Question

The force in Newtons on a particle directed along the x-axis is given by F(x)=exp(−(x/5)+5) for x≥0 where x is in meters. The particle is constrained to move along the x-axis. Find the work done in Joules on the particle, W, in moving it from x=0 to x=1 using the fact that F=dW/dx. For your reference, 1 Joule = 1 Newton × 1 meter.

Answer 1

To find the work done on a particle moving from x=0 to x=1 with a force F(x)=exp(-(x/5)+5) along the x-axis, you need to integrate F(x) dx over the range from x=0 to x=1. The work done is the area under the force vs. displacement graph, which can be calculated using calculus.

Step-by-step explanation:

The student has asked about how to calculate work done on a particle when it is moved along the x-axis, given a force F(x) that is a function of the particle's position. The concept of work in physics relates to the force applied on an object and the displacement it causes; formally, work done W can be calculated by integrating the force over the displacement:

W = ∫ F(x) dx, over the limits of the initial and final positions.

For the given function F(x) = exp( - (x/5) + 5 ), you would compute the work done from x = 0 to x = 1 by integrating:

W = ∫_{0}^{1} exp( - (x/5) + 5 ) dx

This integral can be solved using standard calculus techniques. The solution to this integral will give you the total work done on the particle in Joules.

Answer 2

from F= dW/dx u will integrate nad will have : W = Integralfrom [0 to 1] (F(x) dx)  => W= Intgral [0..1] exp[ (-x/5)+5] dx all u need is to solve this integral.