Need help with showing work for these questions:

1. A 50.0 kg steel file cabinet is in the back of a dump truck. The truck's bed, also made of steel, is slowly tilted. What is the magnitude of the static friction force on the cabinet when the bed is tilted 20 ? At what angle will the file cabinet begin to slide?

2. In the sport of parasailing, a person is attached to a rope being pulled by a boat while hanging from a parachute-like sail. A rider is towed at a constant speed by a rope that is at an angle of 15 from horizontal. The tension in the rope is 2300 N. The force of the sail on the rider is 30 from horizontal. What is the weight of the rider?

3. A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if

a. The box is at rest?

b. The box moves at a steady 5.0 mis?

c. The box has Vx = 5.0 mis and ax = 5.0 m/s2 ?

4. A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that = 0.50 and k = 0.30. a. Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed.

b. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.

c. What is the maximum acceleration the belt can have without the crate slipping?

d. If the acceleration of the belt exceeds the value determined in part c, what is the acceleration of the crate?

5. At a history center, an old canal boat is pulled by two draft horses. It doesn't take much force to keep the boat moving; the drag force is quite small. But it takes some work to get the 55,000 kg boat up to speed! The horses can pull with a steady force and put a 1400 N tension in the rope that connects to the boat. The rope is straight and level. The boat starts from rest, and the horses pull steadily as they begin their walk down the towpath. How much distance do the horses cover as they bring the boat up to its final speed of 0.70 mis?

6. At a history center, an old canal boat is pulled by two draft horses. It doesn't take much force to keep the boat moving; the drag force is quite small. But it takes some work to get the 55,000 kg boat up to speed! The horses can pull with a steady force and put a 1400 N tension in the rope that connects to the boat. The rope is straight and level. The boat starts from rest, and the horses pull steadily as they begin their walk down the towpath. How much distance do the horses cover as they bring the boat up to its final speed of 0.70 mis?

7. A spring-loaded toy gun is used to launch a 10 g plastic ball. The spring, which has a spring constant of 10 Nim, is compressed by 10 cm as the ball is pushed into the barrel. When the trigger is pulled, the spring is released and shoots the ball back out horizontally. What is the ball's speed as it leaves the barrel? Assume that friction is negligible.

8. I A boy flies a kite with the string at a 30 angle to the horizontal. The tension in the string is 4.5 N. How much work does the string do on the boy if the boy

A. Stands still?

B. Walks a horizontal distance of 11 m away from the kite?

C. Walks a horizontal distance of 11 m toward the kite?

9. If you mix food in a blender, the electric motor does work on the system, which consists of the food inside the container. This work can noticeably warm up the food. Suppose the blender motor runs at a power of 250 W for 40 s. During this time, 2000 J of heat flow from the nowwarmer food to its cooler surroundings. By how much does the thermal energy of the food increase?

10. Iceland has both high geothermal activity, with high temperatures near the surface, and abundant cold surface water. Iceland has many power plants that take advantage of the proximity of these natural hot and cold reservoirs. One plant uses an underground source at 122 C as the hot reservoir and a nearby lake at 5 C as the cold reservoir. The plant draws 16 MW from the hot reservoir to produce 1.8 MW of electricity. How does the actual efficiency of the plant compare to the theoretical maximum efficiency?

11. 600 J of heat energy are transferred to a system that does 400 J of work. By how much does the system's thermal energy change?

12. 200 g of an unknown metal is heated to 90.0 C, then dropped into 50.0 g of water at 20.0 C in an insulated container. The water temperature rises within a few seconds to 27.7 C, then changes no further. Identify the metal.

13. Your 500 mL diet soda, with a mass of 500 g, is at 20 C, room temperature, so you cool it by adding 100 g of ice from the -20C freezer. Does all the ice melt? If so, what is the final temperature? If not, what fraction of the ice melts? Assume that you have a well-insulated cup.

14. 30 g of copper pellets are removed from a 300 C oven and immediately dropped into 100 mL of water at 20 C in an insulated cup. What will the new water temperature be?

15. If a person has a dangerously high fever, submerging her in ice water is a bad idea, but an ice pack can help to quickly bring her body temperature down. How many grams of ice at 0 C will be melted in bringing down a 60 kg patient's fever from 40 C to 39 C?

16. Legend has it that Archimedes was asked by King Hiero of Syracuse to determine whether a crown was pure gold or had been adulterated with a less valuable metal by an unscrupulous goldsmith. It was this problem that led Archimedes to the principle that bears his name. In a modern version of his method, a crown weighing 8.30 N is suspended underwater from a string. The tension in the string is measured to be 7.81 N. Is the crown pure gold?

17. A 2.0 g latex balloon is filled with helium. When it is completely inflated, its shape is approximately spherical with a diameter of 24 cm. If the balloon is released, what is its initial upward acceleration?

18. You need to determine the density of a ceramic statue. If you suspend it from a spring scale, the scale reads 28.4 N. If you then lower the statue into a tub of water so that it is completely submerged, the scale reads 17.0 N. What is the density?

19. What are the wavelengths of sound waves at the limits of human hearing and at the midrange frequency of 500 Hz? Notes sung by human voices are near 500 Hz, as are notes played by striking keys near the center of a piano keyboard.

20. The wavelength of microwaves in a microwave oven is 12 cm. What is the frequency of the waves?

21. A dolphin emits ultrasound at 100 kHz and uses the timing of reflections to determine the position of objects in the water. What is the wavelength of this ultrasound?