Work, power & energy Questions and Answers

particle must be parallel to the velocity at all times A particle moves in one dimensional field with total mechanical energy E If its potential energy is U x then A particle has zero speed where U x 0 B particle has zero acceleration where U x E C particle has zero velocity where D particle has zero acceleration where dU x dx 0 dU x dx 0

m m s m k vooroor m smooth All blocks are identical and are of mass 1kg The two blocks attached with the light spring are initially at rest If the collision is perfectly inelastic the maximum compression of the spring after the collision can be k 60 000 Nm 1 1 67 cm 3 5 56 cm 2 3 33 cm 4 1 11 cm

Q19 Find the acceleration of 3 kg mass when acceleration of 2 kg mass is 2 ms as shown in figure 3kg 10N A 3 ms 2 B 2 ms 2kg 2ms C 0 5 ms D zero

A ring of mass m can slide along a fixed rough vertical rod as shown The ring is connected by a spring of constant K where 2R is the natural length of spring The other end of spring is fixed to the ground at point A at a horizontal distance of 2R from the base of the rod 4mg R 3R If the ring is released from a height of and it reaches the ground with a speed of 3gR 2 The coefficient friction between the rod and ring is 1 A 413 n2 wwww 2R 1 B 4 3 2 n2 3R 2 1 C 813 4 02

22 If two persons A and B take 2 seconds and 4 seconds respectively to lift an object to the same height h then the ratio of their potential energies at highest point is 1 1 2 3 2 1 2 1 1 4 1 3

15 A stone can slide down one of four different frictionless ramps as shown in the figure For which ramp w the speed of the ball be the greatest at the bottom Ramp Z X The speed of the ball will be the same for all ramps Ramp Y Z

A trolley of mass 18 kg is pulled with a velocity which depends on time and given as v 3t Sand is falling vertically on the trolley at a rate of 18 kg s Assume sand sticks to the trolley If rate of increase of Kinetic energy of the trolley at t 2 sec is n x 324 find the value of n O 3 O 4 05

A tank is full of water Find the work required to pump the water out of the spout Use the fact that water weighs 62 5 lb ft Assume a 3 ft b 4 ft and c 5 ft 62 5 32 2 19008 R T x T ft lb

Turbine Moved by Cyclist Pedaling at Medium Speed With A Fluorescent Light Bulb System Intro Energy Systems In this system converted to a lot of bit of UUS energy Energy Symbols Forms of Energy E Mechanical Electrical Thermal E Light Chemical Reset All energy from the cyclist is energy and a little energy The energy from the turning bicycle wheel spins the turbine which generates energy The fluorescent light bulb converts this energy into two new forms a lot of energy and very little

A hoop of radius 0 50 m and a mass of 0 20 kg is released from rest and allowed to roll down an inclined plane How fast is it moving after dropping a vertical distance of 6 05 m 3 8 m s 7 7 m s 5 4 m s 2 2 m s

A 1 60 kg disk starts at rest at the top of a 6 40 m high track A Its height at B is 4 00 m and its height at C is 2 00 m Assuming mechanical energy conservation determine the potential energy PE and kinetic energy KE values at locations A B C and D Use g 9 8 N kg PEA KEA A J Tap on an energy box to enter or edit its value PEB KEB B J PEc KEc De CC PED KED For best results avoid early rounding Enter answers to at least 3 significant digits Color Coding Key d yo

Using the Concept Builder The Stepping Up to PE and KE Concept Builder is shown in the iFrame below There is a hot spot in the lower right corner of the hot spot allows you to change the size of iFrame to whatever dimensions you prefer Consider the 4 step staircase All steps provide an equal elevation gain The potential energy PE on the top step is 60 0 J Determine the PE and KE values of the ball at the indicated positions PE J PE4 J 1 2 45 0 3 4 15 0 For best results enter answers to 3 significant digits PE J PE3 J PE5 J KE5 J 0 O Color Coding Key KE 8 J 5 30 0 Use the Number P the value o KES J 7 4 1 0 C 8 5 2 Er

