Question

A pendulum is used in a large clock. The pendulum has a mass of 2 kg. If the pendulum is moving at a speed of 2.9 m/s when it reaches the lowest point on its path, what is the maximum height of the pendulum?

Answer 1

This is a classic example of conservation of energy. Assuming that there are no losses due to friction with air we'll proceed by saying that the total energy mus be conserved.
$E_m=E_k+E_p$
Now having information on the speed at the lowest point we can say that the energy of the system at this point is purely kinetic:
$E_m=Ek=\frac{1}{2}mv^2$
Where m is the mass of the pendulum. Because of conservation of energy, the total energy at maximum height won't change, but at this point the energy will be purely potential energy instead.
$E_m=E_p$
This is the part where we exploit the Energy's conservation, I'm really insisting on this fact right here but it's very very important, The totam energy Em was
$E_M=\frac{1}{2}mv^2$
It hasn't changed! So inserting this into the equation relating the total energy at the highest point we'll have:
$E_p=mgh=E_m=\frac{1}{2}mv^2$
Solving for h gives us:
$h=\frac{v^2}{2g}.$
It doesn't depend on mass!

Answer 2

Answer:The maximum height of the pendulum is 0.4290 m.

Explanation:

Mass of pendulum = 2kg

Speed of the pendulum = 2.9 m/s

Kinetic energy at the lowest point is equal to the potential energy at the highest point.

$K.E=P.E$

$\frac{1}{2}mv^2=mgh$

$\frac{1}{2}v^2=g\times h$

$h=\frac{1}{2\times g}v^2=0.4290 m$

The maximum height of the pendulum is 0.4290 m.