Calculating Pendulum Bob Properties: Mass 500g, Length 2m, 10° Displacement

In summary: This amount of error is within the limits of the experiment.In summary, a 500g mass is used as a pendulum bob with a length of 2m and an angle of 10 degrees. The pendulum is 0.03m above its original position, has a magnitude of 0.15J of energy, and a maximum speed of 0.77m/s when released. The formula used for calculations are L-Lcos0 for A, GPE=mgh for B, and v=squareroot of 2gh for C. 10 degrees is not too large of an oscillation for a simple pendulum as the resulting error is within experimental limits.
  • #1
ThenewKid
3
0
1. A mass of 500g is used as a pendulum bob so that it forms a pendulum that is 2meters long. The pendulum is displaced from its rest position by an angle of 10 degrees.
A. How high is the pendulum bob above its original position?
B. What is the magnitude of the energy that the pendulum bob possesses in this position?
C. What is the maximum speed of the the pendulum bob when it is released.



2. GPE= Weight x Height mgh
Ke= 1/2mv2
v=squareroot of 2gh
L-Lcos0

3. For A I used the L-Lcos0 equation and got -3.35m. Pretty sure that's wrong.
For B I used GPE=mgh and got 9.8 for the magnitude. Pretty sure this is correct.
For C I used v=squareroot of 2gh and got 6.26m/s as the maximum speed. Positive this is correct.

God, this homecourse really does not give much to go on...jeez.
 
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  • #2
Isn't 10 degrees too large of an oscillation for it to be simple pendulum?
 
  • #3
A you hsve the right idea but have the numbers wrong - draw a diagram
B,C use PE and KE = correct
 
  • #4
1.A. h= 2m-(cos10*2m)
h=.03m

B. gpe=(.5kg)(9.8m/s^2)(.03m)
GPE=.15J

C. .15J=(.25kg)(v^2)
√(.6)=v
.77m/s=v
 
  • #5
malty said:
Isn't 10 degrees too large of an oscillation for it to be simple pendulum?

At 10 degrees the value for period is only about one quarter of a percent off the real value.
 

FAQ: Calculating Pendulum Bob Properties: Mass 500g, Length 2m, 10° Displacement

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

The formula for calculating the period of a pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s²).

How does the mass of the pendulum bob affect its period?

The mass of the pendulum bob does not affect its period. The formula for calculating the period of a pendulum does not include the mass of the bob. However, a heavier bob will have a slightly higher center of mass which can affect the accuracy of the pendulum's swing.

What is the relationship between the length of a pendulum and its period?

The length of a pendulum is directly proportional to its period. This means that as the length of the pendulum increases, the period also increases. This relationship is described by the formula T = 2π√(L/g), where T is the period and L is the length of the pendulum.

How does the angle of displacement affect the period of a pendulum?

The angle of displacement does not have a significant effect on the period of a pendulum. The formula for calculating the period of a pendulum assumes small angles of displacement (less than 5°). However, for larger angles, the period may slightly increase due to the pendulum's swinging motion becoming more elliptical rather than purely back and forth.

Can the properties of a pendulum be used to measure gravity?

Yes, the properties of a pendulum can be used to measure gravity. By measuring the length and period of a pendulum, the acceleration due to gravity can be calculated using the formula g = 4π²L/T². This method is known as a pendulum-based gravimeter and is commonly used in scientific experiments.

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