A spring is used to stop a crate of mass 50 kg which is sliding on a horizontal surface. The spring has a spring constant k = 20 kN/m and is initially in its equilibrium state. In position A shown in the top diagram the crate has a velocity of 3.0 m/s. The compression of the spring when the crate is instantaneously at rest (position B in the bottom diagram) is 120 mm. (i) What is the work done by the spring as the crate is brought to a stop? (ii) Write an expression for the work done by friction during the stopping of the crate (in terms of the coefficient of kinetic friction). (iii) Determine the coefficient of friction between the crate and the surface. (iv) What will be the velocity of the crate as it passes again through position A after rebounding off the spring (Fig. 2.14a, b)?