**Work, Power and Energy**

- This video introduces us to the concept of work, power and energy.
- This video introduces the concept of kinetic energy and formula for calculating it from velocity and mass of the object. It also explains the derivation of formula for the kinetic energy.
- This video explains the concept of work done by a constant force to move an object to a certain distance, as the change in kinetic energy gained/lost by the object.
- Find the work done by the normal reaction in the cases as shown in figure.
- Find whether the work done by the friction acting on the block in the situations as shown in figure is positive, negative or zero (0).
- Three cosntant forces (in vector form) acting simultaneously on a particle, displaces it from one position to other and then another (coordinates of positions are given). Find the total work done by forces.
- A ball is thrown vertically upwards with a given speed. Find the work done by gravity for the upward motion and the downward motion of the ball.
- This video explains the method of determining force in case of variable force acting on an object.
- Which of the following is true/false?In case of circular motion, work is done by centripetal force if
- (a) speed of the particle does not change. (b) Speed of the particle changes.
- This video discusses the work done by a gravitational force on an object for different situation.
- This video discusses the work done by spring force on an object attached to an ideal spring with help of graphs.
- This video explains the work done by friction force when an object slides very slowly in a curved path over a rough surface, ignoring the centripetal force.
- This video explains the dependence of kinetic energy and work done with respect to inertial and non-inertial frames of reference.
- As shown in figure, a worker on a railway cart is pushing a box of known mass which results into change in velocity of the box relative to cart in given time. The cart is moving at a constant speed of by some external agent. What will be the value of change in kinetic energy and work done by worker as calculated by the (a) observer standing inside the cart (b) observer standing on ground.
- A body of mass m is moving with a velocity V relative to an observer O and with a velocity V' relative to O'. The velocity of O' relative to O is v. If KE and KE' be the kinetic energies of the particle as measured by O and O' then find the relation between KE and KE'.
- This video explains the difference between the conservative and non-conservative force in terms of dependence on the path taken.
- The figure shows four paths connecting points 'a' and 'b'. A single force F does the indicated work on a particle moving along each path in the indicated direction. On the basis of this information, is force F conservative?
- Find speed of the object at the bottom of the frictionless ramp as shown in figure which starts from rest at the top of the slide and moves under force of gravity and normal reaction.
- This video introduce the concept of potential energy as the part of work done by conservative forces and can be termed as energy associated with the state or configuration of system.
- This video explains in detail, the change in potential energy of an object, taking example of gravitational and elastic potential energy.
- This video outlines the importance of internal forces of a system of particles in determining the work done and changes in kinetic energy.
- This video explains the concept of mechanical energy as a sum of kinetic and potential energy of a system. It also explains the conditions for conservation of mechanical energy of a system.
- Figure shows one direct path and four indirect paths from point i to point f. Along the direct path and three of the indirect path, only a conservation force Fc acts on a certain object. Along the fourth indirect path, both Fc and a non-conservative force Fnc act on the object. The change ΔEmec in the object's mechanical energy in going from 'I' to 'f' is indicated along each straight- line segment of the indirect paths. What is ΔEmec (a) from i to f along the direct path (b) due to Fnc
- This video illustrates the law of conservation of energy which states that energy can neither be created nor be destroyed. It can only change from one form to another.
- Mark the correct alternative for each statement. (i) The negative of the work done by the conservative internal forces on a system equals the change in (ii) The work done by the external forces on a system equals the change in (iii) The work done by all the forces (external and internal) on a system equals the change in(a) total energy (b) kinetic energy(c) potential energy (d) none of these
- This video explains the concept of power as rate of energy transfer or rate of work done. It also shows the derivation of its formula as product of force and velocity.
- This video illustrates the definition of a conservative force as a negative derivative of potential energy for 1-D and 3-D motion.
- This video shows the method to derive forces at different points of a potential energy graph. It also explains the stable, unstable and neutral equilibrium point for a potential energy curve.
- This video shows the method to calculate kinetic energy and to identify turning point from a potential energy graph when total mechanical energy of the system is known.
- A small, initially stationary block is released on a frictionless ramp as shown in figure. Assuming that the hills have identical circular tops and the block does not leave contact with ramp at any point, answer the following. (a) Which hill is the first the block cannot cross? (b) What does the block do after failing to cross that hill? On which hilltop is (c) the centripetal acceleration of the block greatest and (d) the normal force on the block least?
- A ball tied to a mass-less string is made to move in a vertical circle of radius R. Find the relation between the (a) speed of the ball at the highest and lowest points (b) tension in the string at highest and lowest points (c) speed as a function of angle θ(d) tension as a function of angle θ where θ s the angle made by string with lowest point of the ball.
- A small block of mass m can slide along the frictionless loop-d-loop, with loop radius R. The block is released from rest at point P, at height h = 5.0R above the bottom of the loop. Find the work done by gravitational force as the block travels to different point and potential energy at those points. Also find the minimum ratio h/R for the block to complete the circle.
