Solving a Mechanical Energy Problem Involving a Swing

[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

501.66-115.08=386.58 J =Answer

This however did not work..please help?

 

[PhanthomJay]

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.

 

[kerimek]

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.