As shown in the figure below, a box of mass m = 18.4 kg is released from rest (at position A) at the top of a 30.0° frictionless incline. point of release The box slides a distance d = 4.40 m down the incline before it encounters (at position B) a spring and compresses it an amount xc = 0.300 m (to point C) before coming momentarily to rest. Using energy content, determine the following. (a) the speed (in m/s) of the box at position B 6.57 m/s (b) the spring constant (in N/m) k =

The figure below shows a plot of potential energy U versus position x of a 0.76 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) In the graphs, the potential energies are UA = 20.0 J, UB = 35.0 J, and Uc = 45.0 J. Uc UB UA 4 х (m) The particle is released at x = 4.5 m with an initial speed of 6.0 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.0 m, what is its speed there, and if it cannot, what is its turning point? m (b) What are the magnitude and direction of the force on the particle as it begins to move to the left of x = 4.0 m? magnitude direction +X Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 6.0 m/s. (c) If the particle can reach x = 7.0 m, what is its speed there, and if it cannot, what is its turning point? m (d) What are the magnitude and direction of the force on the particle as it begins to move to the right of x = 5.0 m? magnitude…

A 3.6 g marble is fired vertically upward using a spring gun. The spring must be compressed 2.9 cm if the marble is to just reach a target 18 m above the marble's position on the compressed spring. (a) What is the change AU in the gravitational potential energy of the marble-Earth system during the 18 m ascent? (b) What is the change AU in the elastic potential energy of the spring during its launch of the marble? (c) What is the spring constant of the spring? (a) Number (b) Number ogres (c) Number Units Units Units

If the hand does 40 J of work on the 2.5 kg cart, how fast will it travel?  If the person does 480 J of work on the 32kg box to move it at a speed of 4 m/s, how much energy is dissipated due friction? If the spring is compressed 12 cm and has a constant of 860 N/m, how high will the 1.3 kg chicken go?Use the values given in the problem. How much work does the weightlifter do?Use the values given in the problem. How much work does the cable do?