answering a problem set – Work & Energy
PROBLEM SET 7: Work & Energy 1. A 5.00-kg package slides 1.50 m down a long ramp that is inclined at 24.0° below the horizontal. The coefficient of kinetic friction between the package and the ramp is μk = 0.310. Calculate (a) the work done on the package by friction; (b) the work done on the package by gravity; (c) the work done on the package by the normal force; (d) the total work done on the package. (e) If the package has a speed of 2.20 m/s at the top of the ramp, what is its speed after sliding 1.50 m down the ramp? ” 2. A net force along the x-axis that has an x-component đč! = −12.0 đ + +0.300 #! – đ„ $ is applied to a 5.00 kg object that is initially at the origin and moving in the – x-direction with a speed of 6.00 m/s. What is the speed of the object when it reaches the point x=5.00 m? 3. A 350-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop shown in the figure. (a) How fast is this roller coaster moving at point B? (b) How hard does it press against the track at point B? 4. Bungee Jump. A bungee cord is 30.0 m long and, when stretched a distance x, it exerts a restoring force of magnitude kx. Your father-in-law (mass 95.0 kg) stands on a platform 45.0 m above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 m before the cord stops him. You had several bungee cords to select from, and you tested them by stretching them out, tying one end to a tree, and pulling on the other end with a force of 380.0 N. When you do this, what distance will the bungee cord that you should select have stretched? 5. A 3.00 kg fish is attached to the lower end of a vertical spring that has negligible mass and force constant 900 N/m. The spring initially is neither stretched nor compressed. The fish is released from rest. (a) What is its speed after it has descended 0.0500 m from its initial position? (b) What is the maximum speed of the fish as it descends? 6. A new event has been proposed for the Winter Olympics. As seen in the figure, an athlete will sprint 100 m, starting from rest, then leap onto a 20 kg bobsled. The person and bobsled will then slide down a 50-m-long ice-covered ramp, sloped at 20°, and into a spring with a carefully calibrated spring constant of 2000 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40 kg, has been training for this event. She can reach a maximum speed of 12 m/s in the 100 m dash. (a) How far will Lisa compress the spring? (b) The Olympic committee has very exact specifications about the shape and angle of the ramp. Is this necessary? What factors about the ramp are important? 1
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