Proving the Law of Conservation of Energy Using a Pendulum

In summary, the conversation revolves around calculating the mechanical energy of a pendulum at two different positions, A and B, to determine if it demonstrates the law of conservation of energy. The mass of the pendulum, diameter of the bob, initial height, and length of the string are given. There is discussion about calculating the velocity and potential energy lost due to friction and air resistance. The importance of measuring the height at the center of gravity is also mentioned. There is a question about the weight of the pendulum string and its effect on the calculations.
  • #1
physicsgal
164
0
im suppose to do some calculations to prove whether or not the pendulum demonstrates the law of conservation of energy.

mass of pendulum = 240.3g = 0.2403 kg
diamter of pendulum bob = 3.50
initial height of pendulum bob = 48 cm = 0.48 m
length of pendulum string = 2.14 m
time interval of photogate light interruption = 11.8 m/s

so there's position 'A' and position 'B'
for 'A"
Emechanical = Ek + Eg
= (0.5)mv^2 + mgh
= 0 + (0.2403kg)(9.8)(0.48m)
= 1.13J

for 'B'
Emechanical = Ek + Eg
= (0.5)mv^2 + mgh
= (.5)(0.2403kg)(11.8^2) + 0
= 16.73J

i must be missing something (my calculations aint proving anything).. any help will be appreciated!

~Amy
 
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  • #2
Did you calculate the speed correctly? You list it as time but give units of speed, suggesting an error there. Furthermore, 12 m/s is pretty fast for a 2m long pendulum.
 
  • #3
k, i think i see the mistake! it says "11.8 ms" and i thought they meant meters per second.

so 11ms = 0.011s?

so for B i'd go:
Emechanical = Ek + Eg
= (0.5)mv^2 + mgh
= (.5)(0.2403kg)((d/0.011)^2) + 0 = 1.13

im short on time but will figure this out tomorrow and post my results.


~Amy
 
  • #4
just thought of something else. to find the velocity i just take the diameter of the bob divided by 11ms?

~Amy
 
  • #5
physicsgal said:
just thought of something else. to find the velocity i just take the diameter of the bob divided by 11ms?

so 11ms = 0.011s?

~Amy
Yes, but use the 11.8 ms as it was in your data. And yes, ms is milliseconds so 11.8 ms = .0118 s
 
  • #6
i changed all the units to regular units (meters, kg, s, etc.) just to play thing safe.

for Ek (A)
i got: mgh
= (0.2403kg)(9.8 m/s^2)(0.48m)
= 1.13J

for Eg (B)
i got: 0.5mv^2
=(0.5)(0.2403kg)(2.966^2)
=1.057J

(to get the 2.966 velocity i took 0.035/0.01185s).

and then i just explain that mechanical energy becomes heat energy so the total mechanical energy gradually decreases. ?

~Amy
 
  • #7
Yes, a certain amount of potential energy is lost to friction and air resistance, although 6% may be a little high. All measurements have uncertainty or inaccuracy, and that will also be a factor. One final question: when you measured the height of the pendulum, did you measure at the center of the weight at both positions A and B? It's important to measure the heights at the center of gravity.
 
  • #8
i didnt do any of the measurements myself. I am taking an independent learning course, and the measurements are listed in the book, I am just suppose to do some qualculations and write a lab report explaining why and whether or the pendulum lab demonstrates the law of conservation of energy.

slight ot: does the weight of the pendulum string make a difference? like a light weight vs. a heavy one?

~Amy
 
  • #9
physicsgal said:
i didnt do any of the measurements myself. I am taking an independent learning course, and the measurements are listed in the book, I am just suppose to do some qualculations and write a lab report explaining why and whether or the pendulum lab demonstrates the law of conservation of energy.
Got it. Thanks!

physicsgal said:
slight ot: does the weight of the pendulum string make a difference? like a light weight vs. a heavy one?

~Amy
Good question. What do think?
 
  • #10
shouldnt the string weight be added to the bob weight?

~Amy
 
  • #11
Not exactly, because it isn't in the same place. Think about where its center of gravity (COG) is and where the bob's is. Any ideas on how you would add the string's mass to your problem?
 

FAQ: Proving the Law of Conservation of Energy Using a Pendulum

How does a pendulum demonstrate the Law of Conservation of Energy?

A pendulum is a physical system that consists of a mass (bob) attached to a string or rod, which is fixed at a pivot point. When the bob is pulled to one side and released, it swings back and forth, converting potential energy into kinetic energy and back again. This continuous back-and-forth motion demonstrates the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed from one form to another.

What are the different forms of energy involved in a pendulum's motion?

In a pendulum, the potential energy is stored in the gravitational field as the bob is lifted to a higher position. As it falls back down towards its resting position, this potential energy is converted into kinetic energy, which is the energy of motion. The pendulum's energy constantly oscillates between these two forms as it swings back and forth, but the total amount of energy remains constant.

How can we measure the energy of a pendulum?

The energy of a pendulum can be measured using the formula E = mgh, where m is the mass of the bob, g is the acceleration due to gravity, and h is the height of the pendulum. This formula calculates the potential energy of the system. The kinetic energy can be calculated using the formula E = 1/2mv^2, where v is the velocity of the pendulum.

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

The length of a pendulum has a direct relationship with its energy. As the length of the pendulum increases, so does its potential energy. This is because longer pendulums have a greater distance to fall, resulting in a higher potential energy. The kinetic energy, however, remains the same regardless of the pendulum's length, as it is dependent on the mass and velocity of the bob.

Can a pendulum ever lose energy?

In theory, a pendulum will continue to swing forever without losing any energy, as there is no external force acting on it. However, in reality, pendulums will eventually lose small amounts of energy due to air resistance and friction at the pivot point. This loss of energy is negligible and does not affect the overall demonstration of the Law of Conservation of Energy.

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