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

Answer:

$F_w=9408\ N$

Weight of the truck=9408 N

Step-by-step 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