What force do you need to push on a large crate to accelerate it at 1.8m/s2 across a rough floor? The crate has mass 32kg and the coefficient of kinetic friction between the crate and floor is 0.57

M*g = 32kg * 9.8m/kg = 313.6 N. = Wt. of

crate. = Normal force(Fn).

Fk = u*Fn = 0.57 * 313.6 = 178.8 N. = Force of kinetic friction.

F-Fk = M*a
F-178.8 = 32 * 1.8 = 57.6
F = 57.6 + 178.8 = 236.4 N.

To determine the force needed to push the crate, we need to consider the forces acting on the crate. In this case, we have two main forces: the force applied to accelerate the crate and the force of kinetic friction opposing its motion.

1. Find the force of kinetic friction:
The force of kinetic friction can be found using the formula: F_friction = coefficient of kinetic friction × normal force.
The normal force is equal to the weight of the crate, which is the mass multiplied by the acceleration due to gravity (9.8 m/s^2).
So, the normal force = mass × gravity = 32 kg × 9.8 m/s^2 = 313.6 N.
Now, we can calculate the force of kinetic friction:
F_friction = 0.57 × 313.6 N = 178.952 N.

2. Calculate the force needed to accelerate the crate:
To accelerate the crate at 1.8 m/s^2, we use Newton's second law: F_net = mass × acceleration.
The net force is equal to the applied force minus the force of friction.
So, F_net = mass × acceleration + F_friction.
F_net = 32 kg × 1.8 m/s^2 + 178.952 N.
F_net ≈ 57.6 N + 178.952 N ≈ 236.552 N.

Therefore, the force needed to push the large crate at an acceleration of 1.8 m/s^2 across the rough floor is approximately 236.552 Newtons.