Work, power & energy Questions and Answers

Two blocks in an at wood machine have masses 2kg and 3kg The work done by the gravity during the fourth second after the system is released from rest is B C 70 J 210J 140J IMELE Correct Answer Your Answer

A heavy box of 40 kg is pushed along 20 m by two coolies over a railway platform whose coefficient of friction with the box is 0 4 The work done by the two coolies is take g 10ms and assume forces applied to be horizontal 2 3200 J Your Answer

A ball hits a floor and rebounds after an inelastic collision In this case a the momentum of the ball just after the collision is same as that just before the collision b the mechanical energy of the ball remains the same during the collision c the total momentum of the ball and the earth is conserved d the total energy of the ball and the earth remains the same

A big block of mass M is placed on horizontal surface Two cubes each of mass m are attached with ideal string pulley system as shown in figure One cube falls in the well dug in to the block as shown Assuming all the surfaces are smooth and system is released from rest Find instantaneous power developed by gravity consider M 2m Assuming that the system starts moving from rest at time t 0 mold M m B

eri 38 A bullet of mass 50 g is fired from below into the bob of mass 450 g of a simple pendulum as shown in Figure The bullet stays inside the bob and the bob rises to a heightsofiev spin 1 8 m Find the speed of bullet g 10 m s wted 201 aieningo A 50 m s B 60 m s C 40 m sns pin on 0 om a s a9Y 8 pm 2 8 29Y A asihan to Inamom bns A bns A libs to rebrily owT A

Find the acceleration of the moon with respect to the earth from the following data Distance between the earth and the moon 3 85 105 km and the time taken by the moon to complete one revolution around the earth 27 3 days

5 Let 0 denote the angular displacement of a simple pendulum oscillating in a vertical plane If the mass o the bob is m the tension in the string is mg cose b never a always c at the extreme positions d at the mean position

c 60 2 A body of mass m kg is lifted by a man to a height of h m in 30 s Another man lifts the same mass to the same height in 60 s The work done by them are in the ratio a 1 2 c 2 1 yo b 1 1 d 4 1 20 load on his head climbs up 20

4 Two horizontal disks of mass Mhave the radii shown above Disk A is attached to an axle of negligible mass spinning freely with angular velocity Disk B not attached to the axle and initially held at rest is released and drops down onto disk A When both disks spin together without slipping the angular velocity of the disks is A B 0 200 D 45 00 Disk A M www haa W NI Single Person Usage

46 In a hypothetical atom potential energy between electron and proton at distance r is given by ke 472 where k is a constant Suppose Bohr theory ils bns betalents riq of atomic structure is valid and n is principle quantum number then total energy E is w proportional to a n5 b n c n6 ni er mots mego byd d n

m Block A is in equilibrium Now block A given velocity V 2 direction Maximum normal reaction on block B is A 3mg C 3mg 2 B 4mg D 2mg in downward E eller 5 2m B

Figure 8 E14 shows a light rod of length 1 rigidly attached to a small heavy block at one end and a hook at the other end The system is released from rest with the rod in a horizontal position There is a fixed smooth ring at a depth h below the initial position of the hook and the hook gets into the ring as it reaches there What should be the minimum value of h so that the block moves in a complete circle about the ring 1

To 0 2 x0 A block of mass m is on a rough horizontal surface and is attached to a spring with spring constant k The coefficient of kinetic friction between the surface and the block is u When the block is at position x 0 the spring is at its unstretched length The block is pulled to position x xo as shown above and released from rest The block then travels to the left and passes through x 0 before coming momentarily to rest at position xo 2 11 15 Which of the following is a correct expression for the kinetic energy of the block as it first travels through position x 0 A 0 B kx 2 C kx 2 umgxo D kx 2 3umgxo 2 Vansh P Single Person Usage vanshraaj

Questions 15 17 Leeeee 00 N x0 A block of mass m is on a rough horizontal surface and is attached to a spring with spring constant k The coefficient of kinetic friction between the urface and the block is u When the block is at sition x 0 the spring is at its unstretched length he block is pulled to position x as shown Dove and released from rest The block then travels the left and passes through x 0 before coming omentarily to rest at position x x 2 16 Which of the following is a correct expression for the coefficient of kinetic friction A B C D kxo 4mg kxo 2mg 3kxo 4mg kxo mg 2AXO mg 17 Which of the following is a differential equation that could be used to solve for the

A cord is used to vertically lower an initially stationary block of mass M 50 kg at a constant downward acceleration o g 8 When the block has fallen a distance d 5 5 m find the work done by the cord s force on the block Submit Answer Tries 0 5 Find the work done by the gravitational force on the block Submit Answer Tries 0 5 Find the kinetic energy of the block Submit Answer Tries 0 5 Find the speed of the block

