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* The velocity of a vibrating object changes as a function of time as
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- A block is attached to a spring, and the block makes contact with a frictionless surface. Sketch a graph of the potential energy of the blockspring system as a function of position along with the corresponding system as in Figure 8.16 (page 224). Use this sketch to show how the block can move to the left from a positive position to a negative position and decrease the elastic potential energy of the system.arrow_forwardThe launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5.39a. If the spring is compressed a distance of 0.120 m and the gun fired vertically as shown, the gun can launch a 20.0-g projectile from rest to a maximum height of 20.0 m above the starting point of the projectile. Neglecting all resistive forces, (a) describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height, (b) determine the spring constant, and (c) find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0), as shown in Figure P5.39b. Figure P5.39arrow_forward(a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water flowing down it. Can the equation for conservation of mechanical energy be used on the child? (b) Is the mass of the child a factor in determining his speed at the bottom of the slide? (c) The child drops straight down rather than following the curved ramp of the slide. In which case will he be traveling faster at ground level? (d) If friction is present, how would the conservation-of-energy equation be modified? (e) Find the maximum speed of the child when the slide is frictionless if the initial height of the slide is 12.0 m.arrow_forward
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- Heedless of danger, a child leaps onto a pile of old mattresses to use them as a trampoline. His motion between two particular points is described by the energy conservation equation 12(46.0kg)(2.40m/s)2+(46.0kg)(9.80m/s2)(2.80m+x)=12(1.94104N/m)x2 (a) Solve the equation for x. (b) Compose the statement of a problem, including data, for which this equation gives the solution. (c) Add the two values of x obtained in part (a) and divide by 2. (d) What is the significance of the resulting value in part (c)?arrow_forwardThe chin-up is one exercise that can be used to strengthen the biceps muscle. This muscle can exert a force of approximately 8.00 102 N as it contracts a distance of 7.5 cm in a 75-kg male.3 (a) How much work can the biceps muscles (one in each arm) perform in a single contraction? (b) Compare this amount of work with the energy required to lift a 75-kg person 40. cm in performing a chin-up. (c) Do you think the biceps muscle is the only muscle involved in performing a chin-up?arrow_forwardOne person drops a ball from the top of a building while another person at the bottom observes its motion. Will these two people agree (a) on the value of the gravitational potential energy of the ball-Earth system? (b) On the change in potential energy? (c) On the kinetic energy of the ball at some point in its motion?arrow_forward
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