1. What is the practical benefit (in terms of time savings and efficiency) of defining the potential energy? Be clear about what is required in terms of calculation if we do not use the concept of potential energy.[br]2. For what type of force is it not possible to define a potential energy expression?[br]3. For the following forces that can do work, indicate if they are conservative or non-conservative: [br] a. A human lifting a box[br] b. An engine propelling a car down the road[br] c. Gravity working against a rising projectile[br] d. The electric repulsion between two electrons[br] e. Sliding friction between a box and the ground[br] f. Air resistance propelling a sailboat across the ocean[br]4. A bobsled starts at the top of a track as human runners sprint from rest and then jump into the sled. Assume they reach 40 km/h from rest after covering a distance of 50 m over flat ice. [br] a. How much work do they do on themselves and the sled which they are pushing given the fact that there are two men of combined mass 185 kg and the sled with a mass of 200 kg? (If you haven't seen bobsledding, watch youtube to understand better what's going on.)[br] b. After this start, the team races down the track and descends vertically by 200 m. At the finish line the sled crosses with a speed of 55 m/s. How much energy was lost to drag and friction along the way down after the men were in the sled?[br]5. A kids BB gun uses a spring to fire little metal BBs at a target. The diameter of a BB is 4.5 mm. Assume the BBs are made of steel with a density of [math]8.0\times 10^3 kg/m^3,[/math] and that the spring in the gun gets compressed by 1.0cm in order to shoot the BB. Answer the following while assuming that non-conservative forces can be ignored even though in reality that would be careless.[br] a. If the BB exits the muzzle at 115 m/s how much energy was stored in the spring? [br] b. What is the elastic constant of the spring?[br] c. What is the acceleration of the BB while the spring is in the act of firing the BB and is still compressed by 0.5 cm? [br]6. In the previous problem, how high in the sky will the gun be able to shoot a BB if we ignore air drag (not a realistic thing to do, but I'm asking anyway)? Please don't use kinematics to answer this, but rather energy considerations from this chapter.

1. No need to do the path integral since result is same every time.[br]2. Non-conservative[br]3. nc, nc, c, c, nc, nc[br]4. 23.7kJ, 1.96x10[sup]5[/sup]J (using g=9.8m/s/s)[br]5. 2.5J, 50000N/m, 6.6x10[sup]5[/sup]m/s[sup]2[br][/sup]6. 661m using g=10m/s[sup]2[/sup]