Alarge cruise ship of mass 6.40 ✕ 107 kg has a speed of 11.6 m/s at some instant. (a) what is the ship's kinetic energy at this time? j (b) how much work is required to stop it? (give the work done on the ship. include the sign of the value in your answer.) j (c) what is the magnitude of the constant force required to stop it as it undergoes a displacement of 3.20 km? n

(a)

The kinetic energy of an object is given by:

where

m is the mass of the object

v is its speed

For the ship in the problem, we have

is the mass

is the speed

So its kinetic energy is

(b)

According to the work-kinetic energy theorem, the work done on an object is equal to the change in kinetic energy of the object:

where

W is the work done

m is the mass of the object

v is the final speed of the object

u is the initial speed of the object

Here we want to find the work done to stop the ship, so the final speed of the ship is v=0, while the initial speed is u=11.6 m/s. So the work done will be

(c)

The work done on an object can be also written as follows

where

F is the magnitude of the force

d is the displacement of the object

Here we know:

is the work done

d = 3.20 km = 3200 m is the displacement of the ship

So we can solve the formula to find F, the force exerted on the ship to stop it:

and the negative sign simply means that the force is opposite to the displacement of the ship (in fact, the force acts against the motion of the ship).