1. ## Energy question

Question:
A moving 4.5 kg block collides with a horizontal spring whose spring constant is 424 N/m (see figure). The block compresses the spring a maximum distance of 13.0 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.36. (a) What is the work done by the spring in bringing the block to rest?

(a) 0.564668J (THIS ANSWER IS WRONG)

(b) How much work was done by the force of friction (non-conservative force = Wnc) while the block is being brought to rest by the spring?

(b) -2.06388J (THIS ANSWER IS CORRECT)

(c) What is the speed of the block when it hits the spring?

(c) 0.50096 m/s (THIS ANSWER IS WRONG)

What I did:
I did f*(deltaX)*(cos180deg) = deltaE where Uf = 1/2 * k * (deltaX)^2, Ui = 0, Kf = 0, Ki = 1/2 * m * v^2 and Ef = Uf + Kf and Ei = Ui + Ki where:

U: potential energy
K: kinetic energy
i: initial
f: final

(just in case it wasn't obvious)

The reason for which I did not use momentum even though this seems to be an inelastic collision is because there is no mass of spring given so I am guessing that that is to be neglected. Can someone please tell me what I am doing wrong and show me how to do it?

Any help would be greatly appreciated!

2. Originally Posted by s3a
Question:
A moving 4.5 kg block collides with a horizontal spring whose spring constant is 424 N/m (see figure). The block compresses the spring a maximum distance of 13.0 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.36. (a) What is the work done by the spring in bringing the block to rest?

(a) 0.564668J (THIS ANSWER IS WRONG)

$\displaystyle \textcolor{red}{|W_s| = \frac{1}{2}kx^2}$

(b) How much work was done by the force of friction (non-conservative force = Wnc) while the block is being brought to rest by the spring?

(b) -2.06388J (THIS ANSWER IS CORRECT)

(c) What is the speed of the block when it hits the spring?

$\displaystyle \textcolor{red}{KE = \frac{1}{2}mv^2 = |W_s| + |W_f|}$

(c) 0.50096 m/s (THIS ANSWER IS WRONG)

...

3. I get both wrong by using those formulae. I also tried something else and got it wrong again.

4. Originally Posted by s3a
I get both wrong by using those formulae. I also tried something else and got it wrong again.
the formulas are correct.

$\displaystyle W_s = -3.58 \, J$

$\displaystyle v = 1.58 \, m/s$