A BODY OF MASS 2 kg IS ACTED UPON BY TWO FORCES 2N AND 5N IN THE DIRECTION OF i^ + j^ AND j^- k^ RESPECTIVELY.IF THE BODY IS DISPLACED FROM [ 3,-2,1 ] TO [-1,2,3 ] , THEN THE WORK DONE IS WHAT ?

To determine the work done on the body by the forces, we first need to understand a few key concepts in physics, particularly related to force, displacement, and how they interact. Work is defined as the dot product of the force vector and the displacement vector. Let's break this down step by step.

Understanding the Forces Acting on the Body

The body is subjected to two forces:

• Force F1 = 2 N in the direction of i^ + j^
• Force F2 = 5 N in the direction of j^- k^

We can express these forces in vector form:

• Force F1 = 2 * (1, 1, 0) = (2, 2, 0) N
• Force F2 = 5 * (0, -1, -1) = (0, -5, -5) N

Calculating the Net Force

Next, we sum these two forces to find the net force acting on the body:

F_net = F1 + F2 = (2, 2, 0) + (0, -5, -5) = (2, -3, -5) N

Determining the Displacement Vector

The displacement is given by moving from the initial position [3, -2, 1] to the final position [-1, 2, 3]. We can calculate the displacement vector as follows:

Displacement vector, D = Final Position - Initial Position = [-1, 2, 3] - [3, -2, 1] = [-1 - 3, 2 - (-2), 3 - 1] = [-4, 4, 2]

Calculating the Work Done

Now, we use the formula for work done, which is the dot product of the net force vector and the displacement vector:

Work = F_net · D = (2, -3, -5) · (-4, 4, 2)

Calculating the dot product:

• Work = (2 * -4) + (-3 * 4) + (-5 * 2)
• Work = -8 - 12 - 10 = -30 J

Final Result

The work done on the body is -30 Joules. The negative sign indicates that the work is done against the direction of the force, meaning the forces are acting in a direction opposite to the displacement.

In summary, by following the steps to determine the net force, the displacement vector, and then applying the work formula, we find that the work done on the body is -30 J. This negative work suggests that energy is being taken from the body as it moves through the applied forces.