Work, Energy and Power

A particle of mass $M$ moves along a horizontal $x$ axis from $x=0$ to $x=L$. The coefficient of kinetic friction varies as a function of $x$ as $\mu_k(x)=\mu_0-\alpha x$, where $\mu_0$, $\alpha$ are constants of appropriate dimensions, so ...

The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s is: $\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right)$

A bob of heavy mass $m$ is suspended by a light string of length $/$. The bob is given a horizontal velocity $v_0$ as shown in figure. If the string gets slack at some point $P$ making an angle $\theta$ from the horizontal, the ratio of the...

The kinetic energies of two similar cars $A$ and $B$ are 100 J and 225 J respectively. On applying breaks, car $A$ stops after 1000 m and car $B$ stops after 1500 m . If $F_A$ and $F_B$ are the forces applied by the breaks on cars $A$ and $...

An object falls from a height of \(10 \mathrm{~m}\) above the ground. After striking the ground it loses \(50 \%\) of its kinetic energy. The height upto which the object can rebounce from the ground is:

An object moving along horizontal \(x\)-direction with kinetic energy \(10 \mathrm{~J}\) is displaced through \(x=(3 \hat{i}) \mathrm{m}\) by the force \(\vec{F}=(-2 \hat{i}+3 \hat{j}) \mathrm{N}\). The kinetic energy of the object at the e...

At any instant of time \(t\), the displacement of any particle is given by \(2 t-1\) (\(\mathrm{SI}\) unit) under the influence of force of \(5 \mathrm{~N}\). The value of instantaneous power is (in \(\mathrm{SI}\) unit):

A particle moves with a velocity \((5 \hat{i}-3 \hat{j}+6 \hat{k}) ~\mathrm{ms}^{-1}\) horizontally under the action of constant force \((10 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+20 \hat{\mathrm{k}}) \mathrm{N}\). The instantaneous power sup...

The potential energy of a long spring when stretched by \(2 \mathrm{~cm}\) is U. If the spring is stretched by \(8 \mathrm{~cm}\), potential energy stored in it will be :

The restoring force of a spring with a block attached to the free end of the spring is represented by

The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is

An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 ms\(-\)1. The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is : (...

Water falls from a height of 60m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? (g = 10 m/s2)

A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectiv...

A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to y = 1 m is :

A body initially at rest
and sliding along a
frictionless track from
a height h (as shown
in the figure)
just completes a vertical circle of diameter
AB = D. The height h is equal to

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m s\(-\)1. Take 'g' constant with a value 10 m s\(-\)2. The work done by the (i) gravitational force and the (ii) resistive ...

A particle moves from a point \(\left( { - 2\widehat i + 5\widehat j} \right)\) to \(\left( {4\widehat j + 3\widehat k} \right)\) when a force of \(\left( {4\widehat i + 3\widehat j} \right)\) N is applied. How much work has been done by th...

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

A body of mass 1 kg begins to move under the action of a time dependent force \(\overrightarrow F = \left( {2t\widehat i + 3{t^2}\widehat J} \right)N,\) where \({\widehat i}\) and \({\widehat j}\) are unit vectors along x and y axis. What ...

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic enegy of the particle becomes equal to 8 \(\times\) 10\(-\)4 J by the end of ...

Two similar springs P and Q have spring constants KP and KQ, such that KP > KQ. They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs WP and WQ are related as, in case (a) and ca...

A block of mass 10 kg, moving in x direction with a constant speed of 10 m s\(-\)1, is subjected to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is

Two particles A and B, move with constant velocities \(\overrightarrow {{v_1}}\) and \(\overrightarrow {{v_2}}\). At the initial moment their position vectors are \(\overrightarrow {{r_1}}\) and \(\overrightarrow {{r_2}}\) respectively....

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 \(\times\) 103 kg/m3 and g = 10 m/s2 then the power (in watt) is

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is
(Take g = 10 m s...

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle \(\theta\) to its initial direction and has...

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio

A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when

A uniform force of \(\left( {3\widehat i + \widehat j} \right)\) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position \(\left( {2\widehat i + \widehat k} \right)\) metre to position $$\left( {4\widehat i + 3...

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s\(-\)1. It collides with a horizontal spring of force constant 200 N m\(-\)1. The maximum compression produced in the spring will be

The potential energy of a particle in a force field is \(U = {A \over {{r^2}}} - {B \over r}\) where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the ...

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to

The potential energy of a system increases if work is done

A particle of mass m is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time ?

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

Force F on a particle moving in a straight line varies with distance d as shown in figure.

The work done on the particle during its displacement of 12 m is

A mass m moving horizontally (along the x-axis) with velocity \(v\) collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) with velocity 2\(v\). The final velocity of the combination is

A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?

A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is

A body of mass 1 kg is thrown upwards with a velocity 20 m/s. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (g = 10 m/s2)

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in t...

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine ? (g = 10 m/s2)

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the p...

300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Work done against friction is (Take g = 10 m/s2)

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = \({1 \over 3}\)t2, where t is in seconds. Work done by the force in 2 seconds is