Work Done By A Constant Force - Practice Questions & MCQ

• Work-

Work is said to be done when a force applied on the body displaces the body through a certain distance along the direction of the force.

•  Work done by a constant force-

1. The scalar product of the force vector $(\vec{F})$ and the displacement vector $(\vec{S})$

   $
   W=\vec{F} \cdot \vec{S}
   $

   2. The product of the magnitude of force $(F){\text { magnitude of displacement }}(S)$ and cosine of the angle between them $(\Theta)$

   $
   W=F S \cos \Theta
   $

   3. If the number of forces $\vec{F}_1, \vec{F}_2, \vec{F}_3 \ldots \ldots, \vec{F}_n$, are acting on a body and it shifts from position vector $\overrightarrow{r_1}$ to position vector $\overrightarrow{r_2}$

   $
   \text { Then } W=\left(\vec{F}_1+\vec{F}_2+\vec{F}_3 \ldots \ldots \ldots+\vec{F}_n\right) \cdot\left(\vec{r}_2-\vec{r}_1\right)=\vec{F}_{n e t} \cdot \vec{r}_{n e t}
   $

   4. Units-
   - SI Unit-Joule
   - CGS Unit- Erg
   - $1 \mathrm{Joule}=10^7 \mathrm{Erg}$
   5. Dimension- $M L^2 T^{-2}$
   6. Dependence of work done by a constant force
   1. Frame of reference

   With a change of frame of reference (inertial) force does not change while displacement may change. So the work done by a force will be different in different frames.
   i.e. A person is pushing a box inside a moving train with a force $\vec{F}$

   Displacement inside train $\vec{S}$
   Displacement of the train in the ground frame is $\vec{S}_0$
   Then work done by the force $\vec{F}$ is $W=\vec{F} \cdot\left(\vec{S}+\vec{S}_0\right)$

1. Positive Work-

• Positive work means that force (or its component) is parallel to displacement.

• Means

  $
  0 \leq \Theta<\frac{\pi}{2}
  $

  
  Where $\Theta$ is the angle between force vectors and displacement vector
  - Maximum work $=W_{\max }=F S$, When $\theta=0^0$
  - E.g When you move a block by pulling it then work done by you on the block is positive
  2. Negative Work
  - Negative work means that force (or its component) is opposite to displacement.
  - Means $\frac{\pi}{2}<\Theta \leq \pi$

  Where $\Theta$ is the angle between force vectors and displacement vector
  - Minimum work= $W_{\min }=-F S$, When $\theta=180^{\circ}$
  - E.g When a body is made to slide over a rough surface, the work done by the frictional force is negative
  3. Zero work
  - Under three condition Work can be zero
  a. If the force is perpendicular to the displacement

  Means

  $
  \Theta=\frac{\pi}{2}
  $
   

                 E.g-When a body moves in a circle the work done by the centripetal force is always zero.

             b. If there is no displacement (means s = 0)

                 E.g- When a person tries to displace a wall by applying a force and can't able to move the wall

                        So the work done by the person on the wall is zero.

             c. If there is no force acting on the body (means F=0)

                 E.g-Motion of an isolated body in free space.