An unknown mass falls 4 meters than hits a spring with constant 1000 n/m and compresses 1 meter, what is mass?

Question

the mass falls four meters than hits the spring which compresses another meter before coming to rest (temporarily)
Friction and air resistance can be ignored.

Answer 1

We will assume that air and spring friction is negligible. We will also assume that the mass starts falling with a velocity of zero (it isn't thrown, for example).

First, we find the velocity of the mass at the time it strikes the spring. distance = (1/2)gt^2 so:
4 = (1/2)(9.8)t^2, t = 0.90 sec.
v = gt = (9.8)(0.90) = 8.85 meters/sec

So the kinetic energy of the mass when it hits is (1/2)mv^2,
which is (1/2)m(8.85)^2 or 39.2m Joules.

The work done by gravity as the spring compresses is f*d or
(9.8)m(1) or 9.8m Joules.

Next, we need to know the work done by the spring as it compresses. This is the integral of force over distance or
Int(1000LdL). Integrating gives 500 L^2 evaluated from 1 to 0 which is -500 Joules.

Finally, we have our equation. The Kinetic energy of the mass is absorbed by the spring, as is the work done by gravity. So we have :

39.2m + 9.8m = 500
49m = 500
m = 10.2 kg.

Answer 2

Think conservation of energy.

The Kin E of the mass must be converted into potential energy stored in the spring.

Answer 3

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