 ##### Introduction

In this video we will discuss about the overview of the work energy chapter and the reason of merging the kinematics and dynamics to further understand more concepts of physics. And what do we mean by energy.

##### Kinetic energy

In this video we will discuss what is the meaning of kinetic energy and its formulation ? mv^2. Is it dependent on the direction of motion. Work done as change of kinetic energy of the object.

##### Work - 1

In this we will discuss what do we mean by work? Work = F.S, when force is constant and how to find net work done. Work energy theorem.

##### Q1

Find the work done by the normal reaction in the cases shown below.

##### Q2

Find whether the work done by the friction acting on the block in the following situations is +ve , -ve or 0.

##### Q3

Three constant forces F1 = 2i - 3j + 2k; F2 = i + j -k and F3 = j - k dispalce a particle from (1,-1,2) to (2,2,0).
Find the total work done by forces.
(Forces are in Newtons and displacement is in metres)

##### Q4

A ball of mass 1kg is thrown vertically upwards with speed of 10 m/s.
Find the work done by gravity for the
a) upward motion of the ball,
b) downward motion of the ball.

##### Work - 2

In this video we will discuss how to find the work done if the force acting on the object is not constant.

##### Q5

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.
True/False

##### Work by Gravity

In this video we will discuss about the work done by gravitation force in different cases like horizntal projectile verticle throw, vertical projectile etc.

##### Work by Spring

In this video we will discuss the meaning of the work done by the spring and deriving the work done by it ? kx^2. And till when that is applicable?

##### Work by Friction

In this video we will discuss the work done by the friction and dependency of it on the path taken by the object.

##### Reference Frames

In this video we will discuss is the work energy theorem depend on the frame of reference? how to apply the work energy theorm in non inertial frame of reference.

##### Q6

A worker on a railway cart is pushing a box. The cart is moving at a constant speed of 10 m/s by some external agent. The box has a mass of 50 kg, and is being pushed forward over a distance of 2 m on the cart by the worker at constant acceleration, increasing its speed from 0 to 2 m/s relative to car. 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.

##### Q7

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

##### Conservative Forces

In this video we will discuss the meaning of conservative and non conservative force, and the dependency of the final and initial position for the work done by the conservative forces. How to know whether a force is conservative or non conservative?

##### Q8

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 ?

##### Q9

Find speed of the object at the bottom of the frictionless ramp.

##### Potential Energy 1

In this video we will discuss how to find the work done by non conservative force in terms of kinetic and the potential energy. What do we mean by potential energy? Change of potential energy in terms of work done by conservative force.

##### Potential Energy 2

In this video we will discuss the meaning of reference frame for finding the potential energy in different system like gravitational and spring potential energy.

##### Sys of Particles

In this video we will discuss the meaning of work done by external and internal forces. And finding the work done on system of particles . Applying work energy theorem on system of particles.

##### Cons of Mech Energy

In this video we will discuss the condition for applying the conservation of mechanical energy and understanding about how to apply that in different cases.

##### Q10

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 nonconservative force Fnc act on the object. The change DEmec in the objects mechanical energy (in joules) in going from i to f is indicated along each straight- line segment of the indirect paths.
What is DEmec
a) from i to f along the direct path
b) due to Fnc

##### Cons of Energy

This video is about the understanding of the conservation of energy which says that the total energy is conserved and energy transform from one form to other form making the net energy of universe constant.

##### Q11

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

##### Power

In this video we discuss the meaning of power and the formulation of power as rate of change of work done, and also P = F.V.

In this video we discuss the graphical meaning of change of potential energy with the displacement. And understanding how F = -dU/dx.

##### PE Curves 1

In this we understand the importance of potential energy curve, and meaning of slope of potential energy curve.

##### PE Curves 2

In this video we understand how to extract information about kinetic energy of the system if we have potential energy curve given along with the knowledge of total mechanical energy. And also we understand the meaning of turning points.

##### 1

In Figure, a small, initially stationary block is released on a frictionless ramp at a height of 3.0 m. Hill height along the ramp are as shown. The hills have identical circular tops, and the block does not fly off any hill.
(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?

