# Kinetic and Potential energy pendulum problem

## Homework Statement

A 3-kg mass is attached to a light string of length 1.5 m to form a pendulum. The mass is given a initial speed of 4 m/s at its lowest position. When the string makes and angle of 30° with the vertical, find (a) the change in potential energy of the mass, and (B) the speed of the mass (c) What is the maximum height reached by the mass above its lowest point?

PE= mgy
KE=1/2mv^2

## The Attempt at a Solution

I was able to solve and get correct all parts of this problem except (a).I attempted to find the answer by finding the total energy using KE=1/2mv^2. I found the total energy to be 24 J. Then I found the height of the pendulum at 30 degrees by doing 1.5 cos 30°. Then I subtracted that value from 1.5 to find the height. I then did 3(9.8)(.2) to find the change in potential energy. I got 5.88 and the books answer says its 5.91 J.

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BiGyElLoWhAt
Gold Member
Have you tried simply using trig? Set up a right triangle with theta at the vertex of the pendulum.

EDIT* Oh wait..

Last edited:
BiGyElLoWhAt
Gold Member
I also got ~5.91 actually 5.908 but w/e.

(1.5m - 1.5cos(30))(3)(9.8)

But it's not actually .2, your difference comes from dropping off those decimal places. Wait until the very end to round.

BiGyElLoWhAt
Gold Member
You did it right. Just bad rounding.

tms
The answer in the book comes from retaining more than 2 significant figures from the result of the cosine. That is, the book set $1.5 - (1.5\; \cos 30^\circ)$ equal to 0.2009619$\ldots$ instead of 0.20, as you did. Both ways are acceptable, although I prefer keeping more figures in intermediate results.

OK I see what I did wrong. Thanks!