5. A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. By compressing the spring, the child can launch the ball up the ramp. The spring has a spring constant k, the ball has a mass m, and the ramp raises a height h. The spring is compressed a distance S in order to launch the ball. When the ball leaves the launching ramp its velocity makes an angle 0 with respect to the horizontal. a. Calculate the velocity of the ball when it just leaves the launching ramp (both magnitude and direction. Be sure to specify your coordinate system.) b. The spring constant 1000.0 N/m, the spring's compression is 4.00 cm, the ball's mass is 55.0 grams, the height of the ramp is 15.0 cm, and the top of the table is 1.10 m above the floor. With what total speed will the ball hit the floor? (Use g = 10.0 m/s²) %3D

5. A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. By compressing the spring, the child can launch the ball up the ramp. The spring has a spring constant k, the ball has a mass m, and the ramp raises a height h. The spring is compressed a distance S in order to launch the ball. When the ball leaves the launching ramp its velocity makes an angle 0 with respect to the horizontal. a. Calculate the velocity of the ball when it just leaves the launching ramp (both magnitude and direction. Be sure to specify your coordinate system.) b. The spring constant 1000.0 N/m, the spring's compression is 4.00 cm, the ball's mass is 55.0 grams, the height of the ramp is 15.0 cm, and the top of the table is 1.10 m above the floor. With what total speed will the ball hit the floor? (Use g = 10.0 m/s²) %3D

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter7: Conservation Of Energy

Section: Chapter Questions

Problem 81P: Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with...

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A child of mass m starts from rest and slides without friction from a height h along a curved waterslide (Fig. P5.46). She is launched from a height h/5 into the pool. (a) Is mechanical energy conserved? Why? (b) Give the gravitational potential energy associated with the child and her kinetic energy in terms of mgh at the following positions: the top of the waterslide, the launching point, and the point where she lands in the pool. (c) Determine her initial speed V0 at the launch point in terms of g and h. (d) Determine her maximum airborne height ymax in terms of h, g, and the horizontal speed at that height, v0x. (e) Use the x-component of the answer to part (c) to eliminate from the answer to part (d), giving the height ymax in terms of g, h, and the launch angle . (f) Would your answers be the same if the waterslide were not frictionless? Explain. Figure P5.46
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In an iconic movie scene, Forrest Gump (https://openstaxcollege.org/l/21ForrGumpvid) runs around the country. If he is running at a constant speed of 3 m/s, would it take him more or less energy to run uphill or downhill and why?
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Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F, on a vine having length L and initially making an angle with the vertical (Fig. P7.81). Take D = 50.0 m, F = 110 N, L = 40.0 m, and = 50.0. (a) With what minimum speed must Jane begin her swing to just make it to the other side? (b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing? Assume Tarzan has a mass of 80.0 kg.
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