The Physics of Trapeze

Investigation 3: The Swinging Trapeze

The swinging trapeze is a much simpler version of the flying trapeze. Whereas the flying trapeze involves a large rig and big net, the swinging trapeze takes much lower (the bar is 2.4m from the ground, and the cables are 3.7m long). The bar weighs around 2.2kg (therefore negligible compared to mass of performer). The main difference between the two is that on the swinging trapeze, the performer jumps to grab the bar, and gets it swinging from a standstill like a playground swing. This should be compared to the flying trapeze, where the performer starts from a height, therefore has speed as soon as he has left the board.

The safety precautions for the swinging trapeze are typically less complex due to the reduced height, but often involve safety lines, and several thick cushioned mats under the bar, and in the area underneath the performer when swinging. They are usually found inside, often in theatres or tents. They are, in fact, banned from being used in theatres in France, but other countries, such as Malaysia do not yet have this rule. The danger is that, if the performer lets go, he could fly into the crowd before the safety lines catch him.

The Standing Seats-Off

This trick, best described by a diagram, involves the performer first standing on the bar, and ending up hanging underneath it from his/her feet.

We will examine this trick because it involves a very large change in the length of the pendulum, and also a very large change in speed.

When we first examine this trick, it is easy to think that the (intuitive) change in speed comes as a result of the change in length of the pendulum, as the man falls underneath it. We must remember that the equation for speed has no term for length in it (v2=2gh) and therefore it cannot be this that causes the acceleration.

When swinging, standing on the bar, the system follows the original principal of a change from PE to KE, as described in Investigation 1. When the man falls back, he converts his PE to KE, which is then added to the KE he would already have had at that point in his swing.

We will assume that the angle of swing (a) is approx. the same as on the flying trapeze (0.8 radians), although of course this can vary.

What is his original maximum speed?

v = (2gh)1/2

v = (2 x 9.8 x (2.8 - (2.8 x cos0.8)))1/2

v = 4.1ms-1

PE at top is mgh = 70 x 9.8 x (2.8 - (2.8 x cos0.8)) (ignore mass of bar)

PE = 582J therefore KE at bottom is 582J

What is his maximum speed after he falls?

Man falls a total distance of 1.8m, therefore he loses how much PE?

PE = mgh = 70 x 9.8 x 1.8 = 1234.8J

This is all converted to KE (assume no air resistance)

1/2mv2 = 1234.8 + 582 = 1816.8J

v2 = 51.9ms-1

v = 7.2ms-1

This is a huge increase in speed (the performer has nearly doubled his original speed). It is easy to see how this trick could be dangerous, it the performer then let go, and flew into the audience at 7ms-1!

Therefore this shows another way that the performer can vary the speed of his swing, but moving his body to increase or decrease his potential energy. This is a theme I will return to when I investigate advanced swinging.

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