Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 134

Redesigning a track with friction. Figure 8.57 shows a small block that is released from rest, which then slides through a valley and up onto and along a plateau. There it slides through length \( L = 8.00 \text{ cm} \), where the coefficient of kinetic friction is \( 0.600 \), and then through distance \( d = 25.0 \text{ cm} \). The only region of friction is length \( L \). The height difference \( \Delta h = h_1 - h_2 \) between the release point and the plateau is \( 15.0 \text{ cm} \). You want to decrease the time through \( d \) by \( 0.100 \text{ s} \). What should the value of \( \Delta h \) then be?