Chapter 14, Problem 94A

(a)

To determine

The time taken by P to complete one full swing using a 10m long rope.

Answer to Problem 94A

Time is $6.34\text{s}$ .

Explanation of Solution

Given:

The length of the rope, $l=10\text{ m}$ ,

Formula used:

  $T=2\pi \sqrt{\frac{l}{g}}$    .......(1)

Here, $T$ is the time period of the pendulum, $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Calculation:

Substituting $10\text{ m}$ in $l$ and $9.8{\text{ m/s}}^2$ in $g$ in equation (1),

  $\begin{array}{l}T=2\pi \sqrt{\frac{10}{9.8}}\\ T=6.34\text{ s}\end{array}$

Conclusion:

Hence, the time is $6.34\text{s}$ .

(b)

To determine

The difference of period of P and Mike.

Explanation of Solution

Given:

The length of the rope, $l=10\text{ m}$ .

It is assumed that, the weight of P be x , then weight of Mike is $x+20$ .

Formula used:

  $T=2\pi \sqrt{\frac{l}{g}}$    .......(1)

Here, $T$ is the time period of the pendulum, $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Calculation:

(b) There is no difference in time period of Mike and P as the mass persons would not effect the time period.

Conclusion:

Hence, no difference is found.

(c)

To determine

The point at which the KE is maximum.

Explanation of Solution

Given:

The length of the rope, $l=10\text{ m}$ .

Formula used:

  $T=2\pi \sqrt{\frac{l}{g}}$    .......(1)

Here, $T$ is the time period of the pendulum, $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Calculation:

The KE or kinetic energy is maximum at the bottom of the swing.

Conclusion:

Hence, KE will take maximum value.

(d)

To determine

The point at which the potential difference is maximum.

Explanation of Solution

Given:

The length of the rope, $l=10\text{ m}$ ,

Formula used:

  $T=2\pi \sqrt{\frac{l}{g}}$    .......(1)

Here, $T$ is the time period of the pendulum, $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Calculation:

The PE or potential energy is maximum at the top point of the swing.

Conclusion:

Hence, potential difference will take maximum values.

(e)

To determine

The point at which the KE is minimum.

Explanation of Solution

Given:

The length of the rope, $l=10\text{ m}$ ,

Formula used:

  $T=2\pi \sqrt{\frac{l}{g}}$    .......(1)

Here, $T$ is the time period of the pendulum, $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Calculation:

The KE or kinetic energy is minimum at the top point of the swing.

Conclusion:

Hence, the required answer are given above.

(f)

To determine

The point at which the potential energy is minimum.

Explanation of Solution

Given:

The length of the rope, $l=10\text{ m}$ ,

Formula used:

  $T=2\pi \sqrt{\frac{l}{g}}$    .......(1)

Here, $T$ is the time period of the pendulum, $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Calculation:

The PE or potential energy is minimum at the bottom point of the swing.

Conclusion:

Hence, the potential energy will take minimum value.