LS DETAI MY NOTES A small block of mass m ls place on top of a hill as shown in the gure at the right, a height h above a horizontal track. The hill is frictionless, but when the block reaches . the horizontal track, there ls a coefcient of friction, u. The block slides along the track for a distance L and comes to a stop. For this motion air resistance can be Ignored. I 3 We will take the origin of the coordinate system to be at A, with x being the horizontal coordinate with positive to the right, and y being the vertical coordinate With It ' shown in the gure: : M 9 M positive up. We will choose our system to include the block, the hill, the surface with friction, and the Earth. The parameters of the problem are those >> ' o L c d o i h, and 6. Also, the block has a speed VB at point B at the bottom of the hill. A d 1 rn, 9. "I 111. L. d2. ' J 2. [-112 Points] see: 7 :VJ energv- , 1. A. As the block slides from the top of the hill to point B at the bottom of the hi Are there any external forces that transfer energy in or out of the system as work nergy is transformed into i B. Use the parameters of the problem to write an expression for the known energy of the block at the top of the hill. l [Lil C. Use the parameters of the problem to write an expression for the known energy of the block at 7 i . L ' i D. Write an expression for t v _F T 3i'77i ' point B at the bottom of the hill. he speed of the block at point at the bottom of the hill. fl energy has decreased and FEEL\"; : energy has increased. 2. A. When the block arrives at point C (where it comes to a stop) from point B at the bottom of the hill, I Are there any external forces that transfer energy in or out of the system as work7 i:- Em ;\\'l B. Use the parameters of the problem to write an expression for the change in the form of energy that has increased from B to C. {,1 . V v l the energy the block had at the top of the hill. i C islele} C. The change in the form of energy that increases from B to he block travels until it comes to a stop, using the other parameters of the problem. D. Write an expression for L, the distance along the horizontal surface t , i *i l our last submission is used for your score. 1. [-/12 Points] DETAILS MY NOTES When bungee jumping from a high bridge over Victoria Falls, an operator first attaches an elastic rope to the jumper. The jumper then jumps off the bridge, falling freely until they reach the unstretched length of the rope. Then, the rope begins to stretch and slows the jumper to a stop. The rope pulls the jumper back up, and they oscillate up and down for a while until the operator pulls the jumper back up to the bridge. The rope is essentially a long spring. Let's label the jumper's mass m, the unstretched length of the rope Lo, the height of the bridge above the water H, the elastic (spring) constant of the rope k, and the gravitational field strength g. The jumper's speed at the point where they've fallen the full length of the unstretched rope is a maximum, Vmax. For simplicity, we will neglect resistive forces like air drag. A. Using the symbols in the problem described above, write an expression for the total mechanical energy of the jumper-rope-Earth system when the jumper is standing at rest on the bridge. Etot 3 What is the height of the jumper above the river when they've fallen the full length of the unstretched rope? height = Write an expression for the total mechanical energy of the jumper-rope-Earth system when they've fallen the full length of the unstretched rope. Your expression should include the maximum speed, Vmax. Etot = C. After falling the full length of the unstretched rope, the rope begins to stretch as the jumper continues falling. The jumper comes to a stop at the botton when the rope has stretched its maximum distance, d. What is the height of the jumper above the river when they've come to a stop and the rope has stretched its maximum distance? height = Write an expression for the total mechanical energy of the jumper-rope-Earth system when the jumper comes to a stop after the rope has stretched its maximum distance. Your expression should include the maximum distance the rope has stretched, d. DI DD A F11 F12 F9 F6 FB F10 80 F7 esc F3 F4 F5 % A & @we are neglecting resistive forces like air drag in this problem. Using A, B, and c to represent the total mechanical energies that you have written In parts A, B, and C above, energies? what is the correct relationship between these 0 A > B > c OA=B=C OAC OA>B=C The jumper has a mass of 50 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 7 m and stretches a distance of 5 m before bringing the ijper to a stop. Determine the maximum speed of the jumper and the spring constant or the rope In your calculation, use 9 : 10 N/kg. ' [(2 lN/m E, Now suppose the jumper has a mass of 80 kg. Do you think the maximum speed of the Jumper will increase, decrease, or stay the same? Will the rope need a larger, smaller, or the same spring constant to bring the jumper to a stop in the same distance as part D? (Your answers to these questions are not graded for correctness.) The maximum speed of the Jumper will ,4 g This answer has not been graded yet The ropewill need a spring constant that is l J E This answer has not been graded yet. Now calculate the maximum speed of this more massive jumper and the spring constant of the rope needed to bring the jumper to a stop after the rope stretches 5 m. (Again, use 9 = 10 N/kg for your calculations) Were your predictions correct? CO webassign.net/web/Student/Assignment-Responses/last?dep=30145901 Q SO The jumper has a mass of 50 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 7 m and stretches a distance of 5 m before bringing the jumper to a stop. Determine the maximum speed of the jumper and the spring constant of the rope. In your calculation, use g = 10 N/kg. Vmax = m/s K= N /m E Now suppose the jumper has a mass of 80 kg. Do you think the maximum speed of the jumper will increase, decrease, or stay the same? Will the rope need a larger, smaller, or the same spring constant to bring the jumper to a stop in the same distance as part D? (Your answers to these questions are not graded for correctness.) The maximum speed of the jumper will This answer has not been graded yet. The rope will need a spring constant that is This answer has not been graded yet. late the maximum speed of this more massive jumper and the spring constant of the rope needed to bring the jumper to a stop after the rope stretches 5 m. (Again, use g = 10 N/kg for your calculations.) Were your predictions correct? Vmax = m/s K = N/m MY NOTES 2. [-/12 Points] DETAILS A small block of mass m is place on top of a hill as shown in the figure at the right, a height h above a horizontal track. The hill is frictionless, but when the block reaches the horizontal track, there is a coefficient of friction, M. The block slides along the track for a distance _ and comes to a stop. For this motion air resistance can be ignored. h with v baine the horizontal car andinat citive to the debt and w baine the