##### 2

A ball tied to a masless 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 q
(d) tension as a function of q

##### 3

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.

##### 4

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. Is the blocks kinetic energy increasing, decreasing, or constant in
(a) Region AB
(b) Region BC
(c) Region CD
(d) Is the blocks mechanical energy increasing, decreasing or constant in those regions ?
(e) The block slides to a stop in a certain distance d. If instead, we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d ?

##### 5

A particle can slide along a track with elevated ends and a flat central part, as shown in Figure. The flat part has length L. The curved portions of the track are frictionless, but for the flat part the coefficient of kinetic friction is ?k = 0.20. 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?

##### 6

A massless rigid rod of length L has a ball of mass m attached to one end. The other end is pivoted in such a way that the ball will move in a vertical circle. First, assume that there is no friction at the pivot. The system is launched downward from the horizontal position A with initial speed v0. The ball just barely reaches point D and then stop.

##### 7

The heavier block in an Atwood machine has a mass twice that of the lighter one. The tension in the string is 16.0 N 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.
Find velocity of block. (take g = 9.8 m/s2)

##### 8

A cord runs around two massless, frictionless pulleys. A block with mass m = 20 kg hangs from one pulley, and you exert a force F on the free end of the cord.

##### 9

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 become equal slowly.
Calculate the work done by the force of gravity during the process. The density of water is.

##### 10

System is released from rest with mass m2 in contact with the ground. Pulley and spring are massless and the friction is absent everywhere.

Find the speed of m1 when m2 just leaves the contact with the ground .

##### 11

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)

##### 12

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 blocks speed is greatest?

##### 13

A collar of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5 m as shown in fig. The spring lying in the plane of the circular track and having spring constant 200 N/m is unstretched 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

##### 14

In Figure, a block of mass m is released from rest on a frictionless incline of
angle q. Below the block is a spring. The block momentarily stops when it compresses the spring.
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?

##### 15

Block of mass m1 falls from height h above the relaxed position of spring ( with spring constant k) and sticks to the spring.Find the height so that the block m2 just leaves contact with the ground.

##### 16

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.

##### 17

A block of mass m is attached to two unscratched 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.

##### 18

Figure shows two blocks A and B, each having a mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block A can slide is smooth. The block A is attached to a spring of spring constant 40 N/m whose other end is fixed to a support 40 cm above the horizontal surface. Initially, the spring is vertical and unstretched when the system is released to move.

##### 19

Find the speed of m1 when m2 falls a distance d?
Given
m1 = m , m2 = 2m , m = 0.1 , d = 9 meter , g = 10 m/s2.

##### 20

A block of mass m = 2.5 kg slides head on into a spring of spring constant
k = 320 N/m. When the block stops, it has compressed the spring by 7.5 cm. The coefficient of kinetic friction between block and floor is 0.25. While the block is in contact with the spring and being brought to rest.

##### 21

The cable of 1800 kg elevator cab in figure snaps when the cab is at a distance d = 3.7 m above an ideal spring of spring constant k = 0.15 MN/m. A safety device clamps the cab against the rails so that a constant frictional force of 4.4 kN opposes the cabs motion. (g = 10 m/s2)
a) Find the speed of the cab just before it hits the spring.
b) Find the maximum distance x that the spring is compressed (the frictional force still acts during the compression).
c) Find the distance that the cab will bounce back up the shaft.
d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest.
(Assume that the frictional force on the cab is negligible when the cab is stationary)

##### 22

A railway compartment moving with constant speed has a spring of constant k fixed to its front wall 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

##### 23

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 arbitary path from point 1 to point 2 which are located at the distances r1 and r2 from the rotation axis?

##### 24

In figure a block is released from rest at height d and slides down a frictionless ramp and onto a first plateau, which has length d and where the coefficient of kinetic friction is 0.50. If the block is still moving , it then slides down a second frictionless ramp through height d/2 and onto a lower plateau , which has length d/2 and where the coefficient of kinetic friction is again 0.50. If the block is still moving, it then slides up a frictionless ramp until it (momentarily) stops. Where does the block stop?

