Assertion (A): A work done by the gravitational force is zero in closed path. Reason (R) : Gravitional force is a conservative force . EASY. View Answer. A particle is moved along the different paths OAC, OBC & ODC as shown in the fig. Path ODC is a parabola, y = 4 x 2.
a force F=x^2i +y^2j +z^2k is acting on a particle the particle displaces from(0,0,0) to(1,1,1) find the work done by the force, Work Done : The work done by a force vector is the dot product of the force vector to the object and the amount of displacement caused to the object.
A force F = x 2 y 2 i + x 2 y 2 j (N) acts on a particle which moves in the XY plane. (a) Determine F is conservative or not and (b) Find the work done by F as it moves the particle from A to C (fig.) along each of the paths ABC, ADC, and AC.
Example 5.1 Find the work done by the force F(x,y) = x2i? xyj in moving a particle along the curve which runs from (1,0) to (0,1) along the unit circle and then from (0,1) to (0,0) along the y-axis (see Figure 5.1). Figure 5.1: Shows the force ?eld F and the curve C. The work done is negative because the ?eld impedes the movement along …
12/6/2012 · find the work done by the force field f(x,y)=x^2i+ye^xj on a particle that moves along the parabola x=y^2+1 from (1,0) to (2,1), 4/28/2013 · Find the work done by the force field F(x, y) = x^2i – xyj in moving a particle along the quarter-circle r(t) = (cost)i + (sint)j 0 ? t ? ?/2.
Answer to: Find the work done by the force field F(x,y) = cos xi + y^2j on a particle that moves along the curve r(t) = ti – t^3j, 0 leq t…
Problem 2. Find the work done by the force ?eld F(x,y) = e?yi ? xe?yj in moving an object from P(0,1) to Q(2,0). Solution. We ?rst verify that the force ?eld is conservative. Setting P = e?y and QQ = ?xe?y, we see that ?P ?y = ?e?y = ?Q ?x. Thus there exists a function f such that F = ?f, and the work done .
Therefore, the work done is Z C F dr = Z 1 0 5t7 4t10 dt = 23 88. 37. The magnitude of the force exerted by gravity on the man and paint can is the combined weight of the man and the paint can. This is 185lb. This force acts in the downward (negative z) direction. Thus, the gravitational force –eld acting on the man and paint can is F(x;y;z …
