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Acceleration on a Swing

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What you see here is our version of the state fair ride, the giant swings. Now this is by no means giant, but do provide very high accelerations, much higher than the state fair ride does. For passengers, we will use these green blooded aliens from the planet Jupiter. Now, they are used to high accelerations because after all, they come from Jupiter where the gravitational field is much higher than the earth. We will put one passenger on each pan, and put them in motion by turning the crank. If you have ever ridden the state fair ride or watched someone else ride it, you know that when it spins the chairs move outward, and the faster it spins the farther they go out.

Now, what you are going to be doing is analyzing this situation. You will be determining the acceleration of the passengers in two different ways, and comparing your results. One method is to simply use the formula for centripetal acceleration, which you already know namely, the square of the speed of the object divided by its path radius. So you will need to measure the speed of the passenger and the radius of its path. For the radius, take the distance from the middle of the passenger to the axis of rotation. Now that has to be a perpendicular distance, because the motion is a horizontal circle. For the speed, you will need to know how fast the passenger is going, or how long it takes for the passenger to go around once. In order to do that, you will use a video analysis program which we will talk about later.

The other method is to do a net force analysis. So, with the passenger in this position, you will identify the forces acting on the object, there are two of them, and write the net force equations and solve for the acceleration. Now, when you are writing your net force equations, be sure to pick one of your coordinate axes in the direction of the acceleration, and remember again that that direction is horizontal, as the motion is a horizontal circular path.

You will be doing the analysis using a video analysis program and some video clips we have already prepared. In order to get your acceleration in units of meters/seconds squared you will need to be able to take the distance measurements in pixels and then convert those to meters. So, to do that, I will measure one distance for you to obtain your scale factors. The distance I will measure is the distance from the inside of one of these uprights to the inside of the other one. Ok, now I have positioned the meter stick, now you have to take a reading. What you need to do is make a reading, I would say read inside the surface of the pole there, and is accurate enough to measure to the smallest unit on the stick, a millimeter. So take that reading now. Now, we are going to look at the reading for the other pole. Here is the pole on the right hand side. Again, I would recommend that you read from the inside of the pole. Take your reading to the nearest millimeter. So the distance you will be interested in is the difference of those two readings. That will be the distance, in meters between the two uprights.

So, with that information, and the physics you already know, you should be able to calculate the acceleration in two different ways and compare. Next you will download the lab instructions and carry out the lab.


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