Two blocks possess equal masses. The contact surface of block A with the floor is smooth, while that of block B has a friction coefficient of 0.10 with the floor. Block A travels at a speed of 10 m/s towards block B, which is initially at rest. Determine the distance travelled by block B if the collision is perfectly inelastic. Take g = 10 m/s ^2 .

Step-by-step solution

Let the mass of each block be m . By the principle of conservation of linear momentum during the perfectly inelastic collision, the common velocity v of the blocks after they stick together is given by: m u_A + m u_B = (m + m) v m(10) + m(0) = 2mv 10m = 2mv v = 5 m/s After the collision, the blocks move together as a single system of mass 2m . The frictional force acts only on block B, as the surface under block A is smooth. Frictional force, f = N_B = mg = 0.10 m 10 = m The deceleration a of the combined system is