Question

A spring is resting vertically on a table. A small box is dropped onto the top of the spring and compresses it. Suppose the spring has a spring constant of 500 N/m and the box has a mass of 2.8 kg. The speed of the box just before it makes contact with the spring is 0.55 m/s. (a) Determine the magnitude of the spring’s displacement at an instant when the acceleration of the box is zero. (b) What is the magnitude of the spring’s displacement when the spring is fully compressed?

Answer 1

(a) the acceleration is zero when the weight is equal to the spring force

mg = kx

x = mg / k

x = 2.8 * 9.8 / 500

x = 0.05488 m

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(b) When the spring is fully compressed, the velocity is zero

1/2mv² + mgx = 1/2kx²

1/2 * 2.8 * 0.55² + 27.44x = 250x²

250x² - 27.44x - 0.4235 = 0

x = 0.123 m (discard the negative value)