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Posted by on Thursday, September 30, 2010 at 3:08pm.

Some sliding rocks approach the base of a hill with a speed of 11.0 m/s. The hill rises at 44.0 degrees above the horizontal and has coefficients of kinetic and static friction of 0.410 and 0.630, respectively, with these rocks.

1) Find the acceleration of the rocks as they slide up the hill.
2) If it slides down, find its acceleration on the way down, else enter 0.

Incorrect answers that I tried:

1) -11.2
2) 2.37

  • Physics - , Thursday, September 30, 2010 at 5:39pm

    1. sliding uphill
    The following forces are present to oppose motion (hence causes deceleration).
    1a. gravity mgsin(θ)
    1b. friction:
    Normal reaction on plane, R
    = mgcos(θ)
    Friction force opposing motion
    = μk R
    = 0.410R
    Acceleration
    = total opposing forces (negative) / mass

    I get about -9.8m/s² (don't have a scientific calculator with me).

    2. Downhill
    Here the acceleration due to gravity effect is positive, and friction force is negative.
    You'd have to first check motion will start (downwrd acceleration should be greater than the force of static friction).
    If motion starts, then calculate the gravity effect, mgsin(θ) less the friction effect (μmgcos(θ)

    Use the coefficient of kinetic friction in both cases involving motion, and the static coefficient applies only to check if motion starts.

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