Swinging, equilibrium, kinetic energy problem

In summary, the conversation discussed a question regarding the kinetic energy of a girl on a swing. The previous parts provided information about the length of the swing, time period, and number of oscillations. The main question asked for the girl's kinetic energy as she passed through the lowest point after being displaced from equilibrium. The equations used were T = t/n, f = 1/T, and KE = 0.5mw^2(A^2 - x^2), with A representing amplitude and x representing displacement. It was determined that the 250 mm displacement mentioned in the question was a vertical displacement and the correct approach was to use the conservation of energy equation, mgh.
  • #1
slymme
5
0

Homework Statement


This is a more than one part question that depends on answers from the previous parts, which I have so I will not rewrite those questions. I will write the question I am facing difficulty with:
Answers from previous parts:
Length = 1.95 m (From top of chains to center, its a swing)
Time Period = 2.8 s
15 complete oscillations of the swing took 42 s

To set her swinging, the girl and seat were displaced from equilibrium and released from rest. This initial displacement of the girl raised the center of mass of the girl and seat 250 mm above its lowest position. If the mass of the girl was 18 kg, what was her kinetic energy as she first passed through this lowest point?

Homework Equations


T = t/n
f = 1/T
Kinetic Energy (KE) = 0.5mw^2(A^2 - x^2)
where A is amplitude and x is displacement

The Attempt at a Solution


I simply subbed in the numbers into the KE equation. I think my problem has to do with the amplitude or displacement, I might have mixed them up. But I tried swapping the numbers around but to no avail. Also, I may have quite probably interpreted the question wrong and plugged in the wrong numbers into the A and x.I put L in as the A amd 250 mm (after conversion to meter) as the x. And yes, I changed w to 2pif.
Would greatly appreciate some help :)
 
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  • #2
The 250 mm is a vertical displacement of the center of mass, not a horizontal displacement.

Hint: Try a conservation law approach.
 
  • #3
I've solved the question already. You were right though, I used mgh. Thanks :)
 

1. What is "swinging" in physics?

Swinging refers to the motion of an object back and forth around a fixed point or axis. This type of motion is governed by the laws of physics and can be observed in various systems, such as a pendulum or a playground swing.

2. What is equilibrium in physics?

Equilibrium refers to a state in which all forces acting on an object are balanced, resulting in a stable and unchanging motion. This can occur in both static (no motion) and dynamic (constant motion) systems and is an important concept in understanding the behavior of objects in the physical world.

3. How is kinetic energy related to swinging and equilibrium?

Kinetic energy is the energy an object possesses due to its motion. In the context of swinging and equilibrium, kinetic energy is directly related to an object's speed and mass. When an object is swinging, it constantly alternates between potential and kinetic energy, with its maximum kinetic energy occurring at the bottom of its swing when it has the highest speed.

4. What is the relationship between kinetic energy and potential energy in a swinging system?

In a swinging system, potential and kinetic energy are constantly changing and are inversely related. As the object swings up and gains potential energy, it loses kinetic energy, and vice versa. At the highest point of the swing, all of the energy is in the form of potential energy, and at the lowest point, all of the energy is in the form of kinetic energy.

5. How can I solve a kinetic energy problem related to swinging and equilibrium?

To solve a kinetic energy problem in a swinging system, you will need to use the equations for kinetic energy and potential energy, as well as the laws of motion and conservation of energy. It is important to accurately identify the initial and final states of the system and properly apply the relevant equations to solve for the unknown variables.

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