- #1

TheSwedeAtLarge

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I am currently working on an assignment for my dynamics course in which we need to create our own "real world" problems. I chose to do a problem which would solve the time at which the string of a lanyard would break when it is swung in a circle. My problem is with my end numbers. They seem very unreasonable but I am not sure if it is due to a calculation error, a dynamics error, or if it is simply the nature of the problem. I estimated the mass of the keys. The maximum load is from this website: http://www.engineeringtoolbox.com/polyester-rope-strength-d_1514.html

The torque of the motor is an arbitrary number that I chose.

Any feedback would be greatly appreciated.

1. Homework Statement

1. Homework Statement

A motor is set up to spin a lanyard from rest with keys attached with a torque of 5 Nm. The polyester lanyard is 50 centimeters long with a diameter of 6 mm, assume it is massless. The keys have a mass m = 100 grams. The maximum load of polyester rope is Tmax = 3400 N. At what time will the rod break and after how many revolutions? Gravity acts in the -j direction. Neglect bending stresses and air resistance.

Schematic: http://imgur.com/V6mSuuD

FBD/KD: http://imgur.com/AQShsEv

## Homework Equations

F=ma

w = w0 + at

## The Attempt at a Solution

Find Angular Velocity[/B]

*Sum forces in the y-direction and solve for w*

Tmax – mg = mrw2

w = 260.7 rad/s

**Find Angular Acceleration**

*Sum moments about the origin*

M = (mra) * (r)

a=M/mr^2

a = 200 rad/s2

*Use kinematics to find the time to break*

w = w0 + at

260.7 rad/s = 200 rad/s2 * t

t = 1.3 s