A Cable Lifts A 1010-kg Elevator At A Constant Velocity For A Distance Of 34.5 M. What Is The Work Done By:(a) The Tension In The Cable?- Number- Units(b) The Elevator's Weight?- Number- Units

Feb 27, 2025 by ADMIN 193 views

Work Done by Forces: Understanding the Concept

When it comes to understanding the concept of work done by forces, it's essential to grasp the fundamental principles that govern this phenomenon. Work is a measure of the energy transferred by a force to an object as it moves through a distance. In this article, we will delve into the world of work done by forces, focusing on the specific scenario of a cable lifting an elevator at a constant velocity.

Work Done by the Tension in the Cable

To determine the work done by the tension in the cable, we need to consider the force exerted by the cable and the distance over which it is applied. The tension in the cable is the force that opposes the weight of the elevator, allowing it to move at a constant velocity.

Force exerted by the cable: The force exerted by the cable is equal to the weight of the elevator, which is given by the formula F = mg, where m is the mass of the elevator and g is the acceleration due to gravity.
Distance over which the force is applied: The distance over which the force is applied is given as 34.5 m.

Using the formula for work done, W = F * d, we can calculate the work done by the tension in the cable.

Work Done by the Tension in the Cable Calculation

W = F * d = (1010 kg * 9.8 m/s^2) * 34.5 m = 335,511 J

Therefore, the work done by the tension in the cable is 335,511 J.

Work Done by the Elevator's Weight

To determine the work done by the elevator's weight, we need to consider the force exerted by the weight and the distance over which it is applied. The weight of the elevator is the force that opposes the motion of the elevator, causing it to accelerate downward.

Force exerted by the weight: The force exerted by the weight is given by the formula F = mg, where m is the mass of the elevator and g is the acceleration due to gravity.
Distance over which the force is applied: The distance over which the force is applied is given as 34.5 m.

Using the formula for work done, W = F * d, we can calculate the work done by the elevator's weight.

Work Done by the Elevator's Weight Calculation

W = F * d = (1010 kg * 9.8 m/s^2) * 34.5 m = -335,511 J

Note that the work done by the elevator's weight is negative, indicating that the force is opposing the motion of the elevator.

Therefore, the work done by the elevator's weight is -335,511 J.

Conclusion

In conclusion, the work done by the tension in the cable is 335,511 J, while the work done by the elevator's weight is -335,511 J. These results demonstrate the importance of considering the direction of the force when calculating work done. By understanding the concept of work done by forces, we can gain a deeper appreciation for the fundamental principles that govern the behavior of objects in the physical world.

Key Takeaways

Work is a measure of the energy transferred by a force to an object as it moves through a distance.
The work done by a force is given by the formula W = F * d.
The direction of the force is crucial when calculating work done.
The tension in the cable and the elevator's weight are two forces that can do work on an object.

Frequently Asked Questions

What is work done by a force?
How is work done by a force calculated?
What is the difference between work done by a force and the force itself?
Can a force do negative work?

References

Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Glossary

Work: A measure of the energy transferred by a force to an object as it moves through a distance.
Force: A push or pull that causes an object to change its motion.
Distance: A measure of the length between two points.
Acceleration: The rate of change of velocity of an object.
Work Done by Forces: Q&A

In our previous article, we explored the concept of work done by forces, focusing on the specific scenario of a cable lifting an elevator at a constant velocity. We calculated the work done by the tension in the cable and the elevator's weight, and discussed the importance of considering the direction of the force when calculating work done.

In this article, we will address some of the most frequently asked questions related to work done by forces. Whether you're a student looking for clarification on a concept or a professional seeking to deepen your understanding of the subject, this Q&A article is for you.

Q: What is work done by a force?

A: Work done by a force is a measure of the energy transferred by the force to an object as it moves through a distance. It is calculated using the formula W = F * d, where F is the force and d is the distance over which the force is applied.

Q: How is work done by a force calculated?

A: Work done by a force is calculated using the formula W = F * d, where F is the force and d is the distance over which the force is applied. The direction of the force is crucial when calculating work done, as a force can do positive or negative work depending on the direction of the force relative to the direction of motion.

Q: What is the difference between work done by a force and the force itself?

A: The force itself is a push or pull that causes an object to change its motion. Work done by a force, on the other hand, is a measure of the energy transferred by the force to an object as it moves through a distance. While the force itself is a vector quantity, work done by a force is a scalar quantity.

Q: Can a force do negative work?

A: Yes, a force can do negative work. This occurs when the force is opposing the motion of the object, causing it to slow down or change direction. In such cases, the work done by the force is negative, indicating that the force is doing work against the motion of the object.

Q: What is the unit of work?

A: The unit of work is the joule (J). It is defined as the energy transferred by a force of 1 newton (N) over a distance of 1 meter (m).

Q: Can work be done by a force on an object if the object is not moving?

A: No, work cannot be done by a force on an object if the object is not moving. Work is a measure of the energy transferred by a force to an object as it moves through a distance. If the object is not moving, there is no energy transferred, and therefore no work done.

Q: What is the relationship between work and energy?

A: Work and energy are closely related. Work is a measure of the energy transferred by a force to an object as it moves through a distance. Energy is the ability to do work, and work is the transfer of energy from one object to another.

Q: Can work be done by a force on an object if the force is not constant?

A: Yes, work can be done by a force on an object even if the force is not constant. In such cases, the work done is calculated using the formula W = ∫F * dx, where F is the force and dx is the infinitesimal distance over which the force is applied.

Q: What is the significance of work done by forces in real-world applications?

A: Work done by forces is significant in a wide range of real-world applications, including engineering, physics, and mechanics. It is used to calculate the energy transferred by forces to objects, and is essential in designing and optimizing systems that involve forces and motion.