Chapter 17 : Work Done
Introduction:
In engineering, the study of work done on bodies moving on planes is essential for analyzing the efficiency and performance of various systems. This chapter focuses on understanding the work done in the presence of frictional forces, both on horizontal and inclined planes. The inclusion of friction adds complexity to the analysis, making it more representative of real-world scenarios.
Work Done on Bodies Moving on a Horizontal Plane:
When a force is applied to a body moving on a horizontal plane, and there is friction present, the work done can be calculated using the equation:
W=F⋅d⋅cos(θ)−f⋅d
Where:
- W is the work done,
- F is the applied force,
- d is the displacement,
- θ is the angle between the force and the direction of motion,
- f is the force of friction.
This equation accounts for both the work done by the applied force and the work done against friction.
Work Done on Bodies Moving on an Inclined Plane
When a body moves on an inclined plane, the gravitational force can be decomposed into components parallel and perpendicular to the plane. The work done against gravity can then be calculated as:
Wgravity=m⋅g⋅d⋅sin(α)
Where:
- m is the mass of the body,
- g is the acceleration due to gravity,
- d is the displacement,
- α is the angle of inclination.
Similarly, the work done against friction can be expressed as:
Wfriction=f⋅d
The net work done is the sum of the work done against gravity and friction:
Wnet=Wgravity+Wfriction
Practical Considerations and Efficiency
In real-world scenarios, engineers need to consider the efficiency of systems. The efficiency (ηη) is defined as the ratio of useful work done to the energy input:
η=Useful Work/DoneEnergy Input
Frictional forces often lead to energy losses, reducing the overall efficiency of a system. Engineers aim to minimize these losses through the use of lubrication, appropriate materials, and efficient design. The analysis of work done on bodies moving on horizontal and inclined planes with frictional forces is crucial for designing and optimizing engineering systems. By considering these factors, engineers can enhance the performance and efficiency of mechanical components and structures, leading to more sustainable and effective solutions in various applications.
