# Find the speed at the bottom of it's swing

• Dark Visitor
In summary, a simple pendulum with a length of 2 meters is released with an initial velocity from an angle of 25 degrees from the vertical. Using conservation of energy, the speed at the bottom of the swing can be found by calculating the change in height from the geometry and the potential energy. The final speed is found to be 2.3 m/s.
Dark Visitor
A simple pendulum, 2 m in length, is released with a push (i.e. - it has an initial velocity) when the support string is at an angle of 25 degrees from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, use conservation of energy to find it's speed at the bottom of the swing.

* 2.3 m/s
* 2.6 m/s
* 2 m/s
* .5 m/s

I don't really understand how to use conservation of energy that well, so I need help. How would I apply that for this problem? And how do I solve from there? Any help would be much appreciated. I need it by tomorrow night. Thanks.

Do you understand what would happen if there were no push? Energy is continually transferred back and forth between kinetic and potential, but the sum is constant at all times.

First, find the height of the bob above its position at the bottom from the geometr, ie the vertical displacement between 25 degrees and vertical.

Keep track of what the item's total energy is (PE+KE) and this cannot change. At the bottom of the swing all the energy is kinetic (since it's convenient to define PE=0 at the bottom of the swing in this case). :)

What do you mean by the bob and geometer? And I would think the height would always remain 2 m due to the length.

To Matterwave: You're saying that at the bottom when PE = 0, that KE will still equal all of the energy that was there when PE did not equal 0?

Dark Visitor said:
What do you mean by the bob and geometer? And I would think the height would always remain 2 m due to the length.

To Matterwave: You're saying that at the bottom when PE = 0, that KE will still equal all of the energy that was there when PE did not equal 0?

er sorry, that was meant to be geometry and the bob is just the mass on the end. The change in height is given by L(1-cos(25)). Can you see why?

The kinetic energy at the bottom will be the sum of the kinetic energy from the push plus the potential energy from it being displaced by 25 degrees, see above.

It's okay. Well, I see that the cos25 gives me the length on the "x axis" of the pendulum when it is at the 25 degree angle, but I don't know where the 1 comes in, or what L stands for, unless it is length.

Dark Visitor said:
It's okay. Well, I see that the cos25 gives me the length on the "x axis" of the pendulum when it is at the 25 degree angle, but I don't know where the 1 comes in, or what L stands for, unless it is length.
Right L is length = 2m. I'll post a pic here in a minute.

Okay, I think I understand a little more. So the length won't be 2 meters anymore. It will be:
2 m(1 - cos25), which makes it a lot smaller.

My question now is how does this help me get the final speed?

The displacement of the bob vertically is given by L - L(cos(25))=L(1-cos(25))

The potential energy is mgh where h is described as L(1-cos(25)). The total energy is the initial kinetic from the push (1/2mV^2) + the potential energy (mgh). That do it?

Yes, quite a bit. One thing I still don't get is how we can use either of those when we don't have the mass (m) for the equations. Do we assume anything, or do we need to find it?

OOps, I forgot what we we're trying to calculate. Well since all masses fall at the same rate, it doesn't matter. Just add the velocity it would have attained if dropped from that height. Different ways to get this, but V'^2=V^2+2(g*h) is the most straight froward at this point. V' is the final velocity, v is the initial.

Okay:

vf2 = vi2 + 2(g)(h)
= (1.2)2 + 2(9.8)(.1874)
= 5.11304

Then I square-rooted that and got 2.2612, which 2.3 m/s is an answer.

Good job.

Thanks, and thanks for all the help. I really appreciate it. If you have some free time to spare, please help me on some of my other posts. I got a lot of them, and not many people helping me. If you can't, it's fine. Thanks.

Dark Visitor said:
Thanks, and thanks for all the help. I really appreciate it. If you have some free time to spare, please help me on some of my other posts. I got a lot of them, and not many people helping me. If you can't, it's fine. Thanks.

Sure I'll look for them--must be a sunday, things are humming here. ;-D

Yeah. I posted most yesterday to allow time for people to see them and respond, but didn't happen too much. Fortunately, I still have time to complete them all.

## 1. What does "Find the speed at the bottom of its swing" mean?

"Find the speed at the bottom of its swing" refers to determining the velocity of an object at the lowest point of its swinging motion. This can be calculated using the object's mass, length of the swing, and the force of gravity.

## 2. Why is it important to find the speed at the bottom of its swing?

Knowing the speed at the bottom of an object's swing can provide important information about its energy, momentum, and trajectory. This can be useful in understanding the behavior of pendulums, as well as other swinging objects.

## 3. How do you calculate the speed at the bottom of its swing?

The speed at the bottom of an object's swing can be calculated using the formula v = √(2gh), where v is the velocity, g is the acceleration due to gravity, and h is the height of the swing at its lowest point.

## 4. Can the speed at the bottom of its swing be different from the speed at the top?

Yes, the speed at the bottom of its swing can be different from the speed at the top. This is because the object's speed is affected by the force of gravity, which increases as the object moves closer to the ground. Therefore, the object will have a higher speed at the bottom of its swing compared to the top.

## 5. How does the length of the swing affect the speed at the bottom of its swing?

The length of the swing affects the speed at the bottom of its swing by changing the object's potential and kinetic energy. A longer swing will have a higher potential energy at the top, resulting in a higher speed at the bottom. However, the effect of length on speed is not linear, and other factors such as mass and air resistance also play a role.

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