Pendulum Problem: Calculate Initial Speed of Actor

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In summary, an actor with a mass of 65.0 kg attaches himself to a cable with a length of 5.00 m to make a grand entrance onto a stage. He is given an initial speed at a height of 1.5 m above the lowest point of his motion and swings through the lowest point with a speed of 6 m/s. To find the initial speed of the actor, use the conservation of energy principle by considering the actor's initial and final kinetic energies and potential energy at the lowest point. The details about the pendulum may not be necessary for this problem.
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KCEWMG
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Homework Statement [/b]
An actor of mass 65.0 kg wishes to make a grand entrance onto a stage during a play. He attaches himself to a cable having length R=5.00 m. A stagehand gives the actor a push, imparting an initial speed onto the actor at heigh 1.5 m above the lowpoint of his ensuing motion. As the actor swings through the lowest point of his motion, his speed is 6 m/s. Length R remains Constant. What is the initial speed of the actor?




The attempt at a solution[/b]
I think I have literally tried everything. I attempted to find theta between the two points and, if done correctly, got that to be 25.8 degrees. I then tried finding arc length, which came out to a crazy number. Then I tried using angular acceleration equations. THEN I tried calculating it using K+U(initial)=K+U(final), but I ran into troubles there when it came to "y".
 
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  • #2
Look at the problem from an energy conservation standpoint. You have an unknown initial KE. You have a known final KE. You can determine the change in PE.
 
  • #3
You can tackle this by considering PE and KE. When the actor is pushed he is given some KE and he also has some PE relative to the lowest point (1.5m) of his swing
KE = 0.5mv^2 PE = mgh
At the lowest point he has KE
The details about the pendulum seem to be irrelevant unless you have been asked something else
 

1. How do I calculate the initial speed of an actor in a pendulum problem?

To calculate the initial speed of an actor in a pendulum problem, you will need to use the formula v = √(gL(1-cosθ)), where v is the initial speed, g is the acceleration due to gravity, L is the length of the pendulum, and θ is the initial angle of the pendulum. Plug in the values and solve for v to get the initial speed of the actor.

2. What is the significance of the initial speed in a pendulum problem?

The initial speed in a pendulum problem is important because it determines the maximum height the pendulum will reach and the maximum speed it will achieve during its swing. It also affects the period of the pendulum, which is the time it takes for the pendulum to complete one full swing.

3. How does the length of the pendulum affect the initial speed in a pendulum problem?

The length of the pendulum directly affects the initial speed in a pendulum problem. The longer the pendulum, the longer it will take for the pendulum to complete one full swing, resulting in a slower initial speed. On the other hand, a shorter pendulum will have a faster initial speed.

4. Can the initial speed in a pendulum problem be negative?

Yes, the initial speed in a pendulum problem can be negative. This usually means that the pendulum is initially swinging in the opposite direction from its rest position. It is important to pay attention to the direction of the initial speed when solving pendulum problems.

5. How does the initial angle of the pendulum affect the initial speed in a pendulum problem?

The initial angle of the pendulum has a significant impact on the initial speed in a pendulum problem. A larger initial angle will result in a faster initial speed, while a smaller initial angle will result in a slower initial speed. This is because a larger initial angle results in a greater potential energy, which is then converted into kinetic energy as the pendulum swings.

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