A1.30-kg object is held 1.10 m above a relaxed, massless vertical spring with a force constant of 315 n/m. the object is dropped onto the spring. (a) how far does the object compress the spring?

0.345m

Explanation:

Let x (m) be the length that the spring is compress. If we take the point where the spring is compressed as a reference point, then the distance from that point to point where the ball is held is x + 1.1 m.

And so the potential energy of the object at the held point is:

where m = 1.3 kg is the object mass, g = 10m/s2 is the gravitational acceleration and h = x + 1.1 m is the height of the object with respect to the reference point

According to the conservation law of energy, this potential energy is converted to spring elastic energy once it's compressed

where k = 315 is the spring constant and x is the compressed length

x = 0.345 m or x = -0.263 m

Since x can only be positive we will pick the 0.345m

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