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Chapter 10: Problem 19

What three factors affect the torque created by a force relative to a specific pivot point?

Short Answer

Expert verified
The three factors that affect the torque created by a force relative to a specific pivot point are: 1) The force applied, 2) The distance from the pivot point, and 3) The angle at which the force is applied.

Step by step solution

01

Factor 1: Force

The first factor affecting torque is the force applied. The greater the force applied to the object, the greater the torque. That's why, when you push a door open, it swings faster if you push harder.
02

Factor 2: Distance

The second factor is the distance from the pivot point to the point where the force is applied, often called the 'lever arm'. The longer the lever arm, the less force is needed to create the same amount of torque. That's why door handles are placed at the far edge of the door, not near the hinges.
03

Factor 3: Angle

The last factor is the angle at which the force is applied. If the force is applied perpendicular (at a 90-degree angle) to the lever arm, it creates the most torque. As the angle decreases from 90 degrees, the effective force that contributes to rotation decreases, thus decreasing the torque. That's why it's easier to open a door by pushing it at a right angle, and harder when pushing it at a lower angle.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Force
Torque is largely influenced by the amount of force applied. Imagine you're trying to open a door. The harder you push, the more effectively the door swings open.
This is because torque (\( \tau \)), which is the measure of how effectively a force causes an object to rotate, is directly proportional to the force applied.
  • The stronger the applied force, the greater the resulting torque.
  • A larger force results in quicker rotation of an object.
Therefore, maximizing force is crucial when we want to achieve greater torque. This concept finds practical application in various real-life scenarios, like tightening bolts with a wrench or pushing swings in a playground.
Lever Arm
In understanding torque, the distance from the pivot, known as the lever arm, is just as pivotal as the force itself. The lever arm is the straight-line distance between the pivot point and the point of force application.
  • A longer lever arm allows you to exert the same torque with less force.
  • A shorter lever arm requires more force to achieve the same torque.
An excellent example is a seesaw, where pushing at the end of the seesaw requires less effort than pushing near the pivot. This is because the lengthened distance amplifies the torque effect. Similarly, door handles are intentionally designed to be far from the hinges to reduce the effort needed to open or close the door.
Angle of Force Application
The angle at which force is applied relative to the lever arm significantly affects torque production.
For the best results, you want to apply the force at an angle that leverages the full potential of that force.
  • The most torque is generated when the force is applied at a 90-degree angle to the lever arm.
  • Angles less than 90 degrees decrease the effective component of force that contributes to torque.
  • At 0 degrees, the applied force is wasted since it contributes no torque.
Visualize it as pushing a door at a right angle, which maximizes the door's swinging motion as opposed to pushing diagonally, where the door resists swinging. Understanding this concept is essential in mechanical applications, such as using tools, where optimal force application angles increase efficiency.

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Most popular questions from this chapter

A child with mass 40 kg sits on the edge of a merrygo-round at a distance of \(3.0 \mathrm{m}\) from its axis of rotation. The merry-go-round accelerates from rest up to \(0.4 \mathrm{rev} / \mathrm{s}\) in 10 s. If the coefficient of static friction between the child and the surface of the merry-go-round is 0.6, does the child fall off before \(5 \mathrm{s} ?\)

In circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction. Explain your answer.

A compact disc rotates at 500 rev/min. If the diameter of the disc is \(120 \mathrm{mm},\) (a) what is the tangential speed of a point at the edge of the disc? (b) At a point halfway to the center of the disc?

A uniform rod of mass \(1.0 \mathrm{kg}\) and length \(2.0 \mathrm{m}\) is free to rotate about one end (see the following figure). If the rod is released from rest at an angle of \(60^{\circ}\) with respect to the horizontal, what is the speed of the tip of the rod as it passes the horizontal position?

A system consists of a disk of mass \(2.0 \mathrm{kg}\) and radius \(50 \mathrm{cm}\) upon which is mounted an annular cylinder of mass \(1.0 \mathrm{kg}\) with inner radius \(20 \mathrm{cm}\) and outer radius \(30 \mathrm{cm}\) (see below). The system rotates about an axis through the center of the disk and annular cylinder at 10 rev/s. (a) What is the moment of inertia of the system? (b) What is its rotational kinetic energy?
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