blakemartel09
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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?

Respuesta :

Hummingbeard
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.
[tex]E_m=E_k+E_p[/tex]
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:
[tex]E_m=Ek=\frac{1}{2}mv^2[/tex]
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.
[tex]E_m=E_p[/tex]
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
[tex]E_M=\frac{1}{2}mv^2[/tex]
It hasn't changed! So inserting this into the equation relating the total energy at the highest point we'll have:
[tex]E_p=mgh=E_m=\frac{1}{2}mv^2[/tex]
Solving for h gives us:
[tex]h=\frac{v^2}{2g}. [/tex]
It doesn't depend on mass!

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.

[tex]K.E=P.E[/tex]

[tex]\frac{1}{2}mv^2=mgh[/tex]

[tex]\frac{1}{2}v^2=g\times h[/tex]

[tex]h=\frac{1}{2\times g}v^2=0.4290 m[/tex]

The maximum height of the pendulum is 0.4290 m.

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