- As shown in figure, a block slides from 'A' to 'C' along a frictionless ramp, and then it passes through horizontal region CD, where a frictional force acts on it. In which part, the kinetic energy and mechanical energy of block increasing, decreasing, or constant. If the block slides to a stop in a certain distance d, will the stopping distance change, when mass of block is increased.
- A particle can slide along a track with smooth elevated ends and a rough flat central part, as shown in Figure. The particle is released from rest at point A, which is at height h = L/2. How far from the left edge of the flat part does the particle finally stop?
- A mass-less rigid rod of length L has a ball of mass m attached to one end, free to move in a vertical circle, as shown in figure. The system is launched downward from the horizontal position A with initial speed v0. The ball just barely reaches point D and then stop. Find an expression for v0 and tension in rod at point 'B'. If there is friction at pivot and ball barely reaches 'C', find the decrease in mechanical energy.
- The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is known when the system is set into motion. Find the decrease in the gravitational potential energy during the first second after the system is released from rest and velocity of block.
- A cord runs around two mass-less, frictionless pulleys as shown in figure. A block hangs from one pulley and a force F is exerted on the free end of the cord. Find the force 'F' to lift the block at constant speed and distance to which free end be pulled to lift the block by a certain height. Also, find the work done by force and gravity during lift.
- Two cylindrical vessels of equal cross-sectional area A contain water up to height h1 and h2. The vessels are interconnected so that the levels in them slowly become equal. Calculate the work done by the force of gravity during the process. Given is the density of water.
- System shown in figure is released from rest with mass m2 in contact with the ground. Pulley and spring are mass-less and the friction is absent everywhere. Find the speed of m1 when m2 just leaves the contact with the ground.
- a) A block of mass m is resting on a spring of spring constant k. What is the compression in the spring? (b) If the block is now held at the height of relaxed position of spring and then released, what is the maximum compression in the spring? (c) Explain the difference in the energy of the system in part (a) & (b)
- A block of mass m is dropped from height h onto a spring of spring constant k. What is the distance between the point of the first block-spring contact and the point where the block's speed is greatest?
- A collar is constrained to move along a horizontal smooth and fixed circular track as shown in figure. The spring lying in the plane of the circular track and is un-stretched when the collar is at point A. If the collar starts from rest at point B, the normal reaction exerted by the track on the collar when it passes through point A is…?
- As shown in figure, a block of mass m is released from rest on a frictionless incline with a spring at the bottom. The block momentarily stops when it compresses the spring. Answer the following (a) How far does the block move down the incline from its rest position to this stopping point? (b) What is the speed of the block just as it touches the spring?
- Block of mass m1 falls from height h above the relaxed position of spring and sticks to the spring as shown in figure. Find the height so that the block m2 just leaves contact with the ground.
- A Block of mass m is dropped from a height h onto the spring with spring constant k. Find the maximum compression in the spring. If the mass recoils without any loss of energy, Find the maximum height reached by the block if,(a) The block does not stick to the spring. (b) The block sticks to the spring.
- A block of mass m is attached to two un-stretched springs of spring constants k1 and k2 as shown in figure. The block is displaced through a distance x and is released. Find the speed of the block as it passes through the mean position.
- Figure shows two blocks A and B are connected by a light string passing over a smooth light pulley. Block A is kept over a smooth surface and attached to a spring whose other end is fixed to a ceiling. Initially, the spring is vertical and un-stretched when the system is released to move. Find the velocity of block A at the instant it breaks off the surface.
- For the system shown in figure, find the speed of m1 when m2 falls a distance d?
- A block of known mass slides head on into a spring as shown in figure. When the block stops, it has compressed the spring by a certain distance. The coefficient of kinetic friction between block and floor is given. While the block is in contact with the spring and being brought to rest. Find the work done by spring force, increase in thermal energy and block's speed just as it reaches the spring.
- As shown in figure, the cable of the elevator cab snaps when the cab is at a distance above an ideal spring. A safety device clamps the cab against the rails so that a constant frictional force opposes the cab's motion. Find the speed of the cab just before it hits the spring, the maximum distance x that the spring is compressed, the distance that the cab will bounce back up the shaft. Using conservation of energy, also find the approximate total distance that the cab will move before coming to rest.
- A railway compartment moving with constant speed has a spring fixed to its front wall, as shown in figure. A boy compresses this spring by distance x and in the mean time the compartment moves by a distance s. Find the work done by a boy with respect to (a) Compartment (b)Earth.
- A small body of mass m moves in the reference frame rotating about a stationary axis with a constant angular velocity w. What work does the centrifugal force perform during the transfer of this body along an arbitrary path from point 1 to point 2 which are located at the distances r1 and r2 from the rotation axis?
- As shown in figure, a block is released from rest at a height and slides down a frictionless ramp and onto a first plateau. If the block is still moving, it then slides down a second frictionless ramp and onto a lower plateau. If the block is still moving, it then slides up a frictionless ramp until it (momentarily) stops. Where does the block stop? Given is length and coefficient of friction of plateau.
