Question

One end of a spring of spring constant k is attached to a wall, and the other end is attached to a block of mass M, as shown. The block is pulled to the right, stretching the spring from its equilibrium position, and is then held in place by a taut cord, the other end of which is attached to the opposite wall. The spring and the cord have negligible mass, and the tension in the cord is F_T. Friction between the block and the surface is negligible. Express all algebraic answers in terms of M, k, F_T, and fundamental constants. 

(a) On the dot below that represents the block, draw and label a free-body diagram for the block.

(b) Calculate the distance that the spring has been stretched from its equilibrium position. The cord suddenly breaks so that the block initially moves to the left and then oscillates back and forth.

(c) Calculate the speed of the block when it has moved half the distance from its release point to its equilibrium position.

(d) Suppose instead that friction is not negligible and that the coefficient of kinetic friction between the block and the surface is µ_k. After the cord breaks, the block again initially moves to the left. Calculate the initial acceleration of the block just after the cord breaks.

Answer 1

(d) The forces acting on the block in the x direction are the spring force and the friction force. Using left as + we get 

F_net = ma F_sp – f_k = ma 

From (b) we know that the initial value of F_sp is equal to F_t which is an acceptable variable so we simply plug in F_t for F_sp to get F_t – µ_kmg = ma → a = F_t/m – µ_kg