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SPH 3U1 Problem Set 4 : Work and Energy Name: ______________________________________ K/U: /51 T/I: /64 Com: /10 Apps: /27 Level 0 0-49% Level 1 50-59 Level 2 60-69 % Level 3 70-79% Level 4 80-100% • Significant digits not used • Grasp/Grams not followed • Solution are not logical or easy to follow • Questions are done out of order • Solutions are not neat • Units often ignored • Significant digits often forgotten • Grasp/Grams forgotten most of the time • Solutions are not easy to follow • Questions are out of order and many not attempted • Solutions lack neatness • Units used inconsistently • Significant digits used occasionally • Grasp/Grams used occasionally • Solution is logical and somewhat easy to follow • Questions are done in order • Solutions are neat • Units properly used occasionally • Significant digits used most of the time • Grasp/Grams used most of the time • Solutions are logical and easy to follow most of the time • Questions are done in order • Solutions are neat • Units properly used most of the time • Significant digits used extensively • Grasp/Grams used extensively • Solution are logical and easy to follow • Questions are done in order • Solutions are neat and easy to read • Units thoroughly and consistently used Knowledge/Understanding (51 marks) 1. A 1500 kg accelerates uniformly from rest to a speed of 100 km/h in 10.0 s. How much work does the car do in this time interval? (4) 2. A force of 355 N is applied to a small cart of mass 50 kg on a railroad track. The force is at an angle of 60o to the track. If the cart moves 45.0 m a) how much work is done on the cart? b) what is the cart’s final speed if all its energy is kinetic energy? (4) 3. If the work required to speed up a car from 10 km/h to 20 km/h is 5.0 X 103 J, what would be the work required to increase the car’s speed from 20 km/h to 30 km/h? (4) 4. A person pushes a shovel into the ground to do some spring gardening. He applies a force to the shovel over the following distances. a) Draw a graph to represent the situation. b) Calculate the work done by the man on the shovel over the 6.0 cm. (4) 5. A boy who can generate 1.2 hp running up a flight of stairs in 5.0 s. How high are the stairs if the boy has a mass of 62 kg? (3) 6. How much power is being developed by a machine that can do 600 kWh of work in 12? (3) 7. How much force is required to accelerate a 150 kg motorbike from 10 m/s to 20 m/s over a distance of 25 m? Draw a FBD diagram for this situation as well (assume no friction). (4) 8. A 300 kg snowmobile is travelling at 16 m/s when it comes to the edge of a small cliff. Since there is deep fluffy snowdrift 2.5 m below the cliff, the drive doesn’t slow down but goes over the edge without changing speed. How fast is the snowmobile going when it lands on the snowdrift? (4) 9. A container factor uses a 370 W motor to operate a conveyor belt that lifts containers from one floor to another. To raise 250 1-kg containers a vertical distance of 3.6 m, the motor runs for 45 s. a) Determine the useful energy output. b) How much energy does the motor use? c) What is the efficiency of the motorized conveyor system? (6) 10. The motor for an elevator can produce 2200 W of power. The elevator has a mass of 1100 kg complete with contents. At what constant speed will the elevator rise? (3) 11. A ball with a mass of 0.30 kg is rolled off a ledge at a height of 12 m with a speed of 10 m/s. With what speed does the ball hit the ground? (4) 12. Write the nuclear reaction equation for each of the following a) Radium-223 undergoing alpha decay b) Sulfur-35 undergoing beta-negative decay c) Calcium-39 undergoing beta-positive decay d) Carbon-11 undergoing electron capture (8) Thinking/Inquiry (64 mark) 13. A 2.0 kg object rolls down an incline 20 m high at a speed of 5.0 m/s, then rolls up a ramp inclined at 30o. a. Find the speed at the bottom of the incline. b. Find the height reached on the ramp. c. Find the distance travelled up the ramp. (6) 14. A ball of mass 0.25 kg is thrown vertically upward from the roof of a building 18 m high with a speed of 16 m/s, and just misses the building on the way down, as shown. With what velocity does the ball hit the ground? (4) 15. Engineers has long desired of harnessing the tides in the Bay of Fundy. Although in places the difference between high tide and low tide can be as much as 17 m, the average change in height for the entire bay is about 4.0 m. The bay has the same area as a rectangle that is about 300 km long and 65 km wide. Water has a density of 1000 kg/m3. a) Calculate the volume of water and the mass of the water that flows out of the bay between high and low tide. b) Determine the loss in gravitational potential energy when the water flows out of the bay. Assume that the decrease in gravitational potential energy is equal