##### 25

In Figure, a block slides along a path that is without friction until the block reaches the section of length L = 0.75m, which begins at height h = 2.0 m on a ramp of angle q = 300. In that section, the coefficient of kinetic friction is 0.40. The block passes throught 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?

##### 26

A heavy particle is suspended by a string of length l. The particle is given a horizontal velocity v0. The string becomes slack at some angle and the particle proceeds on a parabola.
a) Find the value of v0 if the particle passes through the point of suspension.
b) Find the max height reached by the particle.

##### 27

A water pump, rated 1000 W, has an efficiency of 75%. If it is employed to raise water through a height 10 m, find the volume of water drawn in 10 min.

##### 28

A pump is required to lift 1000 kg of water per minute from a well 20 m deep and eject it at a rate of 20 m/s.
Find the power delivered by pump?

##### 29

Figure 8-108 shows a plot of potential energy U versus position x of a 0.200 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9.00 J, UC = 20.00 J and UD = 24.00 J. The particle is released at the point where U forms a \"potential hill\" of \"height\" UB = 12.00 J, with kinetic energy 4.00 J. What is the speed of the particle at
(a) x = 3.5 m and
(b) x = 6.5 m What is the position of the turning point on
(c) the right side and
(d) the left side?

##### 30

A uniform chain of mass m and length l overhangs a table with its two third part on the table.
a) Find the work to be done by a person to slowly put the hanging part back on the table.
b) Find the kinetic energy of the chain as it completly slips off the table.

##### 31

A uniform chain of mass M and length L overhangs a horizontal table with its two third part on the table. The friction coefficient between the table and the chain is m.
Find the work done by the friction during the period the chain slips off the table.

##### 32

A uniform rope of linear mass density l and length l 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

##### 33

A chain of length l and mass m lies on the surface of a smooth sphere of radius R >> l with one end tied to the top of the sphere.
a) Find the gravitational potential energy of the chain with reference level at the centre of the sphere.
b) Suppose the chain is released and slides down the sphere. Find the kinetic energy of the chain, when it has slid an angle f.
c) Find the tangential acceleration of the chain when the chain starts sliding down.

##### 34

A block moving over a smooth horizontal surface of ice at a velocity v0, drives out on a horizontal road and comes to halt after distance d. The block has a length l, mass m, and friction between block and road is m.
Find the distance d

##### 35

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, of negligable mass and friction and at a height h, 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?

##### 36

A vessel in the shape of on inverted cone of height h and radius R is filled with a liquid of density r.
Find the loss in PE as entire liquid leaks out from the vessel on the floor?

##### 37

A body of mass m was slowly pulled up the hill (Figure) 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 is h, the length of its base is L, and the coefficient of friction is m.

##### 38

A particle of mass m is moved along the surface given by 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 m. Ignore the dimensions of particle.

##### 39

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.

##### 40

The Kinetic energy of a particle moving along a circle of radius R depends on the distance covered s as KE = Ks2 ,where K is a constant. Find the force acting on the particle as a function of s.

##### 41

A horizontal plane supports a stationary vertical cylinder of radius R and a disc A attached to the cylinder by horizontal thread AB of length l0. An initial velocity v0 is imparted to the disc as shown in the figure. How long will it move along the plane until it strikes against the cylinder? The friction is assumed to be absent.

##### 42

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.

##### 43

A body of mass m is thrown at an angle a to the horizontal with the initial velocity vo. 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.

##### 44

The potential energy of a diatomic molecule (a two-atom molecule) is given by U = A / r12 - B / r6
Where r is the separation of the two atoms of the molecule and A and 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 atoms is zero.
Is the force repulsive (the atoms are pushed apart) or attractive (they are pulled together) if their separation is
b) Smaller and
c) Larger
than the equilibrium separation?

##### 45

A particle of mass m moves along a circle of radius R with a normal acceleration varying with time as an = Kt2 , 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.

##### 46

If potential energy due to a conservative force is given by the equation
U = 4x2y + 2yz2, find force.

##### 47

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.

##### 48

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 + ax3. Here k and a are positive constants. For x 0, the graph of the potential energy U(x) of the particle is