A forklift pushes a 185kg box into a 335kg box, which slides into a 80kg box. If all 3 boxes slide across the floor at 4.5m/s, how much force does the 185kg box exert on
the 335kg box? The coefficient of friction between each box and the floor are listed
in the table below:

The amount of force the 185 kg box exerts on the 335 kg box is 2,675.165 N

Explanation:

The given information are;

The mass of the boxes and their coefficient of friction are as follows;

1) Mass, m₁ = 185 kg, coefficient of friction, μ₁ = 0.700

2) Mass, m₂ = 335 kg, coefficient of friction, μ₂ = 0.705

3) Mass, m₃ = 80 kg, coefficient of friction, μ₃ = 0.460

The frictional forces of the blocks are;

1) 185 × 9.8 × 0.700 = 1269.1 N

2) 335 × 9.8 × 0.705 = 2314.515 N

3) 80 × 9.8 × 0.460 = 360.64 N

Therefore, the total resistances of the boxes to motion, starting from the 80 kg box is given as follows;

360.64 N → (360.65 + 2314.515) N → (360.64 + 2314.515 + 1269.1) N

360.64 N → 2,675.165 N → 3944.255 N

Which gives;

Force exerted by forklift on 185 kg box = 3944.255 N

Force exerted by 185 kg box on 335 kg box = 2,675.165 N

Force exerted by 335 kg box on 80 kg box = 360.64 N

Therefore, the amount of force the 185 kg box exerts on the 335 kg box = 2,675.165 N.