A block of mass m sliding on a smooth horizontal surfac with a velocity v meets a long horizontal spring fixed a one end and having spring constant k as shown in figur 8 E10 Find the maximum compression of the spring Will the velocity of the block be the same as u when i comes back to the original position shown E m k

3 Figure 8 E7 shows a spring fixed at the bottom end of an incline of inclination 37 A small block of mass 2 kg starts slipping down the incline from a point 4 8 m away from the spring The block compresses the spring by 20 cm stops momentarily and then rebounds through a distance of 1 m up the incline Find a the friction coefficient between the plane and the block and b the spring constant of the spring Take g 10 m s ooooooo 37

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

1 A block of mass 5 0 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block The block is given a sharp impulse from below so that it acquires an upward speed of 2 0 m s How high will it rise Take g 10 m s

OY A J B 9 J 81 C 1 D 27 J x m 0 1 2 3 4 28 A specially designed spring is stretched from equilibrium to the distances x given in the table above and the restoring force F is measured and recorded in each case What is the potential energy of the spring when it is stretched 3 m from equilibrium J F N 0 1 8 27 64

d it mov Consider two observers moving with respect to each other at a speed u along a straight line They observe a block of mass m moving a distance on a rough surface The following quantities will be same as observed by the two observers 1 a kinetic energy of the block at time t b work done by friction c total work done on the block d acceleration of the block

9 One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed o a smooth horizontal surface In a displacement the work done by the spring is kx The possible cases are 2 a the spring was initially compressed by a distance and was finally in its natural length b it was initially streched by a distance x and finally was in its natural length c it was initially in its natural length and finally in a compressed position d it was initially in its natural length and finally in a stretched position

7 A block weighing 10 N travels down a smooth curved track AB joined to a rough a rough horizontal surface figure 8 E5 The rough surface has a friction coefficient of 0 20 with the block If the block starts slipping on the track from a point 10 m above the horizontal surface how far will it move on the rough surface 1 0 m B

A pea is placed on a vertical spring which has a spring constant of 11N m and the spring is compressed 15cm Upon release the spring travels a height of 2 9m What is the mass of the pea 10 marks

9 Two masses M and M are connected by a light ro and the system is slipping down a rough incline of angle 0 with the horizontal The friction coefficient at both the contacts is u Find the acceleration of the system and the force by the rod on one of the blocks

50 When a certain spring is stretched by an amount x it produces a restoring force of F x ax bx2 where a and b are constants How much work is done by an external force in stretching the spring by an amount D from its equilibrium length A aD bD B a 2bD C aD bD 3 D aD bD E 2aD 3bD

You lift a suitcase from the floor and keep it on a tabl The work done by you on the suitcase does not depen on a the path taken by the suitcase b the time taken by you in doing so c the weight of the suitcase d your weight

5 An unruly demonstrator lifts a stone of mass 200 from the ground and throws it at his opponent At the time of projection the stone is 150 cm above the ground and has a speed of 3 00 m s Calculate the work done by the demonstrator during the process If it takes one second for the demonstrator to lift the stone and throw what horsepower does he use

3 A car weighing 1400 kg is moving at a speed of 54 km h up a hill when the motor stops If it is just able to reach the destination which is at a height of 10 m above the point calculate the work done against friction negative of the work done by the friction

2 The 200 m free style women s swimming gold medal at Seol Olympic 1988 went to Heike Friendrich of East Germany when she set a new Olympic record of 1 minute and 57 56 seconds Assume that she covered most of the distance with a uniform speed and had to exert 460 W to maintain her speed Calculate the average force of resistance offered by the water during the swim

3 The US athlete Florence Griffith Joyner won the 100 m sprint gold medal at Seol Olympic 1988 setting a new Olympic record of 10 54 s Assume that she achieved her maximum speed in a very short time and then ran the race with that speed till she crossed the line Take her mass to be 50 kg a Calculate the kinetic energy of Griffith Joyner at her full speed b Assuming that the track the wind etc offered an average resistance of one tenth of her weight calculate the work done by the resistance during the run c What power Griffith Joyner had to evert to maintain uniform spoed

The two particles of mass m and 2m respectively are connected by a light rod of negligible mass and slide with negligible friction on a circular path of radius r on the inside of a fixed vertical circular ring If the system is released from rest at 0 0 and 9 is taken from positive x axis in clockwise direction A The speed of the particles when the rod passes the horizontal position is B The maximum speed of the particles is er 1 gr 5 1 C The maximum speed of the particles is at 0 tan D The maximum value of 0 is 2tan 2 m 2m 2gr 3 3 2

