How Is the Mass of a Block Determined When It Compresses a Spring?

[dorian_stokes]

Homework Statement

A block is dropped onto a spring with k = 31 N/m. The block has a speed of 3.5 m/s just before it strikes the spring. If the spring compresses an amount 0.11 m before bringing the block to rest, what is the mass of the block?

Homework Equations

0.5mv^2=0.5kx^2

The Attempt at a Solution

0.5m3.5=0.5*31*.11

 

[Delphi51]

Looks like you forgot to square the 3.5 and the .11.

 

[tomcue]

^2

m=0.5*31*.11^2/(0.5*3.5)

m=0.5 kg

I would first like to clarify that the given information is not enough to accurately determine the mass of the block. We would need to know the initial height at which the block was dropped and the total distance the spring compressed to accurately calculate the mass.

However, assuming that the initial height and the total distance are known, the equation used in the attempt at a solution is correct. The block's initial kinetic energy is equal to the potential energy stored in the spring when it is compressed. Rearranging the equation, we can solve for the mass of the block.

Based on the given information, the mass of the block is approximately 0.5 kg. However, without knowing the initial height and total distance, this value cannot be confirmed. Further experimentation and data collection may be necessary to accurately determine the mass of the block.