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=(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=(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=(1)/(2)mv^2`
Solving for h gives us:

`h=(v^2)/(2g).`
It doesn't depend on mass!

Answer 2

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

Step-by-step 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`

`(1)/(2)mv^2=mgh`

`(1)/(2)v^2=g* h`

`h=(1)/(2* g)v^2=0.4290 m`

The maximum height of the pendulum is 0.4290 m.