Is it possible to carry a car weighing 3 tons across the river on a raft made of 15 pine logs with a volume of 2m3 each?

Given:

V = 2 cubic meters – the volume of a pine log;

n = 15 – the number of pine logs in the raft;

ro = 500 kg / m3 is the density of the pine tree;

ro1 = 1000 kg / m3 – water density;

g = 10 m / s2 – free fall acceleration;

m1 = 3 tons = 3000 kilograms – vehicle weight.

It is required to determine whether it is possible to transport a car across the river on a raft.

In order to transport a car across the river, the Archimedean force acting on the raft must be greater than the force of gravity acting on the raft along with the car.

Let’s find the force of gravity:

F = (m + m1) * g, where m1 is the mass of the raft;

F = (m + n * V * ro) * g = (3000 + 500 * 15 * 2) * 10 =

= (3000 + 15000) * 10 = 18000 * 10 = 180000 Newton.

Let’s find the Archimedean force:

A = n * V * g * ro1 = 15 * 2 * 10 * 1000 = 30 * 10 * 1000 = 300000 Newtons.

Since A> F (300,000> 180,000), the car can be transported across the river.

Answer: The car can be transported across the river on a raft.