Question

A body is constrained to move in the y-direction. It is subjected to force (\[ - 2\vec i + 15\vec j + 6\vec k\]) newton. The work done by this force in moving the body through a distance of 10m in positive y-direction is:
A) \[150J\]
B) \[\;60J\]
C) \[ - 20J\]
D) \[ - 150J\]

Answer 1

Hint: According to Newton's second law \[F = ma\], force acting on an object is directly proportional to the mass of the body and acceleration of the body. Here we have to find the amount of work done by displacing the body from one direction to another direction. And we have the measure of distance and the vector of force already acting on a body.

Formula used:
\[w = \vec f.d\]
Where,
W=work done
\[\vec f\] =force and the arrow mark describes that the force is the vector quantity.
d= displacement.

Complete step by step answer:
(i) The force already acting on a body is \[ - 2\vec i + 15\vec j + 6\vec k\].The i, j, k denotes the x, y, z direction. As we have to displace the body only in the direction of y. Therefore the displacement vector only has \[\vec j\]. And we have to move that body to 10m in positive y-direction. Therefore, the displacement vector is \[0\vec i + 10\vec j + 0\vec k\]
(ii) the work done in this action is can be found by the formula, \[w = \vec f.d\]
(iii) Applying the known values in this formula gives,
 \[ \Rightarrow w = ( - 2\vec i + 15\vec j + 6\vec k).(0\vec i + 10\vec j + 0\vec k)\]
\[\therefore w = 150J\].

Hence, the correct answer is option (A).

Additional information:
(i) The force is the product of mass and acceleration according to Newton's second law of motion. There are two types of balanced and unbalanced forces.
(ii) If the body is in motion, there are many forces acting on it. They are frictional and normal forces.

Note: The work done in moving the body by displacement can be found by the force already acting on a body and the amount of displacement we have done. The product of displacement and the force is the amount of work done. The unit of work is denoted as Joules. The vector quantities have both magnitude and direction. The arrow on the quantity describes that the quantity has direction too.