Question

An object with a mass of `8 kg` is on a ramp at an incline of `pi/8`. If the object is being pushed up the ramp with a force of `7 N`, what is the minimum coefficient of static friction needed for the object to remain put?

Answer 1

Total force acting on the object downward along the plane is `mg sin ((pi)/8)=8*9.8* sin((pi)/8)=30N`

And applied force is `7N` upward along the plane.

So,net force on the object is `30-7=23N` downwards along the plane.

So,static frictioanl force that needs to act to balance this amount of force should act upwards along the plane.

Now,here,static frictional force that can act is `mu mg cos ((pi)/8)=72.42mu N` (where, `mu` is the coefficient of static frictional force)

So,`72.42 mu =23`

or, `mu=0.32`