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Chapter 10: Problem 76

The local historical society has asked your assistance in writing the interpretive material for a display featuring an old steam locomotive. You have information on the torque in a flywheel but need to know the force applied by means of an attached horizontal rod. The rod joins the wheel with a flexible connection \(95 \mathrm{cm}\) from the wheel's axis. The maximum torque the rod produces on the flywheel is \(10.1 \mathrm{kN} \cdot \mathrm{m}\). What force does the rod apply?

Short Answer

Expert verified
The force applied by the rod is approximately 10632 N.

Step by step solution

01

Understanding the given values

The torque \(\tau\) produced on the flywheel by the rod is given as \(10.1 \mathrm{kN} \cdot \mathrm{m}\) which can be converted into \(10100 \mathrm{Nm}\). The distance from the wheel's axis to the point where the rod is attached (radius) is \(95 \mathrm{cm}\) which can be converted into meters as \(0.95 \mathrm{m}\) because the unit of torque given is in \(\mathrm{Nm}\) and the force we need to calculate will be in Newtons (N).
02

Calculate the force using the equation

Use the fundamental relation of torque \( \tau = F \cdot r \), where \( F \) is the force and \( r \) is the radius. Isolate \( F \) to find the force the rod applies: \( F = \frac{\tau}{r} \).
03

Substitute the values into the equation

Insert the given values into the equation: \( F = \frac{10100 \mathrm{Nm}}{0.95 \mathrm{m}} \)

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