Question

A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into the river. What is the weight of the truck?

Answer 1

`F_w=9408\ N`

Weight of the truck=9408 N

Explanation:

Boat is experiencing the buoyant force as it is in the water and is sinking

According to the force balance in y direction. As both is floating, two forces balance each other:

`F_b-F_w=0`

where:

`F_b` is the buoyant force

`F_w` is the weight=mg

`F_b=F_w` Eq (1)

Buoyant force is equal to the mass of water displaced * gravitational acceleration.

`F_b=m_(water\ displaced)*g\\F_b=\rho Vg\\`

Taking density of water to be 1000 Kg/m^3

`F_b=1000*(6*4*4*10^(-2))*9.8\\F_b=9408 N`

From Eq(1):

`F_w=9408\ N`

Weight of the truck=9408 N