A block with mass m is being pushed by a constant force F
that makes an angle of θ with the
horizontal as shown below. The block is moving with constant velocity on a
level surface. The coefficient of kinetic friction between the block and the
surface is µk. Which one of the
following equations is correct for the magnitude of F?
Solution
Let |F| is the magnitude of
the force F
Given Data: m, F, θ, a=0, µk
|F| = |F(m, θ, µk)|=?
FNET=0 because a=0
X direction: |F|·cos θ + f = FNET, X = 0
Y direction: N – mg – |F|·sin θ = FNET, Y = 0,
where N is the normal force,
g is the gravity acceleration
g is the gravity acceleration
f= µk N
|F|·cos θ + µk (mg-
|F|·sin θ) = 0
|F|·cos θ + µk mg -
µk |F|·sin θ = 0
|F|·cos θ - µk |F|·sin θ = µk
mg
|F|·( cos θ - µk sin θ) = µk mg
|F| = µk mg/( cos θ - µk sin θ)
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