13. A child of mass m starts from rest and slides without fric-|GP tion from a height h along a slide next to a pool (Fig. P8.13).QIC She is launched from a height h/5 into the air over the pool.S We wish to find the maximum height she reaches above thewater in her projectile motion. (a) Is the child-Earth systemisolated or nonisolated? Why? (b) Is there a nonconservativeforce acting within the system? (c) Define the configurationof the system when the child is at the water level as havingzero gravitational potential energy. Express the total energyof the system when the child is at the top of the waterslide.(d) Express the total energy of the system when the child isat the launching point. (e) Express the total energy of thesystem when the child is at the highest point in her projec-tile motion. (f) From parts (c) and (d), determine her initialУmaxth/5 1Figure P8.13 speed v, at the launch point in terms of g and h. (g) Fromparts (d), (e), and (f), determine her maximum airborneheight yma in terms of h and the launch angle 0. (h) Wouldyour answers be the same if the waterslide were not friction-less? Explain.

Since we only answer up to 3 subparts, we will answer the first three subparts. Please resubmit the…

Answered: 13. A child of mass m starts from rest…

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter8: Conservation Of Energy

Section: Chapter Questions

Problem 13P

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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
Two blocks of masses m and 3m are placed on a frictionless, horizontal surface. A light spring is attached to the more massive block, and the blocks are pushed together with the spring between them (Fig. P8.7). A cord initially holding the blocks together is burned; after that happens, the block of mass 3m moves to the right with a speed of 2.00 m/s. (a) What is the velocity of the block of mass m? (b) Find the systems original elastic potential energy, taking m = 0.350 kg. (c) Is the original energy in the spring or in the cord? (d) Explain your answer to part (c). (e) Is the momentum of the system conserved in the bursting-apart process? Explain how that is possible considering (f) there are large forces acting and (g) there is no motion beforehand and plenty of motion afterward? Figure P8.7
You hold a slingshot at arms length, pull the light elastic band back to your chin, and release it to launch a pebble horizontally with speed 200 cm/s. With the same procedure, you fire a bean with speed 600 cm/s. What is the ratio of the mass of the bean to the mass of the pebble? (a) 19 (b) 13 (c) 1 (d) 3 (e) 9
Check Your Understanding There is a second solution to the system of equations solved in this example (because the energy equation is quadratic): v1.f=-2.5m/s , v2.f=0 . This solution is unacceptable on physical grounds; what’s with it?
The coefficient of friction between the block of mass m1 = 3.00 kg and ilie surface in Figure P8.22 is k = 0.400. The system starts from rest. What is the speed of the ball of mass m2 = 5.00 kg when it has fallen a distance h = 1.50 m?
Ezra (m = 25.0 kg) has a tire swing and wants to swing as high as possible. He thinks that his best option is to run as fast as he can and jump onto the tire at full speed. The tire has a mass of 10.0 kg and hangs 3.75 m straight down from a tree branch. Ezra stands back 10.0 m and accelerates to a speed of 3.50 m /s before jumping onto the tire swing. a. How fast are Ezra and the tire moving immediately after he jumps onto the swing? b. How high does the tire travel above its initial height?
A block with mass m1 = 0.500 kg is released from rest on a frictionless track at a distance h1, = 2.50 m above the top of a table. It then collides elastically with an object having mass m2 = 1.00 kg that is initially at rest on the table, as shown in Figure P6.71. (a) Determine the velocities of the two objects just after the collision. (b) How high up the track does the 0.500-kg object travel back after the collision? (c) How far away from the bottom of the table does the1.00-kg object land, given that the height of the table h2 = 2.00 m? (d) How far away from the bottom of the table does the 0.500-kg object eventually band? Figure P6.71
A pitcher claims he can throw a 0.145-kg baseball with as much momentum as a 3.00-kg bullet moving with a speed of 1.50 103 m/s (a) What must the baseballs speed be if the pitchers claim is valid? (b) Which has greater kinetic energy, the ball or the bullet?
At the start of a basketball game, a referee tosses a basketball straight into the air by giving it some initial speed. After being given that speed, the ball reaches a maximum height of 4.25 m above where it started. Using conservation of energy, find a. the balls initial speed and b. the height of the ball when it has a speed of 2.5 m/s.
A giant swing at an amusement park consists of a 365-kg uniform arm 10.0 m long, with two seats of negligible mass connected at the lower end of the arm (Fig. P8.53). (a) How far from the upper end is the center of mass of the arm? (b) The gravitational potential energy of the arm is the same as if all its mass were concentrated at the center of mass. If the arm is raised through a 45.0 angle, find the gravitational potential energy, where the zero level is taken to be 10.0 m below the axis, (c) The arm drops from rest from the position described in part (b). Find the gravitational potential energy of the system when it reaches the vertical orientation. (d) Find the speed of the seats at the bottom of the swing.
Two gliders are set in motion on a horizontal air track. A spring of force constant k is attached to the back end of the second glider. As shown in Figure P8.48, the first glider, of mass m1, moves to the right with speed v1, and the second glider, of mass m2, moves more slowly to the right with speed v2. When m1 collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of v1, v2, m1, m2, and k, find (a) the speed rat maximum compression, (b) the maximum compression xmax, and (c) the velocity of each glider after m1 has lost contact with the spring.
Calculate the final speed of a 110-kg rugby player who is initially running at 8.00 m/s butt collides head-on with a padded goalpost and experiences a backward force of l.76104N for 5.50102s .

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