B M Sharma Solutions for Chapter: Work, Energy and Power, Exercise 50: CONCEPT APPLICATION EXERCISE 8.3

A particle moves in the $x-y$ plane in figure under the influence of a friction force with magnitude $3.00 \mathrm{N}$ and acting in the direction opposite to the particle’s displacement. Calculate the work done by the friction force on particle as it moves along the following closed paths:

(a) path $OA$ followed by the return path $AO$

(b) path $OA$ followed by $AC$ and the return path $CO$

(c) path $OC$ followed by the return path $CO$

(d) each of your three answers should be non-zero.

What is the significance of this observation?

A single conservative force acting on a particle varies as $\overrightarrow{F}=\left(-Ax+B{x}^2\right)\hat{\mathrm{i}} N,$ where $A$ and $B$ are constants and $x$ is in metre. Calculate the potential energy function $U\left(x\right)$ associated with this force, taking $U=0$ at $x=0$. 

A potential energy function for a two-dimensional force is of the form $U=3x^{3}y-7x.$ Find the force that acts at the point $\left(x, y\right).$

For the potential energy curve shown in figure. Determine whether the force $F_x$ is positive, negative, or zero at the five points indicated.

A particle is confined to move on $x$-axis only and its mechanical energy is $60 \mathrm{J}$. The potential energy of the particle is given as $U=x^2-7x+30$. Find how this particle will move.

A particle can move along $x$-axis under influence of a conservative force. The potential energy of the particle is given by $U=5x^2-20x+2 \mathrm{joule}$ where $x$ is co-ordinate of the particle expressed in meter. The particle is released at $x=-3 \mathrm{m}$.

$\left(\mathrm{a}\right)$ Find the maximum kinetic energy of the particle during subsequent motion.

$\left(\mathrm{b}\right)$ Find the maximum $x$ coordinate of the particle.

A particle moves in $x-y$ plane under the action of a force $\overrightarrow{F}=2A{x}^{2}y\hat{\mathrm{i}}+Ax{y}^2\hat{\mathrm{j}}$. Calculate the work done in going in an anticlockwise direction along the side of a square of vertices $\left(0, 0\right)$, $\left(1, 0\right)$, $\left(1, 1\right)$ and $\left(0, 1\right)$. Can this force be conservative?

A conservative force does $2 \mathrm{J}$ of work in moving a particle from $A$ to $C$ via $ABC$. The force does $-1 \mathrm{J}$ work when moving from $D$ to $F$, $3 \mathrm{J}$ for the path $EB$, $1 \mathrm{J}$ for $EF$ and $1 \mathrm{J}$ for $BC$. What is the work done by the force when the particle moves from $D$ to $C$?