# Analyzing Energy Conservation in a Swinging System

• Giuseppe
In summary, at the low point of the swing, the child had zero velocity relative to the ground. However, after leaving the swing, the child gained a velocity relative to the ground.
Giuseppe
Hey, I was wondering if anyone can help analyze this problem with me. Here is the question.

A swing seat of mass M is connected to a fixed point P by a massless cord of length L. A child also of mass M sits on the seat and begins to sing with zero velocity at a position of which the cord makes a 60 degree angle with the vertical. The swing continues down until the cord is exactly vertical at which the time the child jumps off in a horizontal direction. The swing continues in the same direction until the cord makes a 45 degree angle with the vertical. At that point, it begins to swing in the reverse direction. With what velocity relative to the ground did the child leave the swing?

I known I have to use conservation of energy. Is this basically asking to find the speed of the swing at the low point. If so, why would you need to know that the swing goes up to 45 degrees. I am not sure how to link the two pieces of information concerning the angles in order to solve the problem

No, it's bit trickier than that.
Hint:
When the child leaves the seat, the angular momentum of system child+seat with respect to P must be conserved..(why?)

Of course, you'll need to use energy conservation as well..

Last edited:
would that be because there is no external torques acting on the system?

Giuseppe said:
would that be because there is no external torques acting on the system?
Exactly!
At that moment, the torque from gravity is zero.
Assume that the child gains a leaving velocity relative to the seat, but that the cord remains strictly vertically aligned in the time period from the child has equal velocity with the seat to the time when it has reached its leaving velocity.

Use energy conservation to determine what the velocity of the seat must be just prior and just after the child has left (that's where the angle info is needed).

Use this and conservation of angular momentum to determine the child's velocity.

Last edited:
ok thanks, I got it!

## What is energy conservation problem?

The energy conservation problem refers to the issue of decreasing energy resources and the need to find alternative ways to conserve and use energy more efficiently.

## Why is energy conservation important?

Energy conservation is important because it helps to reduce our dependence on non-renewable energy sources, such as fossil fuels, which are finite and contribute to pollution and climate change. It also helps to save money and resources in the long term.

## What are some examples of energy conservation?

Examples of energy conservation include turning off lights and electronics when not in use, using energy-efficient appliances and light bulbs, carpooling or using public transportation, and using renewable energy sources like solar or wind power.

## What impact does energy conservation have on the environment?

Energy conservation has a positive impact on the environment by reducing carbon emissions and pollution, preserving natural resources, and protecting ecosystems. It also helps to mitigate the effects of climate change.

## How can individuals contribute to energy conservation?

Individuals can contribute to energy conservation by making small changes in their daily habits, such as turning off lights and unplugging electronics when not in use, using public transportation or carpooling, and using energy-efficient products. They can also support policies and initiatives that promote renewable energy and energy conservation.

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