(PHYSICS) Newton's Laws Application Help?

a) An eraser of mass m is placed on a wooden plank. One end of the plank is slowly raised. When the plank is tilted by the angle θmax from the horizontal the block begins to slide with acceleration a down the slope. Find the coefficient of static friction μs and the coefficient of kinetic friction μk. 

b) Solve the problem if m = 2.0kg, θmax = 40° the block begins to slide and accelerates at 2.7m/s2 down the slope. Find the coefficient of static friction μs and the coefficient of kinetic friction μk. 

2 Answers

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  • NCS
    Lv 7
    4 weeks ago

    a) static:

    Just at the threshold of sliding, the downslope component of the weight is equal to the static friction force:

    m*g*sin(Θmax) = µs*m*g*cos(Θmax)

    µs = tan(Θmax)

    kinetic:

    Newton's Second gives us

    m*a = m*g*sin(Θmax) - µk*m*g*cos(Θmax)

    a = g*(sin(Θmax) - µk*cos(Θmax))

    µk = [sin(Θmax) - (a/g)] / cos(Θmax)

    b) µs = tan40º = 0.84

    µk = [sin40º - 2.7/9.8] / cos40º = 0.48

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  • oubaas
    Lv 7
    4 weeks ago

    a)

    m*g*sin 40° = m*g*cos 40°*μs

    μs = tan 40° = 0.839 

    b)

    2.7 = AF/m = m*g*(sin 40°-cos 40°*μk)/m 

    2.7 = 9.806*0.643-9.806*0.766*μk

    μk = (9.806*0.643-2.7)/(9.806*0.766) = 0.480

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