Pendulum Speed at Different Heights

In summary, the pendulum has an unknown mass and air resistance can be ignored. Its speed at the lowest point is 1.4 m/s.
  • #1
xasuma
8
0

Homework Statement


The pendulum shown (http://puu.sh/chwMZ/90f4b96fb1.png [Broken]) swings freely, turning around at a height of 10 cm above the lowest point in its swing. It has an unknown mass, but air resistance can be ignored.

a) Use energy conservation to find its speed at the lowest point of its swing.
b)What is the pendulum speed when it is at a height of only 1 cm above its lowest point?

Homework Equations


PE=mgh
V^2 = (2PE)/m

The Attempt at a Solution


I know I need to use the two equations above. But I don't know how. I can't understand how to do this problem. Therefore there is no attempted solution. I am not asking for a solution, I want to learn, but can someone explain to me what to do here?
 
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  • #2
Your second equation has basically already done most of the work for you, but you have to understand how to use it. In fact, I think that this equation will be more confusing to you than it will be helpful, so let's start with some simpler concepts.

Do you understand the concepts of Potential Energy and Kinetic Energy, and what IS this concept of "Energy conservation"?
 
  • #3
This is my understanding of it.
Potential energy is stored energy which has the potential to be released.
Kinetic energy is the energy an object has while in motion.
And energy conservation means that energy can change from potential to kinetic (or others) , since it can't be destroyed nor created.

I actually came up with the second equation by myself (I mean it wasn't given to me) .The problem I have is the mass. If the mass of the pendulum ball was given to me this would be no problem, but I can't get my head around it being unknown. I know that if air resistance is ignored, the acceleration would be 9.8m/s (if it were going straight down) but with the pendulum motion I get confused. I thought of the tension of the pendulum as well, drew a body diagram for the ball , but I just keep getting more confused.

Maybe the mass =1 , so it won't be important in this equation?
In that case I would say:
PE=9.8*0.1= 0.98N
v^2=(2*0.98)/1 = 1.96
v=1.4 m/sI don't really know though.
 
  • #4
PE=9.8*0.1= 0.98N
PE has units of energy: "Joules" (J); "Newtons" (N) are units of force.
You seem to have written PE = gh ... gh has units of m^2/s^2 - not N or J.
This is a clue and should clear up your confusion.

This is one place where doing all the algebra before you put numbers into the equations really pays off.
You've already figured out that all the gravitational PE lost at the top of the arc goes into kinetic energy at the bottom.
So just write out <the formula for kinetic energy> = <the formula for potential energy> and then cancel terms.
 
  • #5
I see,
so I got:
1/2mv^2 = mgh , solve for v (speed)

v^2 = 2gh
v^2 = 2*9.8*0.1
v= 1.4 m/s

---------------------

Now for B. The speed of the pendulum 1 cm above the lowest point.
I just changed 'h' from 0.1 to 0.09, did the same calculation as above and got:

v= 1.33 m/s

Did I do it right? I believe I get it :)
 
  • #6
It came out with the same answer - just for better reasons.
Well done - the thing about laying it out clearly like that is you end up with more confidence in your results.
Also notice that doing the algebra first gives you an equation that you can use in the next question with no extra work.

You can reality check your answers by thinking about the physics ... the v you calculated before was at the bottom of the swing - do you expect that the speed is faster or slower higher up? Is what you got consistent with that?
 

1. What is energy conservation?

Energy conservation refers to the practice of reducing energy consumption by using energy more efficiently and eliminating energy waste. It is the process of using less energy to achieve the same level of energy output, or achieving the same level of energy output while using less energy.

2. Why is energy conservation important?

Energy conservation is important for several reasons. Firstly, it helps to reduce our dependence on non-renewable energy sources such as fossil fuels, which are finite and contribute to climate change. Secondly, it can save individuals and businesses money on their energy bills. Lastly, it helps to preserve the environment and reduce our carbon footprint.

3. What are some ways to conserve energy?

There are many ways to conserve energy, including:

  • Turning off lights and electronics when not in use
  • Using energy-efficient appliances and light bulbs
  • Sealing air leaks in homes and buildings
  • Using public transportation, biking, or walking instead of driving
  • Planting trees to provide shade and reduce the need for air conditioning
  • Unplugging electronics when not in use to avoid energy vampires

4. How does energy conservation benefit the environment?

Energy conservation has several environmental benefits. It helps to reduce the emission of greenhouse gases, which contribute to climate change. It also helps to preserve natural resources, such as forests and water, which are often used to generate energy. Additionally, energy conservation can help to protect wildlife and their habitats by reducing the need for energy production and associated infrastructure.

5. What role can individuals play in energy conservation?

Individuals can play a significant role in energy conservation by making small changes in their daily habits, such as turning off lights and unplugging electronics when not in use. They can also choose to use energy-efficient products and support businesses and policies that prioritize energy conservation. Furthermore, individuals can educate themselves and others about the importance of energy conservation and take action to reduce their carbon footprint.

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