Paul and Ivan are riding a tandem bike together They re moving at a speed of 5 meters second Paul and Ivan each have a mass of 50 kilograms What can Paul do to increase the bike s kinetic energy OA O B O C O D He can let Ivan off at the next stop He can pedal harder to increase the rate to 10 meters second He can reduce the speed to 3 meters second He can pick up a third rider

Establish the equations Solve for the necessary variable Plug N Chug Express answers to 3 SF 1 2 3 4 5 6 7 8 9 10 The roller coaster s car starts from rest What is the speed of the car after it just loses contact with the spring at the top of the first hill 11 33m 12 63 18m Car Mass 600 kg Spring Const 12000 N m Max Spring Compression 10m The Oinga Boinga Cowabunga 11m No Friction 11 5m Loom 60 Spring s Max Compression 6 6 meters What is the speed of the car when it is 18 meters above the ground What is the speed of the car as it enters the loop How many g s are felt by the rider as the car enters the loop What is the speed of the car when it reaches the top of the loop How many g s are felt by the rider at this point loop What is the speed of the car as the instant before it makes contact with the spring on the right What is the right spring s spring constant What is the speed of the car after the spring has been compressed 4 0 m from equilibrium What average force did the spring exert to stop the car How much time did it take to stop the car How much power was used by the spring to stop the car

33 m 18m The Oinga Boinga Cowabunga 11 m 11 5m Car Mass 600 kg Spring Const 12000 N m Max Spring Compression 10 m The roller coaster s car starts from rest with the spring at max compression No Friction C Ba Spring s Max Compression 6 6 meters What is the speed of the car when it reaches the bottom of the hill

4 Points A cylindrical tank with a length of 10 meters and a radius of 5 meters is on its side and half full of gasoline Set up the integral that shows how much work is required to empty the tank through an outlet pipe at the top of the tank You do not need to compute the total amount of work done The density of gasoline is 737 kg cubic meter Work

How much power is used by a contact lens heating unit that draws 0 051 A of current from a 120 V line

5 A 120 V household circuit that contains a 320 W television a 1 0 x102 W lamp and a 1350 W heater is connected to a 20 0 A fuse Will th fuse melt if all three devices are operating simultaneously Explain

Energy What is it Units Kinetic Energy What is it Equation Energy Review Units of each variable in the equation

For the following scenario draw both system diagrams and energy pie charts A moving cart m 10 0 kg hits a spring traveling at 15 0 m s at the time of contact At the instant the cart is motionless by how much is the spring compressed k 110 N m

Conservation of Energy What does this law state If I start with 1000 J of energy how much should I with What about in the presence of friction how m should I end with

If a spring has 250 000 J of energy and a spring constant of 200 N m by how much is it stretched or compressed

What is the potential energy of a barbell that has a mass of 182 5 kg if the barbell is lifted 1 7 m above the ground

Usain Bolt set a world record in 2009 by running the 100m in 9 58 seconds Calculate his kinetic energy if his mass was 94 0 kg Assume he ran with a constant speed

5 A 60 Watt light bulb uses up J of energy when left on for 1 hour 3600 s

Calculate the work done from the following F d graph over the first 6 0 m 1 Point 60 50 40 30 20 10 O 120 J O 60 J O 40 J 240 1 1 2 3 4 5 6 red

How much work is done by a student carrying a 12 kg backpack while accelerating at a rate of 0 51 m s over a distance of 5 0 m 1 Point O 750 J O OJ O 300 J O 590 J

A 0 20 kg ball is thrown straight up from the edge of a 30 0 m tall building at a velocity of 22 0 m s The ball moves up to the maximum height and then falls to the ground at the base of the building Use the law of conservation of energy to calculate the total energy of the ball at the start and the velocity of the ball when it hits the ground 1 Point O 110 J 33 m s O 110 J 0 m s O 59 J 33 m s O48 J 0 m s

