A mass less spring with force constant k = 400 newtons per meter is fastened at its left end to a vertical wall, as shown in Figure 1. Initially, block C (mass mc = 4.0 kilograms) and block D (mass mD = 2.0 kilograms) rest on a rough horizontal surface with block C in contact with the spring (but not compressing it) and with block D in contact with block C. Block C is then moved to the left, compressing the spring a distance of 0.50 meter, and held in place while block D remains at rest as shown in Figure 11. (Use g = 10 m/s2.)
a. Determine the elastic energy stored in the compressed spring.
Block C is then released and accelerates to the right, toward block D. The surface is rough and the coefficient of friction between each block and the surface is µ = 0.4. The two blocks collide instantaneously, stick together, and move to the right at 3 m/s. Remember that the spring is not attached to block C. Determine each of the following.
b. The speed vc of block C just before it collides with block D
c. The horizontal distance the combined blocks move after leaving the spring before coming to rest
