> How hard does the floor push on the crate?
We
have to find the net vertical (normal) Fn force which results from Fp and
Fg.
We know that the normal component of Fg is just
Fg, which is equal to as 1040N.
From the geometry, the normal component of Fp
can be calculated:
Fpn = Fp * cos(θp)
= 952.5 N * cos(53)
= 573.23 N
The total normal force Fn then is:
Fn = Fg + Fpn
= 1040 + 573.23
= 1613.2 N
> Find the friction force on the crate
We
have to look for the net horizontal force Fh which results from Fp and Fg.
Since Fg is a normal force entirely, so
we can say that the horizontal component is zero:
Fh = Fph + Fgh
= (Fp * sin(θp)) + 0
= 952.5 * sin(53)
= 760.7 N
> What is the minimum coefficient of static friction needed to prevent the crate from slipping on the floor?
We just need to compute the ratio Fh to Fn to get the minimum μs.
μs = Fh / Fn
= 760.7 N / 1613.2 N
= 0.472
