Total Mechanical Energy Swing Problem

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SUMMARY

The discussion revolves around calculating the total mechanical energy of a child on a swing, focusing on kinetic energy (KE) and potential energy (PE). The child, weighing 30 kg, receives 75 J of work from another child pushing the swing. The kinetic energy at position A, immediately after the push, is confirmed to be 75 J, equating the work done to the initial kinetic energy. The conversation emphasizes the conservation of energy principle, where the total energy remains constant, allowing for the calculation of maximum speed and height achieved by the swing.

PREREQUISITES
  • Understanding of kinetic energy (KE = 0.5mv²)
  • Knowledge of potential energy (PE = mgh)
  • Familiarity with the conservation of mechanical energy principle
  • Basic algebra for solving equations
NEXT STEPS
  • Explore the concept of energy conservation in pendulum motion
  • Learn how to calculate maximum height using energy equations
  • Investigate the effects of friction on mechanical energy
  • Study the relationship between work done and energy transfer
USEFUL FOR

Students studying physics, educators teaching mechanics, and anyone interested in understanding energy transformations in simple systems like swings.

Snape1830
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A 30 kg child is playing on a swing. Another child is pushing. That second child does 75 J of work on the swing. Ignore friction. The swing has zero mass compared to the child on the swing. There is a diagram. So basically: Postion A Height = .6 m. Position B Height = .2 m and Postion Height C = ?

a. How much kinetic energy does the child on the swing have at position A just after the push?
Work = change in kinetic energy. So I did 75=.5(30)(v2)-.f(30)(0) to get velocity (I assumed the initial velocity is 0) And then I was going to plug that into KE = .5mv2. Is that right?

c. What is the maximum speed of the child on the swing?
d.What is the maximum height off the ground the child on the swing reaches following the initial push.

Part b is the total energy at positions B and C. I can figure that out. I'm really just confused about c, and I want to know if that is how to do a.

Please help!
 
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The kid on the swing has two different forms of energy. You've already said about kinetic energy, but there is another.
 
BruceW said:
The kid on the swing has two different forms of energy. You've already said about kinetic energy, but there is another.
Potential energy.
 
Yep. The kid also has potential energy. Do you know the equation for it?
 
BruceW said:
Yep. The kid also has potential energy. Do you know the equation for it?
Yup! It's PE = mgh
 
That's the one. You are also given the initial height and kinetic energy, so from this you can calculate the total energy (which is a conserved quantity).
 
BruceW said:
That's the one. You are also given the initial height and kinetic energy, so from this you can calculate the total energy (which is a conserved quantity).
Would the initial kinetic energy be the answer I have for part a? In that case, part a is right?
 
I think you were right that the work done is equal to the initial KE of the kid. So I think you did get a) right. (and you don't need to find the velocity, since it only asks for the KE).
 
BruceW said:
I think you were right that the work done is equal to the initial KE of the kid. So I think you did get a) right. (and you don't need to find the velocity, since it only asks for the KE).
But KE=.5mv^2, so I need to find velocity before I can calculate kinetic energy.
 
  • #10
Snape1830 said:
But KE=.5mv^2, so I need to find velocity before I can calculate kinetic energy.
But you're starting with the kinetic energy. So taking the extra step of solving for the velocity, then plugging it back into the same expression can only give you back what you started with.
 
  • #11
Doc Al said:
But you're starting with the kinetic energy. So taking the extra step of solving for the velocity, then plugging it back into the same expression can only give you back what you started with.
But I never had the kinetic energy to begin with. I had work and mass, but I was never given any velocity.
 
  • #12
Snape1830 said:
But I never had the kinetic energy to begin with. I had work and mass, but I was never given any velocity.
But the work equals the kinetic energy. That's your first equation.
 
  • #13
Doc Al said:
But the work equals the kinetic energy. That's your first equation.
Oh I see what you're saying. Sorry! Thanks! So the kinetic energy is 75 J.
 
  • #14
yep. That's the initial KE.
 
  • #15
BruceW said:
yep. That's the initial KE.
Ok, but now how do I solve part c? And also if Work = the change in kinetic energy, but 75 joules is only the initial energy, how does that work?
 
  • #16
Snape1830 said:
Ok, but now how do I solve part c?
At least give it a try yourself. What physics principles/laws do you think might help?
Snape1830 said:
And also if Work = the change in kinetic energy, but 75 joules is only the initial energy, how does that work?
Yeah, the problem is maybe a bit badly worded. It is most likely that they are saying the kid was initially at rest, then work was done on him to give him kinetic energy. So the best bet is to assume that the work done at the start is the initial KE of the kid.
 
  • #17
BruceW said:
At least give it a try yourself. What physics principles/laws do you think might help?

Yeah, the problem is maybe a bit badly worded. It is most likely that they are saying the kid was initially at rest, then work was done on him to give him kinetic energy. So the best bet is to assume that the work done at the start is the initial KE of the kid.
The only equation that has "speed" is kinetic energy. So would I just say that 75 = .5(30)v62 and solve for v? If that's the case then I have to assume 75 J is the change in kinetic energy, not the initial kinetic energy.
 
  • #18
No, that's not right. The question, as you wrote it in the first post, implies that the kid is pushed, and it is during this time that work is done on him. And at the end of this push, the kid is at position A.

Now I can only assume that the work done on the kid is equal to the kinetic energy of the kid at position A. This is my own interpretation of the question, but I think it is most likely what the question did mean.

So this gives you the initial KE and position of the kid. From now on, no work is being done on the kid. So how would you work out the relationship between KE and position? and how can you use this to find the max KE which the kid will have, once he goes through pendulum motion?
 
  • #19
BruceW said:
No, that's not right. The question, as you wrote it in the first post, implies that the kid is pushed, and it is during this time that work is done on him. And at the end of this push, the kid is at position A.

Now I can only assume that the work done on the kid is equal to the kinetic energy of the kid at position A. This is my own interpretation of the question, but I think it is most likely what the question did mean.

So this gives you the initial KE and position of the kid. From now on, no work is being done on the kid. So how would you work out the relationship between KE and position? and how can you use this to find the max KE which the kid will have, once he goes through pendulum motion?
Well position implies height, right? Which is in the equation for PE (PE = mgh). I really just don't know. I appreciate the help, but I guess I'll just go see the teacher about this.
 
  • #20
You're on the right track there. seeing the teacher is a good idea though.
 

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