accelerate a 1,290 kg car from 0 to 21 m/s in 15 s. The change in momentum is the car’s momentum when traveling 21 m/s minus its momentum when going 0 m/s. (Enter the magnitude.)
2. A pitcher throws a 0.80 kg ball of clay at a 3.0 kg block of wood. The clay sticks to the wood on impact, and their joint velocity afterward is 2.9 m/s. What was the original speed of the clay (in m/s)?
Ans. ________ m/s
3. A running back with a mass of 70 kg and a speed of 7 m/s collides with, and is held by, a 105-kg defensive tackle going in the opposite direction. How fast must the tackle be going before the collision for their speed afterward to be zero?
Ans. ________ m/s
4. A motorist runs out of gas on a level road 240 m from a gas station. The driver pushes the 1,220 kg car to the gas station. If a 140 N force is required to keep the car moving, how much work (in J) does the driver do?
Ans. __________ J
5. In the figure, the rock weighs 105 lb and is lifted 1 ft by the lever.
(a) How much work is done? ________ft-lb (b) The other end of the lever is pushed down 3 ft while lifting the rock. What force had to act on that end? ________ lb
6. A worker at the top of a 597-m-tall television transmitting tower accidentally drops a heavy tool. If air resistance is negligible, how fast (in m/s) is the tool going just before it hits the ground?
7. A student drops a water balloon out of a dorm window 14 m above the ground. What is its speed when it hits the ground? Ans. _______m/s
8. A child on a swing has a speed of 5.2 m/s at the low point of the arc (see the figure below).
How high (in m) will the swing be at the high point?
8. The cliff divers at Acapulco, Mexico, jump off a cliff 28.7 m above the ocean. Ignoring air resistance, how fast are the divers going when they hit the water? Ans. _______m/s
9. A bicycle and rider going 15 m/s approach a hill. Their total mass is 58 kg.
(a) What is their kinetic energy? ________ J (b) If the rider coasts up the hill without pedaling, how high above its starting level will the bicycle be when it finally rolls to a stop? __________ m
10. The ceiling of an arena is 50 m above the floor. What is the minimum speed that a thrown ball would need to just reach the ceiling? Ans. ________m/s
11. Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a hydraulic system. The piston chambers and the connecting tube are filled with an incompressible fluid. The cross-sectional areas of piston 1 and piston 2 are A1 and A2, respectively. A force F1 is exerted on piston 1. Rank the resultant force F2 on piston 2 that results from the combinations of F1, A1, and A2given from greatest to smallest. If any of the combinations yield the same force, give them the same ranking. (Use only “>” or “=” symbols. Do not include any parentheses around the letters or symbols.)
a. F1 = 6.0 N; A1 = 0.7 m2; and A2 = 1.4 m2
b. F1 = 3.0 N; A1 = 0.7 m2; and A2 = 0.35 m2
c. F1 = 3.0 N; A1 = 1.4 m2; and A2 = 2.8 m2
d. F1 = 6.0 N; A1 = 0.35 m2; and A2 = 1.4 m2
e. F1 = 6.0 N; A1 = 0.35 m2; and A2 = 0.7 m2
f. F1 = 3.0 N; A1 = 1.4 m2; and A2 = 0.7 m
12. A bicycle tire pump has a piston with area 0.47 in2. If a person exerts a force of 18 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump? Ans. _______psi
13. A large truck tire is inflated to a gauge pressure of 76 psi. The total area of one sidewall of the tire is 1,220 in2. What is the net outward force (in lb) on the sidewall because of the air pressure? (Enter the magnitude.)
14. A viewing window on the side of a large tank at a public aquarium measures 57 in. by 62 in. The average gauge pressure from the water is 7 psi. What is the total outward force on the window? Ans. ________lb
15. The total mass of the hydrogen gas in the Hindenburg zeppelin was 18,000 kg. What volume did the hydrogen occupy? (Assume that the temperature of the hydrogen was 0°C and that it was at a pressure of 1 atm.) Ans. ________m3
16. A large balloon used to sample the upper atmosphere is filled with 550 m3 of helium. What is the mass of the helium (in kg)?
