Question

what is the blocks speed just as it reaches the spring?
what is an expression for the energy lost due to friction, $|w_{k}|$?
a. $mgx_{f}$
b. $\frac{1}{2}mgx_{f}^{2}$
c. $\mu_{k}mgx_{f}$
d. $\frac{1}{2}\mu_{k}mgx_{f}^{2}$
e. $\frac{1}{2}\mu_{k}mgx_{f}$

Explanation:

Step1: Recall the formula for work done by friction

The work done by friction \(W_f\) is given by \(W_f = F_f\times d\), where \(F_f=\mu_k N\) and \(N = mg\) (since there is no vertical acceleration, normal force \(N\) equals the weight \(mg\) of the block) and \(d=x_f\) (the distance moved).

Step2: Substitute the values

Substitute \(F_f=\mu_k mg\) and \(d = x_f\) into the work - done formula. So, \(W_f=\mu_k mgx_f\).

Answer:

C. \(\mu_kmgx_f\)