What is the Velocity and Energy of a Child on a Swing?

In summary: So, the difference between the two is the energy lost due to friction."In summary, the problem involves a 25.0kg child on a 2.00m long swing being released from rest at an angle of 30 degrees with the vertical. Using conservation of energy, the child's speed at the lowest position can be found by calculating the potential energy at rest and equating it to the kinetic energy at the bottom of the swing. The mechanical energy lost due to friction can be found by subtracting the kinetic energy at the bottom without friction from the actual speed of the child at the bottom."
  • #1
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Homework Statement


A 25.0kg child on a 2.00m long swing is released from rest when the ropes of the swing make an angle of 30 degrees with the vertical. (a) Neglecting friction, find the child's speed at the lowest position. (b) If the actual speed of the child at the lowest position is 2.00 m/s, what is the mechanical energy lost due to friction?


Homework Equations


(1/2)mvf^2 - (1/2)mvi^2


The Attempt at a Solution


Do I need to use an energy equation to solve for velocity?
 
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  • #2
Yep energy is a good idea :) Start by finding the potential energy of the system at rest. You know its at 30 degrees and its 2m long so by using simple trig you can find h, the height. With conservation of energy you know the bottom of the swing, its all kinetic energy so the potential energy at rest is equal to the kinetic energy. The 2nd part is pretty simple but please respond if its not clear to you.
 
  • #3
I don't understand how to solve the 2nd part without given the coefficient of friction.
 
  • #4
You don't actually need to know k since you already know the velocity of the kid at the bottom with friction involved. You also know the kinetic energy of the kid at the bottom without friction.
 

Question 1: What is the velocity of a child on a swing?

The velocity of a child on a swing depends on several factors, including the length of the swing, the angle at which the child is swinging, and the force with which the child is pushing off. Generally, the velocity will increase as the child swings higher and decreases as the child swings lower.

Question 2: How does the velocity of a child on a swing change over time?

The velocity of a child on a swing is constantly changing due to the forces of gravity and the child's own pushing. As the child swings higher, the velocity will increase, and as the child swings lower, the velocity will decrease. However, due to air resistance, the velocity will gradually decrease over time as the child swings back and forth.

Question 3: Can the velocity of a child on a swing be calculated?

Yes, the velocity of a child on a swing can be calculated using the formula v=√(gL(1-cosθ)), where v is the velocity, g is the acceleration due to gravity, L is the length of the swing, and θ is the angle at which the child is swinging. However, this formula assumes no air resistance and is only an approximation.

Question 4: How does the velocity of a child on a swing affect the force exerted on the swing?

The velocity of a child on a swing has a direct impact on the force exerted on the swing. As the child swings higher, the force will increase, and as the child swings lower, the force will decrease. This is due to the conservation of energy, as the child's potential energy at the top of the swing is converted into kinetic energy as they swing forward.

Question 5: Can the velocity of a child on a swing reach a maximum value?

Yes, the velocity of a child on a swing can reach a maximum value. This maximum velocity is dependent on the length of the swing and the angle at which the child is swinging. As the child swings higher and higher, the maximum velocity will decrease due to air resistance and other factors. The maximum velocity can also be affected by the strength and pushing force of the child.

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