- As shown in figure, a block slides along a path that is without friction until the block reaches the section with known coefficient of kinetic friction. The block passes through point A with a speed of 8.0 m/s. If the block can reach point B (where the friction ends), what is its speed there, and if it cannot, what is its greatest height above A?
- A heavy particle is suspended by a string of length l. The particle is given a horizontal velocity. The string becomes slack at some angle and the particle proceeds on a parabola. Find the value of velocity if the particle passes through the point of suspension and maximum height reached by the particle.
- A water pump with known power rating has an efficiency of 75%. If it is employed to raise water through a certain height, find the volume of water drawn in given time. A pump is required to lift water at a given rate from a well and eject it at a certain rate. Find the power delivered by pump.
- Figure shows a plot of potential energy U versus position x of a particle that can travel only along an x axis under the influence of a conservative force. The particle is released at the point where U forms a 'potential hill' of 'height' UB, with a known kinetic energy. What is the speed of the particle at given distances? What is the position of the turning point on the right side and the left side?
- A uniform chain of mass m and length l overhangs a table with its two third parts on the table. Find the work to be done by a person to slowly put the hanging part back on the table and the kinetic energy of the chain as it completely slips off the table.
- A uniform chain of mass M and length L overhangs a horizontal table with its two third parts on the table. The friction coefficient between the table and the chain is known. Find the work done by the friction during the period the chain slips off the table.
- A uniform rope of known linear mass density and length is coiled on a smooth horizontal surface as shown in figure. One end is pulled up with constant velocity v. Then the average power applied by the external agent in pulling the entire rope just off the ground is…?
- A chain of lies on the surface of a smooth sphere with one end tied to the top of the sphere. Find the gravitational potential energy of the chain with reference level at the centre of the sphere. Now, suppose the chain is released and slides down the sphere. Find the kinetic energy of the chain, when it has slid an angle φ and the tangential acceleration of the chain when the chain starts sliding down.
- A block moving over a smooth horizontal surface of ice at a given velocity drives out on a rough horizontal road with known coefficient of friction and comes to halt after a certain distance. Find the distance.
- Figure shows a cord attached to a block that can slide along a frictionless horizontal surface aligned along x-axis. The left end of the cord is pulled over a pulley, so the block slides from x1 to x2. During the move, the tension in the cord is a constant. What is the change in the kinetic energy of the block during the move?
- A vessel in the shape of on inverted cone is filled with a liquid of known density. Find the loss in potential energy as entire liquid leaks out from the vessel on the floor?
- As shown in figure, a body of mass m was slowly pulled up the hill by a force F which at each point was directed along a tangent to the trajectory. Find the work performed by this force, if the height of the hill, the length of its base, and the coefficient of friction is given.
- A particle is moved along the surface given by equation y = x2 from x = 0 to x = l with constant but considerable speed v. Find the work done in the process; if the coefficient of kinetic friction between the particle and surface is known. Ignore the dimensions of particle.
- A locomotive of mass m starts moving so that its velocity varies according to the law v = K√s, where K is a constant, and s is the distance covered. Find the total work performed by all the forces which are acting on the locomotive during the first t seconds after the beginning of motion.
- The Kinetic energy of a particle moving along a circle of radius R depends on the distance covered s as KE = Ks^2, where K is a constant. Find the force acting on the particle as a function of s.
- As shown in figure, a horizontal plane supports a stationary vertical cylinder of radius R and a disc A attached to the cylinder by horizontal thread AB. An initial velocity v0 is imparted to the disc. How long will it move along the plane until it strikes against the cylinder?
- A vehicle of mass 'm' is drawn by a constant power P. Express the instantaneous velocity 'v' of the vehicle as a function of displacement 's', assuming the vehicle to start from rest.
- A body is thrown at an angle to the horizontal with a given initial velocity. It follows projectile motion and reaches the other end at the same horizontal level. Find the mean power developed by gravity over the whole time of motion of the body, and the instantaneous power of gravity as a function of time.
- The potential energy of a diatomic molecule is given by U = (A / r12) – (B / r6), where r is the separation of the two atoms of the molecule and A & B are positive constants. This potential energy is associated with the force that binds the two atoms together. (a) Find the equilibrium separation - that is the distance between the atoms at which the force on each atom is zero. Is the force repulsive or attractive if their separation is (b) Smaller and (c) Larger than the equilibrium separation?
- A particle of mass m moves along a circle of radius R with a normal acceleration varying with time as a = Kt^2 , where K is a constant. Find the time dependence of the power developed by all the forces acting on the particle, and the mean value of this power averaged over the first t seconds after the beginning of motion.
- If potential energy due to a conservative force is given by the equation(x,y,z) = 4x2 y + 2yz2, find force.
- A small body of mass m is located on a horizontal plane at the point O. The body acquires a horizontal velocity vo and then stops due to friction. Find (a) The mean power developed by the friction force during the whole time of motion, if the friction coefficient is k. (b) The maximum instantaneous power developed by the friction force, if the friction coefficient varies as k = ax, where a is a constant, and x is the distance from the point O.
- A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F (x) = -kx + ax^3. For x≥0, the graph of the potential energy U(x) of the particle is….?