How to Calculate Variable Force on a Particle with Varying Coordinates?

In summary, variable force on a particle refers to the changing force that affects the motion of a particle and is directly related to its acceleration. It can be applied to particles of any size and can be calculated and measured through various methods.
  • #1
rudransh verma
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Homework Statement
A force ##\vec F=-k(y\hat i+ x\hat j)## where k is constant acts on the particle moving in x-y plane from origin, the particle is taken along the positive x axis to the point (a,0) and parallel to y axis to a point (a,a). The total W by the Force on the particle is
Relevant Equations
W=F.d
##W=-k(y\hat i+ x\hat j)d##. I am not getting the coordinate of particle correctly so that I can find the value of d. Also the force is varying.
 
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  • #2
Since the force is varying, you'll need to integrate. The formula you gave is for constant force. And the coordinates are given.
 
  • #3
Doc Al said:
Since the force is varying, you'll need to integrate. The formula you gave is for constant force. And the coordinates are given.
Oh yes! Thanks.
 

1. What is variable force on a particle?

Variable force on a particle refers to a situation where the force acting on a particle changes over time or distance. This can be due to changes in the particle's velocity, position, or the environment it is in.

2. How is variable force different from constant force?

Unlike constant force, which remains the same throughout the particle's motion, variable force changes in magnitude or direction. This can result in a non-uniform acceleration for the particle.

3. What factors can cause variable force on a particle?

Variable force can be caused by a variety of factors, such as changes in the particle's speed, direction, or position, as well as external forces like friction, gravity, or electromagnetic fields.

4. How is variable force calculated?

The calculation of variable force depends on the specific situation and factors involved. Generally, it can be calculated using Newton's second law of motion, which states that force equals mass times acceleration (F=ma). However, more complex situations may require the use of other equations or principles.

5. What are some real-life examples of variable force on a particle?

Variable force is a common occurrence in everyday life. Some examples include a car accelerating and decelerating on a road, a pendulum swinging back and forth, or a satellite orbiting around the Earth. In each of these cases, the force acting on the object changes over time or distance, resulting in variable force on the particle.

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