14 A wire has 4x10 C of charge flow through it in 1 minute when it is plugged into a 24 V battery a What is the current b What is the Power c What is the resistance d How much work is done in 48 seconds 15 A bulb is plugged into a 220 Volt outlet The Resistance of the bulb is 45 2 a Calculate the current b Calculate the power c Calculate the work done in 2 minutes

Problem 1 The rollercoaster with a mass of 12 kg was given no initial push when it entered the frictionless track below Based on the following information determine a The total initial energy at point A b The velocity at point B c The velocity at point C 100m v 10 m s 24 5 m s on Al 50 m

7 About how much power does a sprinter produce if he transforms 2 70 kJ of chemical energy from food into kinetic energy and thermal energy in 14 0 s 1 Point O 5 2 W 37 8 W O 0 2 W O 193 W

16 What is the potential energy of a 69 kg person sitting at the top of a 28 m Ferris wheel 1 Point O 20 KJ 18 kJ 21 kJ 19 kJ

2 How much mechanical work does a woman do on a wheel barrow if she applies a force with a magnitude of 35 N in the forward direction and displaces the wheel barrow 4 0 m in the same direction 1 Point O 140 J O 39 J 04 J 35 J

13 A 1100 kg gas powered car is only 15 efficient How much input energy is needed for the car to reach a velocity of 11 m s from rest 1 Point O 37 kJ O 440 kJ O 890 KJ O 10 KJ

6 How much mechanical work is done on a brick wall if a man pushing with a 250 N force fails to move the wall 1 Point O OJ O 250 J O 125 J 2 5 J

3 If a descending parachutist has 8 00 kJ of kinetic energy and 225 00 kJ of mechanical energy how many kJ of gravitational potential energy does the parachutist have 1 oint O 217 00 O 1800 00 O217

49 1 An automobile engine develops a torque of 265 m N at 3350 rpm What is the horsepower of the engine

53 II Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms a that due to its daily rotation about its axis and b that due to its yearly revolution about the Sun Assume the Earth is a uniform sphere with mass 6 0 x 1024 kg radius 6 4 x 106 m and is 1 5 x 108 km from the Sun

Converting Between Grams Moles and Molecules A sample of ammonia NH 17 03 g mol has a mass of 56 6 g How many molecules are in this sample 1 mole 6 022x102 molecules a 3 32 molecules b 17 03 x 1024 molecules c 6 78 x 1023 molecules d 2 00 x 1024 molecules e 1 78 x 1024 molecules ANS d 1 Compositional Stoichiometry Grams Whole Chemical Formula to Number of Atoms that Make up the Chemical Formula How many oxygen atoms are there in 1 55 g of Ca PO4 3 01 x 1022 atoms 1 20 x1023 atoms a b c d 3 01 x 10 8 atoms 1 21 x 1016 atoms e 2 41 x 1022 atoms ANS e Compositional Stoichiometry Grams Whole Chemical Formula to Grams of Atoms that Make up the Chemical Formula NaHCO 84 07 g mol is the active ingredient in baking soda How many grams of oxygen 16 00 g mol spro are in 0 35 g of NaHCO a 0 012 g 0 b 0 022 g O c 0 067 g O d 0 20g0 ANS d How many grams of oxygen are in 1 55 g of Ca3 PO4 2 a 0 640 g 0 b 0 344 g 0 0077

7 II A 980 kg sports car collides into the rear end of a 2300 kg SUV stopped at a red light The bumpers lock the brakes are locked and the two cars skid forward 2 6 m before stopping The polic ficer estimating the coefficient of kinetic friction between tires and road to be 0 80 calculates the speed of the sports car at impact What was that speed

