Λparticle in cquilibrium displaces from (1,1,2) m to (2,0,3) m . If onc of the forces acting on

step 1 This problem covers the concept of work energy theorem and from work energy theorem, the net wor

Λparticle in cquilibrium displaces from (1,1,2) m to (2,0,3)...

$\Lambda$ particle in cquilibrium displaces from $(1,1,2) \mathrm{m}$ to $(2,0,3) \mathrm{m} .$ If onc of the forces acting on the particle is $(\hat{i} \quad \hat{j} \mid 3 \hat{k}) \mathrm{N}$, total work done by the remaining forces acting on the particle is (a) $5 \mathrm{~J}$ (b) $-5 \mathrm{~J}$ (c) Zero (d) $10 \mathrm{~J}$

$\Lambda$ particle in cquilibrium displaces from $(1,1,2) \mathrm{m}$ to $(2,0,3) \mathrm{m} .$ If onc of the forces acting on the particle is $(\hat{i} \quad \hat{j} \mid 3 \hat{k}) \mathrm{N}$, total work done by the remaining forces acting on the particle is
(a) $5 \mathrm{~J}$
(b) $-5 \mathrm{~J}$
(c) Zero
(d) $10 \mathrm{~J}$

Key Concepts

Equilibrium

In mechanics, equilibrium refers to the condition of a body in which the net force acting on it is zero. Even though individual forces might be acting on the particle, their vector sum cancels out so that there is no acceleration. In problems involving work done by forces, equilibrium implies that while forces may do non?zero work on the body, the total work (and hence the change in kinetic energy) will be zero.

Displacement Vector

The displacement vector represents the change in position of a particle from its initial point to its final point. It is obtained by subtracting the initial position vector from the final position vector. This concept is crucial when calculating mechanical work, since work is defined as the dot product of force and displacement.

Dot Product

The dot product is a mathematical operation that takes two vectors and returns a scalar. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them. In physics, the dot product is used to compute work, as work is the dot product of the force vector and the displacement vector.

Work Done by a Force

Work done by a force is the measure of energy transfer when a force causes a displacement. It is calculated as the dot product of the force and displacement vectors. In cases where multiple forces are acting, the work done by the individual forces can be found separately, and under equilibrium conditions the sum of the works must result in no change in kinetic energy.

Work–Energy Theorem

The work–energy theorem states that the net work done on a particle is equal to its change in kinetic energy. For a particle in equilibrium or moving with constant velocity, the net work is zero, which means that the work contributions by various forces must sum to zero. This theorem underpins the analysis of work done when forces balance each other.

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