Chapter 10, Problem 85A

To determine

To Explain: A planet orbiting the Sun does not violate the work energy theorem.

Explanation of Solution

Introduction:

Here it is true that there is no violation of work energy theorem.

Assume that the planet is rotating around the Sun in a circular orbit.

Gravitational force(F) acts on the planet due to the Sun, this gravitational force acts in normal direction with the direction of motion of the planet as shown in the figure.

So, the work done due to the gravitational force is,

  $W=\overrightarrow{F}\cdot \overrightarrow{r}=Fr\cos \theta$

Where, $\theta =90°$

So, $W=\overrightarrow{F}\cdot \overrightarrow{r}=Fr\cos 90°$ = 0

And $\overrightarrow{r}$ represents the direction of motion of the planet at a particular instant.

So, above expression says that here gravitational force F is a no work force.

So, there is no change in kinetic energy of the planet.

And from work energy theorem,

  $W=\Delta KE$

Where, $\Delta KE$ is the change in kinetic energy of the planet.

Since, $W=0$

So, $\Delta KE=0$

That is planet does not slow down or speed up during rotating in a circular orbit.

Conclusion:

Hence, the planet doesn’t violate the work energy theorem.