Super – Quiz
A 45.0 N block is resting on a table. The coefficients of friction for the surfaces are: μs = 0.650 and μk = 0.230. What horizontal force is required to make the block move? What acceleration will the block have if you keep pushing with that force? What force should you push with to keep the block moving at constant speed after it starts moving?
The weight of the block = 45 N = Normal force on the block
When we try to move the block, static friction will oppose the motion. The motion will not take place until the force applied is sufficient to overcome this static friction.
`F - f > 0`
or, `F > mu_3 N`
or, `F > 0.65 xx 45 N`
or, the applied force has to be greater than 29.25 N for the block to start moving.
Once the block begins its motion, the friction force drops and is now called the kinematic friction. The achieved acceleration, because of this would be:
`F - f = ma`
`or, F - mu_k N = m a`
or, 29.25 - 0.23 x 45 = ma = 18.9 N
or, a = 18.9/m = 18.9/(mg/g) = 18.9/(45/9.81) = 4.12 m/s^2
When we apply a force, there will always be acceleration (And hence no constant velocity), unless the applied force is balanced out by the frictional force.
that is, F - f = 0
Since the object is moving, the net applied force should be sufficient to overcome the kinetic friction.
Thus, F - `mu_k N` = 0
or, F = 0.23 x 45 N = 10.35 N
Hope this helps.