to that of the mass calculated in (a) being lowered a distance of 2.0 m. c) If half the gravitational potential energy lost when the tide flows out could be converted to electricity over a 6 h period, determine the amount of electrical power that would be generated. (6) 16. A child of mass m slides down a slide 5.0 m high. The child’s speed at the bottom of the slide is 3.0 m/s a) What percent of the mechanical energy that the child had at the top has been converted to kinetic energy? b) What feature of the slide determines the percentage of mechanical energy that is converted to other forms of energy? (4) 17. A high jumper of mass 55 kg wishes to jump over a bar 1.8 m above the ground. Her center of mass is located 1.0 m above the ground. (We can imagine that all of her mass is located at this point for calculation purposes.) If she wishes to clear the bar while travelling at a speed of 0.4 m/s, how fast must she be travelling the instant her feet leave the ground? (4) 18. 30 g of ice at 0oC is added to 180 g of water at 21oC held in a 100 g aluminum calorimeter cup. What will be the final temperature of the water? (5) 19. A 70 kg hockey player moving at 8.0 m/s stops quickly. How much ice melts due to the friction between the player’s skates and the ice? Assume that only 60 % of the energy lost by the skater goes to melting the ice, and that the temperature of the ice is 0oC. (4) 20. How long does it take a 1000 W electric kettle to bring 1.0 L of water to the boiling point if the initial temperature of the water is 15oC and the kettle is made of 400 g of iron? Assume that no water is boiled, that no heat is lost to the surroundings and that the kettle is 100% efficient. (4) 21. A 250 kg roller coaster cart loaded with people has an initial velocity of 3.0 m/s. Find the velocity of the car at point B. (4) 22. A wrecking ball, with a mass of 315 kg, hangs from a crane on 10.0 m of cable. If the crane swings the wrecking ball so that the angle that the cable makes with the vertical is 30.0 o. a) What is the potential energy of the wrecking ball in relation to its lowest point position? b) What is the speed of the wrecking ball when it falls back to the vertical position? (6) 23. A box is slide along a smooth surface with a speed of 6.0 m/s and then encounters a rough path 3.0 m in length and with a coefficient of friction of 0.25. It then continues onto a smooth surface which rises 0.5 m. Find the final speed of the box. (5) 24. Find the energy liberated in each of the following nuclear reactions. Answer in MeV. All masses are in atomic mass units. (8) a) 235 92 𝑈 + (235.043 925 ) b) 3 2𝐻𝑒 (3.016 03) 1 0𝑛 (1.008 67) + 140 54𝑋𝑒 + (139.921 61) 3 2𝐻𝑒 4 2𝐻𝑒 (3.016 03) (4.002 60) + 94 38 𝑆𝑟 + (93.9153 67) 2 11𝐻 2(1.008 67) 25. Gold-198 is used to treat liver disease and has a half-life of 2.6 days. a) Gold-198 decays into mercury-198. What kind of decay does gold undergo? b) A person is given a dose of 2.5 mg and needs to get another does when there is 0.50 mg remaining. How long will it be before the second dose? (4) 1 0𝑛 (1.008 67) Applications (27 marks) 26. Discuss how the following supports the work-kinetic energy theorem. A cue ball is at rest on a pool table, and then moves being struck by a pool cue. (2) 27. Two identical cars are moving down a highway. Car X is travelling twice as fast as car Y. Both drivers see deer on the road ahead and apply the brakes. The forces of friction that are stopping the cars are the same. What is the ratio of the stopping distance of car x compared to car Y? (2) 28. A standard computer has a power supply of 550 W, and many people just leave their computer on all the time. Calculate the amount of money it costs to run a 550 W computer for 24 hours, if electricity costs 10 ¢/kWh. (3) 29. What is forced air heating? Explain how such a system can be used to heat a building. Include and illustration to aid in your explanation. (3) 30. If you could choose an alternative energy source to produce electricity for your home, which energy source would you chose and why? (3) 31. Create a diagram of a refrigerator and label the different parts. Use this to explain how a refrigerator stays cold. Based on what you have read in this unit, does it seem more efficient to have the freezer at the top of the refrigerator, or at the bottom? (5) 32. Use this diagram to explain how a CANDU reactor is used to produce electricity. (3) 33. Draw a diagram of magnetic confinement fusion reactor and label all the parts. Use this to explain how magnetic confinement can create fusion. (2) 34. Explain how archeologists and geologist are able to use radioactive isotopes to determine the age of fossils and rocks? What assumptions are made when using this method to age samples? (2) 35. Radioactive sources are found in homes, one such source is a smoke detector. Explain how a smoke detector works. (2)