Work

To maintain a speed of $80 \mathrm{km} {\mathrm{h}}^{-1}$ by a bus of mass $500 \mathrm{kg}$ on a plane rough road for $4 \mathrm{km}$ distance, the work done by the engine of the bus will be _____ $\mathrm{kJ}$. [The coefficient of friction between tyre of bus and road is $0.04$]

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 bead of mass$2 \mathrm{kg}$ starts from rest from $A$to move in a vertical plane along a smooth fixed quarter ring of radius$5 \mathrm{m}$, under the action of a constant horizontal force$F=5 \mathrm{N}$ as shown. The speed of bead as it reaches point$B$ is

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 

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 

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

A box of about $10 \mathrm{kg}$ is placed at a point $A$ on a horizontal surface. It is moved to a 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 $60°$ with the horizontal.
(a) Find the work done by the gravitational force on the box.
(b) Calculate the work done by the externally applied force.
$\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A $2 \mathrm{kg}$ block slides down a fixed rough incline of length $5 \mathrm{m}$, with coefficient of friction $0.2$, as shown. Taking $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, calculate the work done by friction force on the block as it slides down to the lowest point.

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The curved portions are smooth and horizontal surface is rough. The block is released from $P$. At what distance from $A$ it will stop (if $\mu =0.2$)

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A person of mass $m$ is standing on one end of a plank of mass $M$ and length $L$ and floating in water. The person moves from one end to another and stops. Work done by normal force is

A body constrained to move along the z-axis, under a constant force $\overrightarrow{F}=-\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}} \mathrm{N}$. Work done by this force in moving the body a distance $4 \mathrm{m}$ along the $z$-axis is

A rope of length $15 \mathrm{m}$ is suspended from a tree. A man of mass $50 \mathrm{kg}$ climbs along the rope in vertical direction with a constant acceleration $\frac{g}{3}$. Find the work done by the rope on the $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

What is the work done by a force of $1 \mathrm{gf}$ in displacing a body of $5g$ through $1 \mathrm{cm}$?