17. Find the gauge pressure (in psi) at the bottom of a freshwater swimming pool that is 18.0 ft deep.
18. The depth of the Pacific Ocean in the Mariana Trench is 36,198 ft. What is the gauge pressure at this depth? Ans. __________psi
19. An ebony log with volume 14.2 ft3 is submerged in water. What is the buoyant force on it (in lb)? (Enter the magnitude.)
21. A modern-day zeppelin holds 9,550 m3 of helium. Compute its maximum payload at sea level. (Assume the helium and air to be at 0°C and 1 atm.) Ans. ________N
22. A boat (with a flat bottom) and its cargo weigh 6,000 N. The area of the boat’s bottom is 3 m2. How far below the surface of the water is the boat’s bottom when it is floating in water? Ans. ___________m
23. A scale reads 278 N when a piece of copper is hanging from it. What does it read (in N) when it is lowered so that the copper is submerged in water?
24. A dentist’s chair with a person in it weighs 1975 N. The output plunger of a hydraulic system starts to lift the chair when the dental assistant’s foot exerts a force of 37 N on the input piston. Neglecting any difference in the heights of the piston and the plunger, what is the ratio of the area of the plunger to the area of the piston?
25. The wing of an airplane has an average cross-sectional area of 13 m2 and experiences a lift force of 79,000 N. What is the average difference in the air pressure between the top and bottom of the wing? Ans. ________N/m2
26. Air flows through a heating duct with a square cross-section with 7-inch sides at a speed of 6.1 ft/s. Just before reaching an outlet in the floor of a room, the duct widens to assume a square cross-section with sides equal to 15 inches. Compute the speed of the air flowing into the room (in ft/s), assuming that we can treat the air as an incompressible fluid.
27. Use the following table to determine which of the other materials from the list would float if placed in a container of ethyl alcohol. Select all correct answers.
None of the above materials would float; they are all solids and would sink in a liquid.
28. A metal bowl with a weight of 1.35 N is placed in a larger kitchen container filled with coconut oil. How much coconut oil must the bowl displace in order to float? For reference, the mass density of coconut oil is about 903 g/liter and its weight density is about 8.85 N/liter. Please give your answer in liters.
29. On a nice winter day at the South Pole, the temperature rises to
What is the approximate temperature in degrees Celsius? Ans._______°C
30. A machinist wishes to insert a steel rod with a diameter of 9 mm into a hole with a diameter of 8.998 mm. By how much would the machinist have to lower the temperature (in °C) of the rod to make it fit the hole?
31. As a gasoline engine is running, an amount of gasoline containing 14,000 J of chemical potential energy is burned in 1 s. During that second, the engine does 3,500 J of work.
What is the engine’s efficiency (in percent)?
32. The burning gasoline has a temperature of about 4,200°F (2,600 K). The waste heat from the engine flows into air at about 88°F (304 K). What is the Carnot efficiency (in percent) of a heat engine operating between these two temperatures?
33. An irreversible process takes place by which the entropy of the universe increases by 1.68 J/K. If the temperature of the environment in which the process occurred is 240 K, how much energy (in J) was made unavailable for useful work as a result?
34. Double-paned thermal insulating windows consist of two glass panels separated by a narrow gap from which most of the air has been removed to create a near vacuum in the space between the panes. Explain how this design helps to better insulate a home than a window that is made from a single sheet of glass. (Select all that apply.)
a. The vacuum between the two panes of glass acts as a very efficient conductor.
b. The double-paned window allows for less heat loss through convection.
c. The vacuum between the two panes of glass acts as a very efficient insulator.
d. The double-paned window allows for less heat loss through conduction.
35. A brass vat is 12 m long at room temperature (20°C). How much longer is it when it contains boiling water at 1 atm pressure? Ans. _____m
36. An aluminum wing on a passenger jet is 28 m long when its temperature is 16°C. At what temperature would the wing be 2 cm (0.02 m) shorter? Ans. ________°C
37. Air in a balloon does 59 J of work while absorbing 99 J of heat. What is its change in internal energy? Ans. __________J
38. An apartment has the dimensions 15 m by 8 m by 5 m. The temperature is 25°C, and the relative humidity is 56 percent. What is the total mass (in kg) of water vapor in the air in the apartment?
39. What is the freezing point of pure water at normal atmospheric pressure? Select all correct answers.