A trained sea lion slides from rest down a long

ramp into a pool of water. If the ramp is inclined at

an angle of 23° above the horizontal and the

coefficient of kinetic friction between the sea lion

and ramp is 0.26. Calculate the acceleration of the

sea lion as it slides down the ramp.

1.5 m/s²

Explanation:

Draw a free body diagram. There are three forces acting on the sea lion: gravity pulling down, normal force perpendicular to the ramp, and friction parallel to the ramp.

Sum of the forces perpendicular to the incline:

∑F = ma

N - mg cos θ = 0

N = mg cos θ

Sum of the forces parallel to the incline:

∑F = ma

mg sin θ - Nμ = ma

Substitute for N:

mg sin θ - (mg cos θ) μ = ma

g sin θ - g cos θ μ = a

a = g (sin θ - μ cos θ)

Given θ = 23° and μ = 0.26:

a = 9.8 (sin 23 - 0.26 cos 23)

a = 1.48

Rounded to two significant figures, the sea lion accelerates at 1.5 m/s².