A 2.0 kg breadbox on a frictionless incline of angle is connected, by a cord that runs over a pulley, to a light spring of spring constant , as shown in Fig. 8-42. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10 cm down the incline? (b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c) magnitude and (d) direction (up or down the incline) of the box’s acceleration at the instant the box momentarily stops?

Question

A 2.0 kg breadbox on a frictionless incline of angle  is connected, by a cord that runs over a pulley, to a light spring of spring constant , as shown in Fig. 8-42. The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10 cm down the incline? (b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c) magnitude and (d) direction (up or down the incline) of the box’s acceleration at the instant the box momentarily stops?

THANKS!

drwls · Accepted Answer

You provide no value for the spring constant (k?) not the angle (A?). You also do not provide the figure 8-42 mentioned. Without this information, we cannot helprovide numerical answers. An energy method can be used for these questions. The loss of potential energy by the box as it falls down the incline equals the gain in kinetic energy by amount X plus the energy stored in the spring.
m g X sin A = (1/2) kX^2 + (1/2) M V^2.
For (b), use the same equation to solve for X when V = 0. . For (c) and (d), solve for X at the two points where V - 0, and use F = kX and a = F/M to get the acceleration (a) there.