Another easy Conservation of Energy Question

In summary, the girl on the swing reaches a maximum height of 2m above the ground and a minimum height of .5m above the ground. Her maximum speed is attained at the bottom of the swing, with a value of 5.42 m/sec. This is because at the top of the swing, she has the most gravitational potential energy, and as she swings down, this energy is converted to kinetic energy. However, not all of it is converted, as she is always at least .5m from the ground. Using the equation v=sqrt(2ghmax), we can calculate her maximum speed at the bottom of the swing.
  • #1
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A girl swings back and forth on a swing with ropes that are 4.00 m long. The maximum height she reaches is 2 m above the ground. At the lowest point of the swing she is .5 m above the ground. (a) The girl attains the maximum speed (1)at the top, (2) in the middle, (3) at the bottom of the swing. Why? (b) What is the girl's maximum speed?



I think 1/2mv^2=mghmax then the M would cancel leaving 1/2v^2=ghmax. Then I ended up with v=square root of 2ghmax.

Well using that equation I keep getting 3.13 m/sec for the lowest point(.5 m) and 6.26 m/sec for the highest point(2 m). The answers are the bottom since the lower the potential energy the higher the kinetic energy. And the other answer is 5.42 m/sec. I'm pretty lost on this one...
 
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  • #2
OK, hopefully you should be able to see the answer to part (a) right off the bat. At the top of the swing she has the most gravitational potential energy, and the lower she goes in the swing, the more of it is converted to kinetic energy.

Not all of it is converted though, because she's always at least 0.5m from the ground.

So her kinetic energy at the bottom of the swing is equal to the change in GPE.

Have another go now and see if you can get it.
 
  • #3


I would like to clarify and provide a more detailed explanation for the answers. Firstly, the conservation of energy states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another. In this situation, the girl's energy is constantly being converted between potential energy and kinetic energy as she swings back and forth on the swing.

(a) The girl attains maximum speed at the bottom of the swing. This is because at the lowest point, all of the potential energy has been converted to kinetic energy, resulting in the highest speed. At the top of the swing, the potential energy is at its maximum and the kinetic energy is at its minimum, resulting in a lower speed.

(b) The girl's maximum speed can be calculated using the equation v=sqrt(2ghmax), where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and hmax is the maximum height reached (2 m). Plugging in these values, we get v=sqrt(2*9.8*2)=4.43 m/s. This is the maximum speed that the girl will reach during her swing.

I hope this explanation helps clarify the concept of conservation of energy and how it applies to this situation. It is important to remember that energy is always conserved, and it is simply converted between different forms as objects move and interact with each other.
 

Related to Another easy Conservation of Energy Question

1. What is Conservation of Energy?

Conservation of Energy is a fundamental principle in physics which states that energy cannot be created or destroyed, only converted from one form to another.

2. How does Conservation of Energy relate to this "easy" question?

This question is likely asking about a specific scenario or problem where the principle of Conservation of Energy can be applied to solve for an unknown quantity. It is considered "easy" because the concept is straightforward and the steps to solve it are relatively simple.

3. What are some real-life examples of Conservation of Energy?

Some common examples include a ball rolling down a hill (where potential energy is converted to kinetic energy), a pendulum swinging (where kinetic energy is converted to potential energy and back), or a car accelerating (where chemical energy from the fuel is converted to kinetic energy).

4. Why is Conservation of Energy important?

Conservation of Energy is important because it allows us to understand and predict the behavior of physical systems, from the smallest particles to the largest galaxies. It also helps us to design and optimize various technologies and processes, such as renewable energy sources.

5. Are there any exceptions to the principle of Conservation of Energy?

There are no known exceptions to the principle of Conservation of Energy in classical physics. However, in some extreme cases involving quantum mechanics or relativity, energy may appear to be "created" or "destroyed" but is actually just converted to a different form. Overall, the principle holds true for all everyday situations and is a fundamental law of the universe.

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