Question

Learning Goal: To understand how to compute thework done by a constant force acting on a particle that moves in astraight line.

In this problem, you will calculate the work done by a constantforce. A force is considered constant if is independent of $r_vec$ . This is the most frequently encountered situation inelementary Newtonian mechanics. $MWE_wi_0_v1_a.jpg$ part AConsider a particle moving in a straight linefrom initial point B to final point A, acted upon by a constantforce $F_vec$ .The force (think of it as a field,having a magnitude and direction atevery position $r_vec$ ) is indicated by a series ofidentical vectors pointingto the left, parallel to the horizontal axis. The vectors are allidentical only because the force is constant along the path.Themagnitude of the force is ,and the displacement vector frompoint B to point A is $L_vec$ (of magnitude ,making and angle (radians) with the positive x axis). Find $W_BA$ , the work that the force $F_vec$ performs on the particle as it moves from point B topoint A.Express the work in terms of,,and . Remember to use radians, not degrees, for anyangles that appear in youranswer. $MWE_wi_0_v1_a.jpg$ $MWE_wi_0_v1_b.jpg$ part BNow consider the same force $F_vec$ acting on aparticle that travels from point A to pointB.The displacement vector $L_vec$ now points in the opposite direction as it did in Part A.Find the work $W_AB$ done by $F_vec$ in this case.Express your answer in terms of,,and .

Answer 1

The work done is given byW = F . L=FL Cos θ 'where θ ' = 1.745*10^-2θ[ θ in degrees , θ ' -radians ]W = 1.745*10^-2 FL Cosθb) W = - 1.745*10^-2 FL Cosθwork is said to be negative as the direction isopposite.