At constant velocity, the crate would be in equilibrium, so that Newton's second law tells us
p + (-f ) = 0
where p and f denote the magnitudes of the added pushing force and friction force, respectively.
The friction force is proportional to the normal force by a factor of µ, the coefficient of friction. There's no vertical movement going on, so Newton's second law says
n + (-w) = 0
where n and w are the magnitude of the normal force and the weight of the crate, respectively.
Compute n :
n = w = (25 kg) (9.80 m/s²) = 245 N
Use this and µ = 0.45 to compute f :
f = µ n = 0.45 (245 N) = 110.25 N
Solve for p :
p + (-110.25 N) = 0
p = 110.25 N ≈ 110 N
The force i.e required to move the crate at a constant velocity across the floor is 110 N.
At the same velocity, the crate should be in equilibrium, so as per Newton's second law, the following formula should be used:
p + (-f ) = 0
p means the magnitudes of the added pushing force
f means the friction force
n = w = (25 kg) (9.80 m/s²) = 245 N
Now
force should be
= µ n
= 0.45 (245 N)
= 110.25 N
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