Question

Question 1 of 32A pendulum is raised to a certain height and released from point A, as shownin the image below. At its release, the pendulum is also given an initialvelocity of 14 m/s. Assuming that the effects of friction and air resistancecan be ignored, what will be the maximum height that the pendulum canreach – that is , what is the height at point B? (Recall that g = 9.8 m/s2.)BA10 mA. 20 mB. 30 mC. 25 mD. 45 m

Answer 1

Given:

The velocity of the bob is

$v=14\text{ m/s}$

The height of the bob when it is at point A is

$h=10\text{ m}$

Required: the new height attained by the bob.

Explanation:

to solve this problem we will apply conservation of energy here.

total energy at point A = total energy at point B.

when the pendulum bob is at A it has kinetic as well as potential energy while when it is at point B it has only potential energy.

apply conservation of energy, we get:

$\begin{gathered} K.E+P.E=P.E \\ \frac{1}{2}mv^2+mgh=mgd \end{gathered}$

where d is the new height.

plugging all the values in the above relation, we get

$\begin{gathered} \frac{1}{2}v^2+gh=gd \\ \frac{1}{2}\times(14\text{ m/s})\times^(14\text{ m/s})+9.8\text{ m/s}^2\times10\text{ m}=9.8\text{ m/s}^2\times d \\ d=\frac{196}{9.8} \\ d=20\text{ m} \end{gathered}$

Thus, the height at the point B is

$20\text{ m}$