The 25lb block has an initial speed of v0 10 fts when it is

The 25-lb block has an initial speed of v_0 = 10 ft/s when it is midway between springs A and B. After striking spring B, it rebounds and slides across the horizontal plane toward spring A, etc. If the coefficient of kinetic friction between the plane and the block is mu_k = 0.4, determine the total distance traveled by the block before it comes to rest.

Solution

Considering ideal spring, there is no energy loss in the two springs. Therefore, the work and energy principle between the initial and the final position can be written as:

U_1-2 = T₂ - T₁

where, work done by friction: U_1-2 = -mu*( m g) s

Final Kinetic energy, E T₂ = 0, Initial Kinetic Energy T₁ = 1/2 m V₀²

Substituting into (1) we get

- 1/2 m V₀² = -mu* (m g) s

s = 3.88 ft