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Chapter 10: Problem 4

Two forces act on an object, but the net force is zero. Must the net torque be zero? If so, why? If not, give a counterexample.

Short Answer

Expert verified
No, the net torque is not necessarily zero if the net force is zero. This is because torque does not only depend on the force but also depends on the point of application of the force. A counterexample would be applying equal and opposite forces on a door at different distances from the hinges. The forces produce a net force of zero, but a net torque that is not zero.

Step by step solution

01

Understanding Forces and Torques

First, it is crucial to understand that both forces and torques rely on vector properties. A force is a vector quantity, meaning it has a direction and a magnitude. Similarly, a torque is also a vector because it also has a direction and magnitude. The 'net force' or 'net torque' refers to the culmination of all forces or torques acting on a body.
02

Concept of Counteracting Forces

If two forces are acting on an object such that they produce a 'net force' of zero, this means the two forces are equal in magnitude but act in opposite directions. Hence, they cancel out each other.
03

Connection between Forces and Torques

A torque, also known as a moment, is the rotational equivalent of linear force. The magnitude of torque depends not only on the magnitude of the force but also on the 'moment arm', the distance between the axis of rotation and the point where the force is applied. Thus, two equal but opposite forces do not necessarily create torques that cancel each other out, unless they are applied at the same distance from the pivot.
04

Counterexample

Consider an object, like a door, that can rotate around an axis (the hinges). If two equal and opposite forces are applied on the door at different distances from the hinges, these forces will create a net force of zero (since they are equal and opposite). However, they will create a net torque that is not zero, because the moments of these forces about the hinge are different, as moment = force x distance. This shows that zero net force does not necessarily result in zero net torque.

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Most popular questions from this chapter

As an automotive engineer, you're charged with improving the fuel economy of your company's vehicles. You realize that the rotational kinetic energy of a car's wheels is a significant factor in fuel consumption, and you set out to lower it. For a typical car, the wheels' rotational energy is \(40 \%\) of their translational kinetic energy. You propose a redesigned wheel with the same radius but \(10 \%\) lower rotational inertia and \(20 \%\) less mass. What do you report for the decrease in the wheel's total kinetic energy at a given speed?

The lower part of a horse's leg contains essentially no muscle. How does this help the horse to run fast? Explain in terms of rotational inertia.

A \(110-\mathrm{N} \cdot \mathrm{m}\) torque is needed to start a revolving door rotating. If a child can push with a maximum force of \(90 \mathrm{N},\) how far from the door's rotation axis must she apply this force?

A 55 -g mouse runs out to the end of the 17 -cm-long minute hand of a grandfather clock when the clock reads 10 past the hour. What torque does the mouse's weight exert about the rotation axis of the clock hand?

A 50 -kg mass is tied to a massless rope wrapped around a solid cylindrical drum, mounted on a frictionless horizontal axle. When the mass is released, it falls with acceleration \(a=3.7 \mathrm{m} / \mathrm{s}^{2} .\) Find (a) the rope tension and (b) the drum's mass.
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