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57. A 70kg hockey player moving at 5.6 m/s collides headon with an 80kg player who is heading in the opposite direction with a speed of 3.5 m/s. The two players entangle and move together across the ice. Determine their aftercollision speed. PSYW
Answer and Explanation: 

Answer: 0.747 m/s Momentum conservation principles must be used to solve this collision problem. Set the initial momentum of the system equal to the final momentum of the system and solve for the unknown velocity. The information can be organized inside of a momentum table as shown below. (NOTE: units have been left off quantities to avoid "messiness".)
112 = 150*v v = (112/150) = 0.747 m/s 
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58. Calculate the work required lift a 2.5kg object a height of 6.0 meters. PSYW
Answer and Explanation: 
Answer: 150 J The work done upon an object is found with the equation In this case, the d=6.0 m; the F=25 N (it takes approx. 25 N of force to lift a 2.5kg object), and the angle between F and d (Theta) is 0 degrees. Substituting these values into the above equation yields 
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59. In the It's All Uphill Lab, a force of 21.2 N is applied parallel to the incline to lift a 3.0kg loaded cart to a height of 0.45 m along an incline which is 0.636m long. Determine the work done upon the cart and the subsequent potential energy change of the cart. PSYW
Answer and Explanation: 
Answer: 13.5 J There are two methods of solving this problem. The first method involves using the equation where F=21.2 N, d=0.636 m, and Theta=0 degrees. Substituting and solving yields The second method is to recognize that the work done in pulling the cart along the incline changes the potential energy of the cart. The work done equals the potential energy change. Thus, 
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60. An 800kg car skids to a stop across a horizontal surface over a distance of 45 m. The average force acting upon the car is 7000N, then determine
Answer and Explanation: 
Answers:
a. The work done upon the car can be found using the equation where F=7000 N, d=45 m, and Theta=180 degrees (the force is in the opposite dir'n as the displacement). Substituting and solving yields 315000 J. b. The initial kinetic energy can be found using the workenergy theorem. The eq'n reduces to (PE_{i} and PE_{f} = 0 J since the car is on the ground; and KE_{f} = 0 J since the car is finally stopped). Rearrange the equation and it takes the form KE_{i} = W_{ext} . So KE_{i} = +315000 J. c. The acceleration of the car can be found using Newton's second law of motion: Fnet = m*a The friction force is the net force (since the up and down forces balance) and the mass is 800 kg. Substituting and solving yields a = 8.75 m/s/s. d. The initial velocity of the car can be found using the KE equation: KE = 0.5*m*v^{2} where m=800 kg and KE_{i}=315000 J. Substituting and solving for velocity (v) yields v = 28.1 m/s. (A kinematic equation could be also used to find the initial velocity.) 
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61. A 50kg hiker ascends a 40meter high hill at a constant speed of 1.2 m/s. If it takes 400 s to climb the hill, then determine
Answer and Explanation: 
Answers:
a. The speed of the hiker is constant so there is no change in kinetic energy  0 J. b. The potential energy change can be found by subtracting the initial PE (0 J) from the final PE (m*g*h_{f}). The final potential energy is 20000 J [from (50 kg)*(10 m/s/s)*(40 m)] and the initial potential energy is 0 J. So Delta PE = +20000 J. c. The work done upon the hiker can be found using the workenergy theorem. The eq'n reduces to (PE_{i} = 0 J since the hiker starts on the ground; and KE_{i } = KE_{f} since the speed is constant; these two terms can be dropped from the equation since they are equal). The final potential energy is 20000 J [from (50 kg)*(10 m/s/s)*(40 m)]. So W = +20000 J. d. The power of the hiker can be found by dividing the work by the time. 
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62. Neel, whose mass is 75kg, ascends the 1.6meter high stairs in 1.2 s. Determine Neel's power rating. PSYW
Answer and Explanation: 
Answer: P = 1000 Watts Neel's power is found by dividing the work which he does by the time in which he does it. The work done in elevating his 75kg mass up the stairs is determined using the equation where F = m*g = 750 N (approx.), d=1.6 m and Theta = 0 degrees (the angle between the upward force and the upward displacement). Solving for W yields 1200 Joules. Now divide the work by the time to determine the power: 
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63. A 500kg roller coaster car starts at a height of 32.0 m. Assuming negligible energy losses to friction and air resistance, determine the PE, KE, and speed of the car at the various locations (A, B, C, D, and E) along the track.

(m) 
(J) 
(J) 
(m/s) 



































Answer and Explanation: 
Answer: See above table (answers in red) The potential energy for every row can be found using the equation PE = m*g*h where m=500 kg and g = 10 m/s/s (approx.). In the first row, the total mechanical energy (KE + PE) equals 160 000 J. Since no work is done by external forces, the total mechanical energy must be 160 000 J in all the other rows. So the KE can be computed by subtracting the PE from 160 000 J. The velocity can be found using the equation: where m=500 kg. 
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64. Use the information in the above table to explain what is meant when it is said that the "total mechanical energy is conserved."
Answer and Explanation: 
Answer: The total mechanical energy is the same in each row of the table. If the kinetic energy and the potential energy is added together, then the sum will be the same throughout the ride. 
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65. Use the workenergy theorem to determine the force required to stop a 1000kg car moving at a speed of 20.0 m/s if there is a distance of 45.0 m in which to stop it. PSYW
Answer and Explanation: 
Answer: F = 4.44*10^{3} N The work energy theorem can be written as The PE_{i} and PE_{f} can be dropped from the equation since they are both 0 (the height of the car is 0 m). The KE_{f} can also be dropped for the same reason (the car is finally stopped). The equation simplifies to The expressions for KE (0.5*m*v^{2}) and W (F*d*cos[Theta]) can be sustituted into the equation: where m=1000 kg, v_{i}=20 m/s, d=45 m, and Theta = 180 degrees. Substituting and solving for F yields 4.44*10^{3} N. 
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66. A 60kg skier accelerates down an icey hill from an original height of 500 meters. Use the workenergy theorem to determine the speed at the bottom of the hill if
Answer and Explanation: 
Answers:
a. Use the work energy theorem: The PE_{f} can be dropped from the equation since the skiier finishes on the ground at zero height. The KE_{i} can also be dropped since the skiier starts from rest. The W_{ext} term is dropped since it is said that no work is done by external forces. The equation simplifies to The expressions for KE (0.5*m*v^{2}) and PE (m*g*h) can be sustituted into the equation: where m=60 kg, h=500 m, g=10 m/s/s (approx.). Substituting and solving for v_{f} yields 100 m/s. b. This equation can be solved in a similar manner, except that now the W_{ext} term is 140000J. So the equation becomes Now substituting and solving for v_{f} yields 73.0 m/s. 
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This page last updated on December 13, 1999.