The block in Figure 7-11a lies on a horizontal frictionless surface and is attac

Question

The block in Figure 7-11a lies on a horizontal frictionless surface and is attached to the free end of the spring, with a spring constant of 40 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 3.1 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. Assume that the stopping point is reached.

During the block's displacement, find the following values.

Explanation / Answer

a) Use Hooke's Law F = k*x => x = F/k = 3.1N/40N/m = 7.75x10^-2m b) W = 3.1N*7.75x10^-2 = 0.24J c) W = -1/2*k*x^2 = -1/2*40*(7.75x10^-2)^2 = - 0.1201J d) W = integral of (3.1 - k*x)dx = 3.1x- 1/2*k*x^2 So max K when dW/dx = 0 = 3.1- kx = 0 This occurs when x = 3.1/40 = 7.75x10^-2m K = 0.24- 0.12 = 0.0604J = 0.1796J

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