Speed of a pendulum at lowest point

In summary, the task is to find the speed of a pendulum bob at the lowest point of the swing, given an initial angle of displacement of θ=5.7° and a period of 2.5 seconds. Using the equations for kinetic energy, period, potential energy, and displacement, the length of the pendulum is first found to be 1.552 m. Plugging this into the final equation, the calculated speed is found to be 2.244 m/s. However, after realizing that the calculator was not set to degrees, the correct answer is determined to be 0.388 m/s.
  • #1
skate_nerd
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Homework Statement



I am told to find the speed of a pendulum bob at the lowest point of the swing where the initial angle of displacement is θ=5.7° and the period of the pendulum is 2.5 seconds.

Homework Equations



K.E.=.5mv2, T=2∏√(L/g), P.E.=mgh, h=L-Lcosθ=L(1-cosθ)

The Attempt at a Solution



So I found the length of the pendulum first by plugging in 9.81 m/s2 for g and 2.5 s for T into the equation T=2∏√(L/g) to get 1.552 m.

Next, we know that the height displacement in a pendulum bob is equal to L-Lcosθ, so I plug this into P.E.=mgh, and also from conservation of energy we know P.E. can be set as .5mv2, so the final equation I used is:
v=√(2gL(1-cosθ))=√(2(9.81)(1.553(1-cos(5.7)))) which got me the answer v=2.244 m/s.

However the answer is apparently v=0.388 m/s. My teacher is kind of notorious for being wrong a lot of the time, so if somebody could let me know which answer is right and why that would be awesome, thanks.
 
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  • #2
Did you set your calculator to degrees (DEG) to calculate sin(5.7°)?
 
  • #3
Wow I feel stupid. Got the answer now, thanks.
 

FAQ: Speed of a pendulum at lowest point

1. What is the equation for calculating the speed of a pendulum at its lowest point?

The equation for calculating the speed of a pendulum at its lowest point is v = √(2gh), where v is the speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the pendulum.

2. Does the length of the pendulum affect its speed at the lowest point?

Yes, the length of the pendulum does affect its speed at the lowest point. According to the equation v = √(2gh), the speed is directly proportional to the square root of the length of the pendulum. This means that a longer pendulum will have a higher speed at its lowest point compared to a shorter pendulum.

3. How does the mass of the pendulum affect its speed at the lowest point?

The mass of the pendulum does not affect its speed at the lowest point. The speed of a pendulum at its lowest point is only dependent on its length and the acceleration due to gravity. This is because the mass of an object does not affect its acceleration due to gravity.

4. What factors can change the speed of a pendulum at its lowest point?

The only factors that can change the speed of a pendulum at its lowest point are the length of the pendulum and the acceleration due to gravity. Any changes in these factors will result in a change in the speed of the pendulum at its lowest point.

5. Can the speed of a pendulum at its lowest point be greater than the initial speed?

No, the speed of a pendulum at its lowest point cannot be greater than the initial speed. This is because of the conservation of energy principle, where the total energy of a system remains constant. At the lowest point, all of the potential energy of the pendulum is converted into kinetic energy, so the speed at this point cannot be higher than the initial speed.

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