Question

A pendulum is made by lettting a 2.0kg object swing at the end of a string that has a length of 1.5m. The maximum angle the string makes with the vertical as the pendulum swings is 30 degrees. What is the speed of the object at the lowest point in its trajectory?

a) 2.0 m/s

b) 2.2 m/s

c) 2.5 m/s

d) 2.7 m/s

e) 3.1 m/s

PLEASE SHOW ME THE WORK? :)

Answer 1

At the lowest point pendulum will only have kinetic energy and the max angle pendulum will only have potential energy.

So using energy conservation

KEi + PEi = KEf + PEf

KEf = 0

PEi = 0

0.5*m*Vi^2 = m*g*h

h = vertical height b/w lowest and highest point

L = length of pendulum, then

cos 30 deg = H/L

H = L*cos 30

H = vetical height between center and highest point of pendulum

h = L - H

h = L - L*cos 30 deg = 1.5 - 1.5*cos 30 deg = 0.20 m

Now

Vf = sqrt (2*g*h)

Vf = sqrt (2*9.81*0.2) = 1.98 m/sec = 2.0 m/sec

Correct option is A.

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