Week 6 Homework Assignment

1. (P.208 Prob.2) A sled is dragged along a horizontal path at a constant speed pf 1.5m/s by a rope that in inclined at an angle of 30.0° with respect to the horizontal (Fig.6.24). The total weight of the sled is 470N. The tension in the rope is 240N. How much work is done by the rope on the sled in a time interval of 10.0s?
   
2. (P.208 Prob.8) A record company executive is on his way to a TV interview and is carrying a promotional CD in his briefcase. The mass of the briefcase and its contents is 5.00kg. The executive realizes that he is going to be late. Starting from rest, he starts to run, reaching a speed of 2.50m/s. What is the work done by the executive on the briefcase during this time?
3. (P.209 Prob.18) Figure 6.27 shows the force exerted on an object versus the position of that object along the x-axis. The force has no components other than along the x-axis. What is the work done by the force on the object as the object is displaced form 0 to 3.0m?
   
4. (P.210 Prob.24) An airline executive decides to economize by reducing the energy, and thus the amount of fuel, required for long distance flights. He orders the ground crew to remove the paint from the outer surface of each plane. The paint removed from a single plane has a mass of approximately 100kg. (a) If the airplane cruises at an altitude of 12,000m, how much energy is saved in not having to lift the paint to that altitude? (b) How much energy is saved by not having to move that amount of paint from rest to a cruising speed of 250m/s?
5. (P.210 Prob.28) When a 0.20-kg mass is suspended from a vertically hanging spring, it stretches the spring from its original length of 5.0cm to a total length of 6.0cm. The spring with the same mass is then placed on a horizontal frictionless surface. The mass is pulled so that the spring stretches to a total length of 10.0cm, then the mass is released and it oscillates back and forth (Fig.6.29). What is the maximum speed of the mass as it oscillates?
   
6. (P.211 Prob.34) An object slides down an inclined plane of angle 30.0° and of incline length 2.0m. If the initial speed of the object is 4.0m/s directed down the incline, what is the speed at the bottom? Neglect friction.
7. (P.212 Prob.52) A car with mass of 1000.0kg accelerates from 0 m/s to 400.m/s in 10.0s. Ignore air resistance. The engine has a 22% efficiency, which means that 22% of the thermal energy released by the burning gasoline is converted into mechanical energy. (a) What is the average mechanical power output of the engine? (b) What volume of gasoline is consumed? Assume that the burning of 1.0L of gasoline releases 46MJ of thermal energy.
8. (P.213 Prob.78) A 0.5-kg block, starting at rest, slides down a 30.0° incline with kinetic friction coefficient 0.25 (Fig.6-32). After sliding 85cm down the incline, it slides across a frictionless horizontal surface and encounters a spring (k = 35N/m). (a) What is the maximum compression of the spring? (b) After the compression of paart (a), the spring rebounds and shoots the block back up the incline. How far along the incline does the block travel before coming to rest?