# A swing in a Playground

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1. Nov 30, 2014

### kukumaluboy

Hi i was just wondering how a person who sits in a swing and starts of with a small motion, and is able to achieve a great swing height just by his body movements? How is one able to do this? Does his muscle contractions give additional potential energy being converted to KE to achieve a greater height?

2. Dec 1, 2014

### ShayanJ

This is an interesting question which I got its answer only a few days ago but what delighted when it came into my mind.
The point is, the gravitational force is applied to the centre of mass of the guy and the seat of the swing. When you're at rest, it means its cancelled. But when you move your body, you're changing your centre of mass and so the direction and the point of application of the force change which means the equilibrium point is now somewhere else. So the gravity forces you to get to that point which means motion. You can change the centre of mass constantly and so be in motion all the time.

3. Dec 1, 2014

### kukumaluboy

Haha thanks for clarifying!

4. Dec 1, 2014

### rcgldr

A person sitting in a swing can't directly generate a lateral force or move his/her center of mass. Instead, a person can lean forwards or backwards on the swing, exerting a torque between swing and where the person holds the chains and initially the center of mass remains at the same spot, but now the chains are angled forwards or backwards, and the tension in the chains now have a backwards or forwards component of tension. It's this horizontal component of tension in the angled chains that initiates and increases the swing.

Once the swing is moving, if the person is standing on the swing, the person can move their center of mass inwards towards the bar at the bottom of the swing where the centripetal force is higher, and outwards away from the bar near the top of the swing where the centripetal force is nearly zero, resulting in net work being perfomed, with a corresponding increase in energy (height of the swinging motion).

Last edited: Dec 1, 2014
5. Dec 1, 2014

### mmeftahpour

Sit relax and just move your feet forward and backward. what append? you and swing start to move backward and forward.
why? consider you stand on boat. if you walk to left, boat goes to right.(system mass center is constant)
In our swing system our feet and rest of the body with swing is a system. if you move your feet forward, your feet mass center goes forward, so rest of body and swing must goes backward to keep system mass center constant.
but the movement of body is very smaller than feet movement.(because mass of body is more than mass of feet) so what append for increasing of movement.
consider you pull and release someone on the swing, The swing start oscillation with a special period.(let call it natural frequency) if we want to increase amplitude, we push swing when it reached to maximum height.(pushing frequency is equal oscillation frequency) so we have resonance and amplification.
in our example same thing happen, player move feet forward in body backward movement and move backward in body forward movement.( frequency of applied force equal to natural frequency) so amplitude increase in each period.

6. Dec 1, 2014

### rcgldr

The key to initiating a swing and increasing the amount of swing for small swing movements is the horizontal component of tension in the chains. If you were in a space station, hovering in the middle, with a board to emulate a swing strapped to your body, you could move your feet back and forth, but you could not generate any net linear velocity. (You could temporarily generate angular velocity by twirling your arms and or legs, this stops once the arms and legs stop, but you can end up facing in a new direction).

Here is a video to an extreme example of the inwards / outwards movemnt to increase the height of swing once cenetripetal force becomes significant.