When we studied the concept of work, we learned that work = force x distance. Now we learn that torque = force x distance. What's different about these two definitions?A) For work, distance and force are in the same direction; for torque they are perpendicular to each other.B) For work, the force must be against gravity, while for torque, not so.C) The units of distance are different for work and torque.D) Actually the two definitions are the same. Only the applications of them differ.E) Work is measured in joules, and torque is measured in pseudo-joules.

Question

When we studied the concept of work, we learned that work = force x distance. Now we learn that torque = force x distance. What's different about these two definitions?A) For work, distance and force are in the same direction; for torque they are perpendicular to each other.B) For work, the force must be against gravity, while for torque, not so.C) The units of distance are different for work and torque.D) Actually the two definitions are the same. Only the applications of them differ.E) Work is measured in joules, and torque is measured in pseudo-joules.

Answer 1

drive the equation of the work done by the torque

Answer 2

The correct answer is A) For work, distance and force are in the same direction; for torque, they are perpendicular to each other.

The key difference between the definitions of work and torque is the orientation of the force and distance involved.

In the definition of work, when calculating the amount of work done, both the force and the distance traveled by the object on which the force is applied need to be in the same direction. This means that the force is exerted parallel to the displacement of the object. In other words, work is done when a force is applied to an object and it moves in the direction of the force. The formula for work is given by W = F × d, where W is work, F is force, and d is distance traveled.

On the other hand, torque is a measure of the ability of a force to rotate an object around an axis. When calculating torque, the force applied to the object and the distance from the axis of rotation (also known as the leverage or moment arm) must be perpendicular to each other. The formula for torque is given by τ = F × r, where τ is torque, F is force, and r is the perpendicular distance between the axis of rotation and the line of action of the force.

So, the main difference between the two definitions is the orientation of the force and distance relative to each other. In work, they are parallel, whereas in torque, they are perpendicular.

Option B is incorrect because for both work and torque, the force can be applied in any direction, not just against gravity. Option C is incorrect because the units of distance for both work and torque are the same (e.g., meters or feet). Option D is incorrect because the definitions of work and torque are fundamentally different. Finally, option E is incorrect as torque is measured in newton-meters (N·m) and work is measured in joules (J), not "pseudo-joules."