A force of 40 N is applied at an angle of 30oabove the horizon to a 5 kg block that is at rest on a rough horizontal surface. After the block starts to move with an acceleration of 3 m/s2, what is the coefficient of kinetic friction between the block and the horizontal surface?

Question

How do I solve a friction problem without knowing the coefficient and vice versa?

bobpursley · Answer

You know friction force is equal to the horizontal pulling force (adjusted for acceleration). 40cos40=friction force-mass*acceleration = (mg-40sin30)mu-ma solve for mu

Angela · Answer

I understand that friction WOULD equal to the horizontal pulling force IF the object is moving at constant velocity, but the question asked about friction force when there is acceleration.

Are you saying that whether or not there is acceleration, the friction force would always equal to that of the pulling force?

drwls · Answer

The friction force is opposite to the direction of motion and acceleration in this case. As Bob has noted, the friction force is reduced because the vertical component of the applied force reduces the force on the ground.

40 cos30 - friction force = mass*acceleration
40 cos30 - (mg -40 sin30)*mu = m a

mu = (40 cos30 -ma)/(mg -40 sin30)

bobpursley · Answer

I have a sign error in my equality. 40cos40=friction force+mass*acceleration

drwls · Answer

<> No. That is not what we are saying. The imbalance between the pulling force and the friction force provides the scceleration, in a kinetic friction situation, as here. That is reflected in the equations that Bob and I have written. In a static-friction situation, the pulling and friction forces are equal, until enough force is applied to cause motion.