PLEASE HELP!!!! ASAP!!!!

Question

A 400 kg box and a 200 kg are to pushed across a horizontal table, the exact same distance with the exact force. Which box will have the most work done on it? Which box will get to the end first? Explain both of your responses.

Answer 1

The acceleration of the smaller mass will be larger compared to the 400 kg box considering the same kinetic friction on the surface. This is because

M*(dv/dt) = F_applied - mu*M*g

where M is the mass, F_applied is the force, mu is the kinetic coeff of friction, v the velocity and g the gravitational acceleration.

so the acceleration for the smaller block is

(dv/dt)₂₀₀ = (F_applied/200) - mu*g

The acceleration for the larger block is

(dv/dt)₄₀₀ = (F_applied/400) - mu*g

So (dv/dt)_{200 >} (dv/dt)_400.

So starting from rest, the smaller block will reach the end of the table faster due to a larger acceleration.

Following the same logic, the net force acting on the smaller block is larger compared to the more massive block.

So the net work done (F.d) will be greater for the smaller block of 200 Kg compared to the larger block of 400Kg.