As shown in the figure, a block of mass m is sliding with a velocity v across a smooth horizontal surface when it encounters a long horizontal spring. The spring has a spring constant k and is fixed at its other end. Determine the maximum compression of the spring. Also, will the velocity of the block be the same as v upon returning to the initial position shown?

Step-by-step solution

By the principle of conservation of mechanical energy, the kinetic energy of the block is completely converted into the elastic potential energy of the spring at the point of maximum compression. 1 2 m v^2 = 1 2 k x_ max ^2 x_ max ^2 = m v^2 k x_ max = v m k Since the surface is smooth, there is no loss of energy. When the block returns to its initial position, its speed will be the same as its initial speed v . However, velocity is a vector quantity. The block will be moving in the opposite direction, so its veloc