A rectangular boat is 11 m wide and 12 m long. After a truck pulls onto the ferry, the boat ends up with a depth of 4 cm submerged under the water.

Question

If the weight of the ferry is 10,000 N, what is the maximum weight of the truck? (Assume the density of water is 1000 kg/m3.)

Answer 1

The key to this is determining the total volume of water displaced by the boat.

First, calculate the volume with the equation:

V=l*w*d;

V is volume, l is length, w is width, and d is depth

V=11m*12m*0.04m=5.28m³

Second, rearrange the density equation and solve for the total mass since we know the volume displaced.

Density=mass/volume

Mass=Density*volume

Total Mass=1000kg/m³*5.28m³=5280kg

Third, solve for the mass of the boat using Newton's Second Law: (Acceleration is 10 m/s²)

Force=Mass*Acceleration

Mass=Force/Acceleration

Boat Mass=10,000N/10m/s²=1000kg

Then solve for mass of just the truck:

Total Mass=Mass Truck+Mass Boat

Mass Truck=Total Mass-Mass Boat

Mass Truck=5280-1000kg=4280kg

Therefore the maximum weight of the truck is 4280kg.