Work and Energy

A force $\overrightarrow{F}=\left(2+3x\right)\hat{i}$ acts on a particle in the $x$ direction where $F$ is in Newton and $x$ is in meter. The work done by this force during a displacement from $x = 0$ to $x=4 \mathrm{m}$ is _____ $\mathrm{J}$.

A variable force $F=5Kx \mathrm{N}$ acts on a body moving along x-axis. Find the work done by this force in displacing the body from $x= 2 \mathrm{m}$ to $x=5 \mathrm{m}$ ($K$ is a constant).

Force acting on a particle moving along $x-$axis is given by $\overrightarrow{F}=(2+3x)\hat{\mathrm{i}}$. The work done by this force from $x=0$ to $x=4 \mathrm{m}$ is

A particle starts to move along the path which locus is given as $x^2=\left(8y\right)$ $(x\&y \text{are in} \mathrm{m})$, due to applied force $\overrightarrow{F}=(ax\hat{\mathrm{i}}+by\hat{\mathrm{j}} ) \mathrm{N}$ $(a>0 \text{and} b>0 \text{and} x \& y \text{are in metre})$. The amount of work done in displacing particle from $x=0$ to $x=1$ metre is

A large box of mass $50 \mathrm{kg}$ rests on a horizontal floor. A man moves the box by pushing it with a horizontal force of $200 \mathrm{N}$. The box moves at a constant speed of $0.25 \mathrm{m} {\mathrm{s}}^{-1}$.

(a) Calculate the work done on the box at each second by the man.

(b) State the rate at which work is done on the box, i.e. power.
(c) State the value of force of friction between the floor and the box. Explain your answer.

A force,$F=(10+x) \mathrm{N}$ acts on a particle of mass $4 \mathrm{kg}$ in $x$ direction, where $x$ is in meter. Find the work done by the force during the time interval its acceleration changes from$2.5 \mathrm{m} {\mathrm{s}}^{-2}$ to  $5.0 \mathrm{m} {\mathrm{s}}^{-2}$
 

An object of mass m moves on a circular track of radius R with constant speed U. The work done by centripetal force after it completes one circle is 

If the potential energy at point $\mathrm{O} (0, 0)$ is ${\mathrm{U}}_0= 10 \mathrm{J}$, find the potential energy at point $\mathrm{D} (4, 0)$ corresponding to the given graph.

A sponge is placed in contact with ground and wall. Force of magnitude $10 \mathrm{N}$ is applied at P which causes the displacement of P by$2.5 \mathrm{cm}$ then,

(a) Work done on sponge is $25\mathrm{x}{10}^{-2} \mathrm{J}$ (b) Work done by F is stored in P.E. of sponge. (c) Work done by is stored in P.E. and K.E. of sponge

Force acting on a particle is $F=3i-2j+4k$ and its displacement is given by $AB=(2,-1,0)$, then the work done is _____.

A force acting on a particle of mass$1\mathrm{kg}$ such that position of particle (x) is varying with time (t) as $\mathrm{x}=2{\mathrm{t}}^2-1$ where x is in m and t is in s. Work done by the force during $0 \mathrm{to} 2 \mathrm{s}$ is 

Calculate the net work done by the force $F$ whose variation with position has been shown as above.

The area of the acceleration-displacement curve of a body gives

A block of mass is placed at origin $(0, 0)$ and a force, $\mathrm{F}=(2\mathrm{x} + 2) \mathrm{N}$, is applied on the block that it reaches at some other point. $\mathrm{P} (5, 0)$. Find the work done by the force.
 

A box of about $10 \mathrm{kg}$is placed at point A on a horizontal surface. It is moved to point B which is at a distance of  $2 \mathrm{m}$ from A by the action of force, $4 \mathrm{N}$applied on the box at an angle of $60°$.
(a) Find the work done by the gravitational force on the box. 
(b) Calculate the work done by the externally applied force. Justify your answer. (Given $\mathrm{g}=10 {\mathrm{ms}}^{-2}$) 

A particle is moving uniformly on a horizontal circular path. Work done by centripetal force on the particle in one half revolution is 
 

In the device the acceleration of block $A$ is $1 \mathrm{m} {\mathrm{s}}^{-2}$. The acceleration of block $B$ will be