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.

Step-by-step 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 \\ (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} (1)/(2)v^2+gh=gd \\ (1)/(2)*(14\text{ m/s})*^(14\text{ m/s})+9.8\text{ m/s}^2*10\text{ m}=9.8\text{ m/s}^2* d \\ d=(196)/(9.8) \\ d=20\text{ m} \end{gathered}`

Thus, the height at the point B is

`20\text{ m}`