Box Sliding down incline with friction

Question

A 2.0 Kg box is sliding down a 20 degree, 5-m long ramp with coefficient of kinetic friction 0.2. if it started at 1.0 m/s, how fast will it be at the bottom of the ramp?

Answer 1

Using energy balance energy at top of ramp + non-conservative work - work of friction = energy at bottom of the ramp

mgh + 1/2 mv₀² - W_F = 1/2mv²

Remember that h = dsinθ

mgsinθ - F_fd = 1/2 mv²

Remember F_f = F_Nμ = mgμcosθ sub in and solve for v.

Using forces: F_net = ma on an incline

ma = mg(sinθ - mgμcosθ) so a = g(sinθ - μcosθ)

Now an equation of motion like

2ad = v² - v₀² can solve for v.