Calculating Maximum Height and Equilibrium Height of Pendulum with Wind Force

In summary, a ball of mass 300 g is attached to a pivot by a string and is acted upon by a constant force F. When released, the ball swings up to a maximum height Hmax before swinging back down. The equations for finding Hmax and the equilibrium height of the ball with wind blowing are requested. The work done by F can be expressed as F multiplied by the displacement in the direction of the force.
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John John
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Homework Statement


A ball of mass m = 300 g is connected by a strong string of length L = 80.0 cm to a pivot and held in place with the string vertical. A wind exerts constant force F to the right on the ball as in the figure below. The ball is released from rest. The wind makes it swing up to attain maximum height Hmax above its starting point before it swings down again.



Homework Equations


(a) Find Hmax as a function of F.
(f) Now consider the equilibrium height of the ball with the wind blowing. Determine it as a function of F.



The Attempt at a Solution


The work done by F is equal to the balls potential energy at height H, but how do I express that work?
 
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  • #2
F*[the displacement in the direction of that force]?
 

Related to Calculating Maximum Height and Equilibrium Height of Pendulum with Wind Force

1. How does wind affect the motion of a pendulum?

Wind can affect the motion of a pendulum by creating air resistance or drag as the pendulum swings back and forth. This can cause the pendulum to slow down or change its direction, impacting its period and amplitude.

2. Can wind change the period of a pendulum?

Yes, wind can affect the period of a pendulum by adding or subtracting energy from the system. If the wind is blowing in the same direction as the pendulum's swing, it can add energy and decrease the period. If the wind is blowing in the opposite direction, it can subtract energy and increase the period.

3. How does the length of the pendulum affect its motion in the wind?

The length of the pendulum does not directly affect its motion in the wind. However, a longer pendulum will have a longer period, meaning it will take more time for the pendulum to complete one swing. This can make it more susceptible to changes in energy caused by wind.

4. Can wind affect the accuracy of a pendulum clock?

Yes, wind can affect the accuracy of a pendulum clock by changing the period of the pendulum. If the wind adds or subtracts energy from the pendulum, it can cause the clock to run slower or faster than it should. This is why pendulum clocks often have protective cases to shield them from wind.

5. Is there a specific wind speed that will stop a pendulum from swinging?

There is no specific wind speed that will stop a pendulum from swinging. However, as wind speeds increase, the effects of air resistance become more significant and can eventually overcome the pendulum's motion. The exact wind speed at which this occurs will depend on factors such as the weight and length of the pendulum.

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