled with 0.200 $\mathrm{kg}$ of water, what is the increase in temperature of the water after the blocks fall through a distance of 3.00 $\mathrm{m} ?$

Salamat A.

### Problem 13

A 0.200 -kg aluminum cup contains 800 . g of water in thermal equilibrium with the cup at $80 .^{\circ} \mathrm{C}$ . The combination of cup and water is cooled uniformly so that the temperature decreases by $1.5^{\circ} \mathrm{C}$ per minute. At what rate is energy being removed? Express your answer in watts.

Averell H.
Carnegie Mellon University

### Problem 14

A 1.5 -kg copper block is given an initial speed of 3.0 $\mathrm{m} / \mathrm{s}$ on a
rough horizontal surface. Because of friction, the block finally comes to rest. (a) If the block absorbs 85$\%$ of its initial kinetic energy as internal energy, calculate its increase in temperature. (b) What happens to the remaining energy?

Salamat A.