Real-Life Examples of Torque: From Wrenches to Doors

📚 Quick Study Guide

• 🔑 Torque is a measure of the force that can cause an object to rotate about an axis.
• 📏 The magnitude of torque depends on the force applied, the length of the lever arm, and the angle between the force vector and the lever arm.
• 📐 The formula for torque is $\tau = rF\sin(\theta)$, where $\tau$ is torque, $r$ is the length of the lever arm, $F$ is the magnitude of the force, and $\theta$ is the angle between the force and the lever arm.
• ➕ Torque has a direction; it can be clockwise or counterclockwise.
• 🔧 Applications of torque include using wrenches, opening doors, and operating levers.

🧪 Practice Quiz

1. Which of the following is the correct formula for calculating torque?
   1. $\tau = rF\cos(\theta)$
   2. $\tau = rF\sin(\theta)$
   3. $\tau = \frac{r}{F}\sin(\theta)$
   4. $\tau = \frac{F}{r}\cos(\theta)$
2. What is the SI unit of torque?
   1. Newton (N)
   2. Meter (m)
   3. Newton-meter (N·m)
   4. Joule (J)
3. Increasing which of the following will always increase the magnitude of the torque (assuming all other factors remain constant and are non-zero)?
   1. The angle between the force and lever arm
   2. The mass of the object
   3. The length of the lever arm
   4. The gravitational constant
4. A wrench is used to tighten a bolt. If the force applied is 50 N and the length of the wrench is 0.2 m, what is the torque applied to the bolt (assuming the force is applied perpendicular to the wrench)?
   1. 5 N·m
   2. 10 N·m
   3. 25 N·m
   4. 100 N·m
5. In which scenario is the torque equal to zero?
   1. When the force is applied at a 45-degree angle.
   2. When the force is applied parallel to the lever arm.
   3. When the force is applied perpendicular to the lever arm.
   4. When the lever arm is very long.
6. Why are door handles placed far from the hinges?
   1. To minimize the force required to open the door.
   2. To maximize the force required to open the door.
   3. To reduce the torque applied to the door.
   4. To increase the speed at which the door opens.
7. A mechanic uses a longer wrench to loosen a rusty bolt. Why does this help?
   1. It decreases the force required to loosen the bolt.
   2. It increases the force required to loosen the bolt.
   3. It decreases the torque applied to the bolt.
   4. It increases the torque applied to the bolt.