# Speed of a Screaming Slingshot Monkey

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## Abstract

The purpose of this experiment is to determine the maximum speed of a Screaming Slingshot Monkey.

## Introduction

In nature, there is no flying monkey; however some monkeys do leap from branch to branch. This is often associated with the squirrel monkey. The monkey best known for its voice is likely the howler monkey, but it is much too large compared to the one used in this experiment. No wild monkey is quite like the Screaming Slingshot Monkey -- not to mention the rubber arms.

A spring stores potential energy and comes in many forms, perhaps the most common one being a metal coil. In the case of the Screaming Slingshot Monkey it is in a different form, that of rubber tubing. Despite this difference, energy is stored in the same way. The amount of energy stored can be found using the general relationship of

F = kx^{n}

Where

F is the force on the spring,

k is the spring constant,

x is the extension, and

n is some power.

When n = 1 the spring is said to be linear and the relationship is known as Hooke's law. This Screaming Slingshot Monkey is non-linear but the general relationship still holds true. We can integrate to find potential energy.

U = k ∫ x^{n} dx

By using one's fingers as a brace, the Monkey can be pulled back on and the tubing extended; this bears great resemblance to a slingshot. Release and the potential energy of the Screaming Slingshot Monkey is transformed into kinetic energy.

K = ½ mv^{2}

The monkey is propelled forward, eventually crash landing with a satisfying scream. The manufacturer claims the monkey can travel up to 50 feet (15 meters).

## Procedure

- Weigh the monkey.
- Measure the length of the monkey.
- Attach a mass to the monkey.
- Record the extension from the original length.
- Repeat steps 3-4 with varying masses.

## Analysis

Graphing extension vs. force and fitting a power curve gives us the general equation for this spring.

F = 100.2 x^{0.72}

Integrating this expression gives us the general equation for the potential energy of this spring.

U = 58.3 x^{1.72}

Because, ideally at least, all potential energy will be converted to kinetic energy we can set this equation equal to K = ½ mv^{2}.

58.3x^{1.72} = 1/2(0.07 kg)v^{2}

To find the maximum speed we plug in the maximum extension achieved (0.37 m) and solve for v.

58.3(0.37 m)^{1.72} = 1/2(0.07 kg)v^{2}

v = 17.4 m/s

Finding the range of the monkey is simple with projectile motion. Assuming an optimal launch angle of 45* we can find the total in the air.

v = v_{0} + at

(-17.4 m/s)(sin 45°) = (17.4 m/s)(sin 45°)–(9.8 m/s^{2}) t

t = 2.45 s

The total time the monkey spends in the air is 2.45 s, we can use this to find its range assuming there is no drag.

s = v_{0}t

s = (17.4 m/s)(cos 45°)(2.45 s)

s = 29.4 m or 96.5 feet.

## Conclusion

The maximum speed of a screaming slingshot monkey is 17.4 m/s or 39 mph. This is surprisingly fast and means that, on your average New York City street, the monkey would be slapped with a speeding ticket. The monkey lives up to its expected range and beyond. 29.4 m or 96.5 feet is almost double the manufacturer's specifications. This discrepancy can be explained by drag.

## Sources of Error

- 0.37 m was not the actual maximum extension of the monkey, it could have been extended longer but fear of it snapping kept us from doing so.
- Drag (air resistance), will cause the maximum speed to be smaller.
- Some energy is lost to friction within the spring.

Dmitriy Gekhman -- 2005

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