Q68P - Fundamentals Of Physics

Question

An iceboat is at rest on a frictionless frozen lake when a sudden wind exerts a constant force of 200 N, toward the east, on the boat. Due to the angle of the sail, the wind causes the boat to slide in a straight line for a distance of 8.0 m in a direction 20 north of east. What is the kinetic energy of the iceboat at the end of that 8.0 m?

Step-by-Step Solution

Answer

The kinetic energy (K.E) of the iceboat is 1.5 kJ.

Step 1: Given information

It is given that,

1. The force exerted on the iceboat is $\mathrm{F}=200 \mathrm{N}$

The displacement of the iceboat is $\mathrm{d}=8.0$ in the direction 20 degrees north of east

Step 2: Determining the concept

This problem deals with the work-energy theorem which states that the net work done by the forces applied on object is equal to the change in its kinetic energy. Find the work done by the wind from the force using the corresponding formula. Then using the work-energy theorem, find the kinetic energy (K.E) of the iceboat.

Formulae:

 $$\begin{gathered} W=F.d \\ =Fd \cos \theta \end{gathered}$$

Work-energy theorem gives $\mathrm{W}=\mathrm{K}.\mathrm{E}.$

Where,

F is force, d is displacement, K.E. is change in kinetic energy and Wis the work done. 

Step 3 determining the kinetic energy (K.E) of the iceboat

The work done by the wind on the iceboat is,

 $$\begin{gathered} W=Fd \cos \theta \\ =\left(200\right)\left(8\right)\cos 20° \\ W=1504J \\ \approx 1.5 kJ \end{gathered}$$

Work energy theorem gives, $W=K.E$

$\mathrm{K}.\mathrm{E}=1504 \mathrm{J}$

Therefore, the kinetic energy (K.E) of the iceboat is $1.5 \mathrm{kJ}.$