A small block of mass 100 g is pushed against a horizontal spring fixed at one end, compressing the spring by 5.0 cm as shown in the figure. The spring constant is 100 N/m . Upon release, the block travels horizontally until it detaches from the spring. At what horizontal distance from the free end of the spring will it strike the ground, which is 2 m below the spring?

Step-by-step solution

By the conservation of mechanical energy, the elastic potential energy of the spring is converted into the kinetic energy of the block when it detaches from the spring at its natural length: 1 2 k x^2 = 1 2 m v^2 v = x k m Substituting the given values k = 100 N/m , m = 100 g = 0.1 kg , and x = 5.0 cm = 0.05 m : v = 0.05 100 0.1 = 0.05 1000 = 0.5 10 m/s The block travels horizontally and falls a vertical distance h = 2 m . The time of flight t is given by: h = 1 2 g t^2 t = 2h g Taking g = 10 m/s ^2 : t = 2 2 10 =