2 A 56 0 N crate starting at rest slides down a rough 8 3 m long ramp inclined at 30 with the horizontal The force of friction between the crate and ramp is 8 0 N Using the work kinetic energy theorem find the velocity of the crate at the bottom of the incline

Dizzy is speeding along at 24 8 m s as she approaches the level section of track near the loading dock of the Whizzer roller coaster ride A braking system abruptly brings the 321 kg car rider mass included to a speed of 2 76 m s over a distance of 5 16 meters Determine the magnitude of the braking force in newtons applied to Dizzy s car

kg cart is moving to the right at 3 m s and a 1 2 kg cart is moving to the left at 5 m s The two carts collide and stick together What is the final velocity of the two carts 40mm 19 IN 5 A 1 5 kg cart is moving on a track with a velocity of 5 m s at a height of 7 m above the ground The track then drops to the ground Find the velocity of the cart once it reaches the ground

all final answers should be to 1 decimal place 9 A 40 000 kg roller coaster starts from rest at point A Assume there is no friction Mo B 54 m 15 m 35 m a Calculate the speed of the roller coaster at point B 3 b Calculate the height of the roller coaster at point C if its speed is 12 m s at point C

4 A child swings on a swing so that her center of mass is located 2 4 m from the point where the rope is attached to the tree If she swings so that her maximum amplitude causes the rope to make an angle of 47 with the vertical calculate the child s maximum speed during the swing A 7 marks

1 A total of 490 J of work is done on a pin when a 5 0 kg sledgehammer strikes it bringing the sledgehammer to rest Calculate the initial speed of the sledgehammer T I 5C 4 marks 2 Two common and identical carts are used to perform an experiment Cart A is pushed toward the stationary cart B with a velocity of 2 6 m s After the collision cart A bounces back with a speed of 0 8 m s and cart B moves of with a speed of 3 4 m s Why is this not possible Justify your answer with appropriate calculations T I 5 marks C 2

Trigonometry An individual lifts an 882 9N barbell overhead t a height of 2m When the barbell is held overhead what are the potential and kinetic energies

Two cars have a rear end collision A 120 kg Honda moving at 20 m s strikes a 100 kg Ford moving at 15 m s Their bumpers become locked and they continue to move as one mass What is their final velocity

Determine whether or not the path travelled has an effect on the work being performed if the startira point and ending point remain the same Consider cases when there is only one constant force acting an object and other times when the forces acting on the object depend on the path Give an example each A student claims that almost all of the energy that we use today is due to the Sun in

Spring 2 initial length m Length of spring m 12cm 14cm 16cm 19cm 22cm 30cm Change in length Ax m 6 5cm 6 5cm 6 5cm 6 5cm 6 5cm 6 5cm Applied force F N 2 2N 2 9N 3 5N 4 6N 5 2N 8 2N Data You can apply force to the spring by hanging slotted weights from it or by clamping c end to a table and pulling on the spring with a spring scale or Vernier force pro connected to the computer The Vernier probe will need to be calibrated with a kno force or standard weight The length of the spring can be measured with a ru Remember however you are graphing the change in length so don t forget to record initial length of the spring Also do not stretch the spring out close to its limit it n the spring and complicates the mathematical model Spring 1 initial length m Length of spring m 14cm 12cm 10cm 1 1 2 3 13cm 15cm 16cm Data Analysis Conclusion Using the Pivot Interactive Spring Has Sprung Graphs graph force F in N vs cha in length of spring or displacement Ax in m for both springs Regardless of which the dependent or independent variable graph F on the y axis and Ax on the x a E Elastic potential slope Ax 2 y int Ax Change in length Ax m 9cm 9cm 9cm 9cm 9cm 9cm 5 25 3N 18 1N 9N 20 8N 26 78N 30 4N T Applied force F N The accepted equations for force and elastic potential energy for a spring include a term called the spring constant k in N m What do you think the spring constants are for spring 1 and spring 2 Explain