Ask Question
24 December, 21:02

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.

+2
Answers (1)
  1. 24 December, 23:01
    0
    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.
Know the Answer?