SolveLancer Test A body of mass 50 gram moves due to external force If the sum of initial and final speed is 20 m s and work done by the force is 500 J Find the change in speed SolveLancer Test a 0 1 m s b 0 01 m s C 0 001 m s d 1 m s

Zere Mariz 0 In all other cases Engine is used to move a mass of 0 8 kg starting from rest a distance of 2 m in a straight line along a frictionless flat surface Engine exerts a constan force of 5 N Find the average power in W exerted by the engine

cm sec cm sec 30 30 The string of pendulum of length I is displaced through 90 from the vertical and released Then the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is 1 mg 2 3 mg 3 5 mg 4 6 mg 3 36 36 I U C

A person in a sledge total mass of 120 kg slides a frictionless icy stope from a height of 3 50 m The sledge is initially at rest and comes to a stop momentarily after compressing a coil spring of negligible mass by 1 00 m Consider the sledge as a point Assume elastic collision between the sledge and the spring Calculate the spring constant K of the spring N m Report the answer of K 1200

9 A small steel ball falls through a syrup at a constant speed of 1 0 m s If the steel ball is pulled upwards with a force equal to twice its effective weight how fast will it move upward a 1 0 m s c 0 5 m s b 2 0 m s d zero

A particle m 1 kg slides down a frictionless track AOC starting from rest at a point A height 2 m After reaching C the particle continues to move freely in air as a projectile When it reaching its highest point P height 1 m the kinetic energy of the particle in J is Figure drawn is schematic and not to scale take g 10 ms A 2m Height P

The time period of a spring block system is T The spring is cut into two parts with their lengths in ratio 2 3 Now the block is attached to smaller part and put to oscillations The ratio of new period to old will be 1

3 A uniform flexible chain of mass m and length 1 hangs in equilibrium over a smooth horizontal pin of negligible diameter One end of the chain is given a small vertical displacement so that the chain slips over the pin The speed of chain when it leaves pin is gl a b gl c 2gl d 3gl

One end of a uniform wire of length L and of mass M is attached rigidly to a point on the ceiling and a block of mass M is suspended from its lower end If area of cross section of the wire is A then stress in the wire at a distance from its lower end will be Mg 4 3Mg 4A 2Mg A 7Mg 4A 3L 4

A bead is free to move along a fixed and smooth parabolic wire of shape y x Bead H is released from height H from rest when height of bead from ground is then at 2 that moment A Speed of bead is gH B Acceleration of bead is 2H 1 2H g H C Magnitude of rate of change of gravitation potential energy is D Rate of change of kinetic energy is 2mg H 1 2H 2mg H 1 2H

3 A chain of length 1 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 through an angle 0 c Find the du tangential acceleration of the chain when the chain dt atarta clidis

A body is thrown horizontally from the top of a tower of 5m height It touches the ground at a distance of 10m from the foot of the tower Then initial velocity of the body is g 10ms 1 2 5 ms 2 5 ms 3 10 ms 4 20 ms 01 Two thin wood screens A and B are separated by 200m A bullet travelling horizontally at a speed of 600ms hits the screen A penetrates through it and finally emerges out from B making holes in A and B If the resistance of air and wood are negligible the difference of heights of the holes in A and B is 49 3 7 Fm 4 zero

A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m in 15 min If the tank is 40 m above the ground and the efficiency of the pump is 30 how much electric power is consumed by the pump

A force F of constant magnitude acts on a block of mass m and t 0 initially along positive x direction The direction of force F starts rotating with a constant angular velocity wir anticlockwise sense Then the magnitude of velocity of the block as a function of time t is initially block was at rest F A sin 2 mo F 2mo C sin B D 2F mo sin 2F 3mo wt 2 sin 2

8 A small block of mass 100 g is pressed against a horizontal spring fixed at one end to compress the spring through 5 0 cm figure 8 E11 The spring constant is 100 N m When released the block moves horizontally till it leaves the spring Where will it hit the ground 2 m below the spring mmmmmm

A box weighing 2000 N is to be slowly slid through 20 m on a straight track having friction coefficient 0 2 with the box a Find the work done by the person pulling the box with a chain at an angle 0 with the horizontal b Find the work when the person has chosen a value of 0 which ensures him the minimum magnitude of the force quor

32 A machine gun of mass 10kg fires 10gm bullets at the rate of two every second Each bullet comes out with a velocity of 200 m s The velocity of recoil of the gun at the end of the fourth second after firing starts is 1 1 6 m s 3 3 2 m s 2 0 8 m s 4 2 0 m s

D A person is painting his house walls He stands on a ladder with a bucket containing paint in one hand and a brush in other Suddenly the bucket slips from his hand and falls down on the floor If the bucket with the paint had a mass of 6 0 kg and was at a height of 20 m at the time it slipped how much gravitational potential energy is lost together with the paint