Question

spring is compressed to a 9.5 in. length, where it is released from rest and accelerates the sliding block A. The acceleration has an initial value of 330 ft/sec2 and then decreases linearly with the x-movement of the block, reaching zero when the spring regains its original 13.4 in. length. Calculate the time t for the block to go (a) 1.95 in. and (b) 3.9 in.

Answer 1

To calculate the time t for the block to go a distance of 1.95 in. and 3.9 in., we can use the equations of motion and consider the decreasing acceleration of the block.

Step-by-step explanation:

To calculate the time t for the block to travel a certain distance, we need to consider the acceleration of the block and use the equations of motion. In this case, the acceleration decreases linearly with the x-movement of the block, reaching zero when the spring regains its original length.

(a) To calculate the time for the block to move 1.95 in., we need to find the acceleration for that distance. We can use the equation x = x0 + v0t + 0.5at^2, where x0 = initial position, v0 = initial velocity, t = time, and a = acceleration. Rearranging the equation and solving for t, we have t = sqrt((x - x0) / (0.5a)). Plugging in the values, we get t = sqrt((1.95 - 0) / (0.5 * 330)).

(b) To calculate the time for the block to move 3.9 in., we use the same equation and plug in the values, t = sqrt((3.9 - 0) / (0.5 * 330)).