# Solving a Mechanical Energy Problem Involving a Swing

• jl39845
In summary, a 42 kg child on a 2.3 m long swing, released from rest at an angle of 32 degrees with the vertical, reaches a speed of 2.34094 m/s at the lowest point. To find the mechanical energy dissipated by resistive forces, potential energy at the release point must be compared to kinetic energy at the lowest point. Using PEg=mgh and KE=.5(m)(v^2), the initial potential energy is calculated to be 501.66 J and the kinetic energy is 115.08 J. Therefore, the mechanical energy dissipated is equal to 386.58 J.
jl39845

## Homework Statement

A 42 kg child on a 2.3 m long swing is released from rest when the swing supports make an angle of 32 degrees with the vertical.
The acceleration of gravity is 9.8 meters per second squared. If the speed of the child at the lowest point is 2.34094 m/s, what is the mechanical energy dissipated by the various resistive forces (e.g. friction, etc.)? Answer in units of J

## Homework Equations

PEg=mgh
KE=.5(m)(v^2)

3. The Attempt at a Solution
Attempted to solve using the lowest point of the swing as zero for potential energy. PEg at release point - KE at lowest point = dissipated energy.

PEg=mg(vertical component of swing length)
KE=.5(m)(v^2)

PEg=42(9.8)(2.3sin(32 degrees)
KE=.5(42)(2.34094^2)

PEg=501.66 J
KE=115.08 J

You did not calculate the initial PE correctly. Draw a sketch and check your trig in determining how high above the low point the child starts.

As a scientist, it is important to carefully consider all the variables and factors involved in a problem before attempting a solution. In this case, we must consider the fact that the child's speed at the lowest point may not be solely due to the release from rest, but could also be affected by the initial angle of the swing and any resistive forces acting on the swing. Additionally, the child's mass may also change as they move on the swing, which would affect the calculation of kinetic energy.

To accurately solve this problem, we would need to gather more information about the swing, such as the specific type of resistive forces present and their magnitudes, as well as the exact change in the child's mass throughout the swing. Without this information, it is not possible to accurately calculate the mechanical energy dissipated by the resistive forces. It is also important to note that the concept of mechanical energy dissipation is complex and may involve other factors such as energy conversion between potential and kinetic energy.

In conclusion, while your attempt at solving the problem was a good start, it is important to consider all the variables and limitations before attempting a solution. In this case, more information is needed to accurately calculate the mechanical energy dissipated by the resistive forces.

## 1. How do I calculate the potential energy of a swing?

The potential energy of a swing can be calculated by multiplying the mass of the swing by the acceleration due to gravity (9.8 m/s^2) and the height of the swing's center of mass above the ground.

## 2. What is the formula for calculating kinetic energy in a swing?

The kinetic energy of a swing can be calculated by multiplying half of the mass of the swing by the square of its velocity.

## 3. How can I determine the total mechanical energy of a swing?

The total mechanical energy of a swing is the sum of its potential energy and kinetic energy. It can be calculated by adding the potential and kinetic energy values together.

## 4. What are the factors that affect the mechanical energy of a swing?

The mechanical energy of a swing is affected by its height, mass, and velocity. The higher the swing is, the more potential energy it has. A heavier swing will have more kinetic energy, and a faster swing will have more kinetic energy due to its higher velocity.

## 5. How does friction affect the mechanical energy of a swing?

Friction can decrease the mechanical energy of a swing by converting some of its energy into heat. This can cause the swing to slow down and decrease its total mechanical energy over time.

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