Solving for the velocity of a Pendulum

In summary, the conversation discusses the speed of a 2 kg pendulum at the bottom of its swing, with options of 6.2 m/s, 60 m/s, 10 m/s, 7.7 m/s, and 40 m/s. The correct answer depends on the length of the pendulum and the initial height above the lowest point of the swing. The correct answer is most likely 6.2 m/s, with 40 m/s being a possible answer if the initial height is 2 m. Answer (e) is included to account for forgetting to take the appropriate square root.
  • #1
momoneedsphysicshelp
23
2
Homework Statement
A 2 kg pendulum is raised to an angle of 53 degrees relative to the vertical, as shown below, and released from rest. What is the speed of the mass at the bottom of its swing?
Relevant Equations
6.2 m/s
60 m/s
10 m/s
7.7 m/s
40 m/s
I think the answer is 6.2 but I also got 40m/s. Which one is right?
 
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  • #2
momoneedsphysicshelp said:
Homework Statement:: A 2 kg pendulum is raised to an angle of 53 degrees relative to the vertical, as shown below, and released from rest. What is the speed of the mass at the bottom of its swing?
Relevant Equations:: 6.2 m/s
60 m/s
10 m/s
7.7 m/s
40 m/s

I think the answer is 6.2 but I also got 40m/s. Which one is right?
Depends on the length of the pendulum.
Please post your working.
 
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  • #3
Also, please post the picture that is supposed to be "shown below". Maybe it shows the initial height above the lowest point of the swing. If it's 2 m (as I suspect), the correct answer for the speed is (a). Answer (e) is included to catch those who forget to take the appropriate square root. Answers may vary slightly depending on what number you use for the acceleration of gravity.
 
Last edited:

What is the formula for calculating the velocity of a pendulum?

The formula for calculating the velocity of a pendulum is v = √(gL(1-cosθ)), where v is the velocity, g is the acceleration due to gravity, L is the length of the pendulum, and θ is the angle of displacement.

How do you determine the length of a pendulum?

The length of a pendulum can be determined by measuring the distance from the point of suspension to the center of mass of the pendulum. It is important to measure from the center of mass, as this is the point that will be swinging back and forth.

What is the role of gravity in calculating the velocity of a pendulum?

Gravity plays a crucial role in determining the velocity of a pendulum. The acceleration due to gravity, denoted as g, is used in the formula for calculating velocity. This is because gravity is the force that causes the pendulum to swing back and forth.

Can the velocity of a pendulum be increased?

Yes, the velocity of a pendulum can be increased by increasing the length of the pendulum or the angle of displacement. However, this also depends on the initial conditions and the forces acting on the pendulum.

What factors can affect the accuracy of the calculated velocity of a pendulum?

The accuracy of the calculated velocity of a pendulum can be affected by factors such as air resistance, friction, and the precision of the measurement of length and angle. These factors can introduce errors in the calculations and should be taken into consideration for more accurate results.

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