Help on Pendulum Homework: A1, A2, & Work Done

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In summary, the conversation discusses a problem with a pendulum of 1 meter in length and a bob with a mass of 1kg. The first question asks for the acceleration of the bob along the curve of its swing and the acceleration towards the center of rotation. The second question asks for the amount of work done to pull the pendulum back 12.7 degrees. The equations used include the sine and cosine functions and the Pythagorean theorem. The conversation also includes a diagram and a request for assistance in solving the problem.
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ataglance05
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Homework Statement


1) A pendulum 1 meter in length is pulled back 12.7 degress and the bob has a mass of 1kg. At the moment the bob is released, a)what's the acceleration in m/sec^2 of the bob along the curve of its swing and b)what is the acceleration toward the center of the bob's rotation?

2) For the pendulum in problem 1, how much work was done to pull the pendulum back 12.7 degrees?


Homework Equations


i think... to get the acceleration of bob along the curve of its swing...you use:
equationa1.jpg


and
equationa2.jpg


and a^2+b^2=c^2

The Attempt at a Solution


First, i drew the pendulum/free body diagram:
pendulum.jpg

My teacher said to just get a1, which is the acceleration of the bob along the curve of its swing, and a2, the other acceleration.

a)so...
a1=sin(77.3)=opposite/10
.9755=opposite/10
opposite=9.755

9.755^2+b^2=10^2
b^2=4.84
b=2.2
so a1=2.2m/sec^2

b)a2=cos(12.7)=adjacent/10
.9755=adjacent/10
adjacent=9.755

9.755^2+b^2=10^2
b^2=4.84
b=2.2
soa2=2.2m/sec^2

1) i don't think this is right since I get the same accelerations. please help?? Did i do it all right or can you help me solve this problem??

2) All I know is that I need to use the equation PE=mgh and where m is mass, g is gravitational acceleration, and h is the height and height=L((1-cos(theta)). The only thing I really know how to do is get h sine I'm not sure what is L. How do I get that??[/b] HELP ME!

THANK YOU!
 
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anyone?:confused:
 
  • #3



It looks like you have a good understanding of the equations and concepts involved in this problem. However, there are a few things that could be improved in your solution.

First, for part a) you are correct that you need to use the equation a1=sin(theta). However, the angle you should be using is not 77.3 degrees, but rather the angle of 12.7 degrees that the pendulum is pulled back to. So your calculation should be a1=sin(12.7)=0.22 m/sec^2.

For part b), you are correct in using the equation a2=cos(theta). However, the angle you should be using is not 12.7 degrees, but rather the angle of 77.3 degrees that the pendulum is released at. So your calculation should be a2=cos(77.3)=0.9755 m/sec^2.

As for the second problem, you are correct in using the equation PE=mgh to calculate the potential energy. However, the length of the pendulum, L, is given in the problem as 1 meter. So your calculation should be PE=(1kg)(9.8m/s^2)(1m)(1-cos(12.7))=0.09 J.

Overall, your understanding of the concepts and equations is good, but make sure to pay attention to the given angles and values in the problem to ensure accurate calculations.
 

1. What is a pendulum?

A pendulum is a weight suspended from a fixed point that is able to swing back and forth under the influence of gravity. It is commonly used in clocks and other timekeeping devices.

2. How do I calculate the period of a pendulum?

The period of a pendulum can be calculated using the equation T = 2π√(L/g), where T is the period (time for one swing), L is the length of the pendulum, and g is the acceleration due to gravity (9.8 m/s^2 on Earth).

3. What is the difference between A1 and A2 in pendulum homework?

A1 and A2 refer to the two different types of motion that a pendulum can have. A1 is when the pendulum swings back and forth in a straight line, while A2 is when it swings in a circular motion.

4. How do I find the work done by a pendulum?

The work done by a pendulum can be calculated using the equation W = mgh, where W is the work done, m is the mass of the pendulum, g is the acceleration due to gravity, and h is the height of the pendulum's swing.

5. What factors affect the motion of a pendulum?

The motion of a pendulum is affected by several factors, including the length of the pendulum, the mass of the bob (weight), the angle at which it is released, and the force of gravity.

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