(Solved): The block shown in Figure 1 has a weight of \( 20 \mathrm{lb} \) and is traveling at an initial sp ...

The block shown in Figure 1 has a weight of \( 20 \mathrm{lb} \) and is traveling at an initial speed of 10 \( \mathrm{ft} / \mathrm{s} \) (as shown in Figure 1). The block strikes spring \( B \) and rebounds. Determine the total distance traveled by the block. Use \( \mu_{\mathrm{k}}=0.2 \). Note that you need to show the application of the principle of work and energy repeatedly as the block moves back and forth before stopping. Also note that the two springs are unstretched in the state shown in Figure 1.