We're given that the length of the string is L.
The change in height is Δh
Let's consider Δh to be the height that the bob rises when it makes an angle of θ with the vertical.
Diagrammatically, we have:
Suppose a pendulum bob is suspended from a pivot by a massless string of length L, measured to the center of the bob.
a) Show that if I draw the pendulum back by an angle θ, the center of the bob is elevated by the distance
delta (h) = L(1-cosθ) = 2Lsin^2(θ/2)
b)Using the results of part (a), show that the speed of the pendulum bob at the bottom of its travel should be
v = 2√gl * sin(θ/2)
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Pendulum Problems concept. You can view video lessons to learn Pendulum Problems. Or if you need more Pendulum Problems practice, you can also practice Pendulum Problems practice problems.