Work, power & energy Questions and Answers

3 A truck of mass 1 3 X 104 kg travelling at 9 0 X 10 km h N collides with a car of mass 1 1 10 kg travelling at 3 0 10 km h N The collision is perfectly inelastic A a Calculate the magnitude and direction of the velocity of the vehicles immediately after the collision b Calculate the total kinetic energy before and after the collision described in a c Determine the decrease in kinetic energy during the collision

Our central air conditioner uses 10 000 watts on 240 volts If we leave the thermostat at 76 degrees it runs an average of 8 hours per day If we move the thermostat to 82 degrees and it runs 3 hours per day how much money can we save in the month of July 05 Cents per KWH 10 Points

A 2 5 hp 1 hp 744 W motor is used to power a hoist to lift a 1700 kg car 1 86 m above the garage floor How much time does it take the hoist to lift the car b The hoist slowly lowers the car back down to the ground How much work does the hoist motor do in lowering the car

A 2 0 kg trolley moving east at 3 0 m s collides head on with a 1 0 kg trolley west at 2 0 m s After the collision the 2 0 kg trolley has a velocity of 1 0 m s E A What is the final velocity of the 1 0 kg trolley B Is the collision elastic or inelastic

4 A washing machine has a power rating of 550 Watts It is used for 3 hours every week a How much energy in kWh does it use in 4 week period one month 6 6 kWh b If the rate of electricity is 7 cents kWh what will be the cost of running the machine for one month one year 0 46 5 54

2 An electric motor used 7 50 103 kJ of electrical energy to do 6 40 103 kJ of work What is the percent efficiency of the motor 85 3

Tries remaining 3 Points out of 1 00 Flag questi n You perform the Hooke s Law experiment and create a plot of Displacement vs Force You add a linear fit and find the following equation for the line 0 180 0 030 What is the spring constant k in N m or kg s

Questions 9 15 A 50 kg sledder starts from rest atop a 5 0 m high hill A She sleds to the bottom and up to the top of the adjacent 3 0 m high hill Ignore friction 5 0 m 3 0 m Find the potential energy at A

d b C 60 Cord m String 1975B7 A pendulum consists of a small object of mass m fastened to the end of an inextensible cord of length L Initially the pendulum is drawn aside through an angle of 60 with the vertical and held by a horizontal string as shown in the diagram above This string is burned so that the pendulum is released to swing to and fro a In the space below draw a force diagram identifying all of the forces acting on the object while it is held by the string Determine the tension in the cord before the string is burned Show that the cord strong enough to support the object before the string is burned is also strong enough to support the object as it passes through the bottom of its swing

2 Calculate the potential energy kinetic energy mechanical energy velocity and height of the ball at the various locations 3 50 kg 3 mm PE KE ME S V PE KE ME VE PE KE ME PE KE ME h y 6 m s h

D X M 1986B2 One end of a spring is attached to a solid wall while the other end just reaches to the edge of a horizontal frictionless tabletop which is a distance h above the floor A block of mass M is placed against the end of the spring and pushed toward the wall until the spring has been compressed a distance X as shown above The block is released follows the trajectory shown and strikes the floor a horizontal distance D from the edge of the table Air resistance is negligible Determine expressions for the following quantities in terms of M X D h and g Note that these symbols do not include the spring constant al The time elapsed from the instant the block leaves the table to the instant it strikes the floor b The horizontal component of the velocity of the block just before it hits the floor c The work done on the block by the spring d The spring constant

1974B7 A ski lift carries skiers along a 600 meter slope inclined at 30 To lift a single rider it is necessary to move 70 kg of mass to the top of the lift Under maximum load conditions six riders per minute arrive at the top If 60 percent of the energy supplied by the motor goes to overcoming friction what average power must the motor supply axy 600 m 30

10 m 30 60 10 m sin 30 0 50 cos 30 0 87 tan 30 0 58 sin 60 a 0 87 cos 600 50 tan 60 1 73 5 0 kg 1991B1 A 5 0 kilogram monkey hangs initially at rest from two vines A and B as shown above Each of the vines has length 10 meters and negligible mass a On the figure below draw and label all of the forces acting on the monkey Do not resolve the forces into components but do indicate their directions b Determine the tension in vine B while the monkey is at rest The monkey releases vine A and swings on vine B Neglect air resistance C Determine the speed of the monkey as it passes through the lowest point of its first swing Determine the tension in vine B as the monkey passes through the lowest point of its first swing

1 kg 16 m s All M Before Collision 4 kg Before Collision After Collision M Px v 0 kg m S View From Above 4 1984B2 Two objects of masses M 1 kilogram and M 4 kilograms are free to slide on a horizontal frictionless surface The objects collide and the magnitudes and directions of the velocities of the two objects before and after the collision are shown on the diagram above sin 37 0 6 cos 37 0 8 tan 37 0 75 a Calculate the x and y components p and p respectively of the momenta of the two objects before and after the collision and write your results in the proper places in the following table M 1 kg M 4 kg Py Py kg m Px M M 1 kg 12 m s After Collision kg m 5 m s 37 kg m b Show using the data that you listed in the table that linear momentum is conserved in this collision c Calculate the kinetic energy of the two object system before and after the collision d Is kinetic energy conserved in the collision

a b m C1991MI A small block of mass 2m initially rests on a track at the bottom of the circular vertical loop the loop shown above which has a radius r The surface contact between the block and the loop is frictionless A bullet of mass m strikes the block horizontally with initial speed v and remains embedded in the block as the block and bullet circle the loop C d Q 2m Determine each of the following in terms of m Vo r and g The speed of the block and bullet immediately after impact The kinetic energy of the block and bullet when they reach point P on the loop The speed Vmin of the block at the top of the loop to remain in contact with track at all times The new required entry speed v of the block and bullet at the bottom of the loop such that the conditions in part c apply The new initial speed of the bullet to produce the speed from part d above e 1

R 1982B3 A child of mass M holds onto a rope and steps off a platform Assume that the initial speed of the child is zero The rope has length R and negligible mass The initial angle of the rope with the vertical is 0 as shown in the drawing above a Using the principle of conservation of energy develop an expression for the speed of the child at the lowest point in the swing in terms of g R and cos 0 b The tension in the rope at the lowest point is 1 5 times the weight of the child Determine the value of cos 0

When you drop a pebble from height H it reaches the ground with kinetic energy K if there is no air resistance From what height should you drop it so it will reach the ground with twice as much kinetic energy 16H H 4H O 8H O2H

Four weightlifters A through D enter a competition The mass and distance that each lifts are shown in the table Which weightlifter does 2 94 x 10 J of work O weightlifter A Oweightlifter B weightlifter C O weightlifter D Weightlifter A B C D Mass kg 100 0 150 0 200 0 275 0 Distance m 2 25 1 76 1 50 1 25

7 You slide a 0 12 kg coffee mug 0 15 m across a table The force you exert is horizontal and of magnitude 0 10 N The coefficient of kinetic friction between the mug and the table is 0 05 How much work is don on the mug

80 m 1979B1 From the top of a cliff 80 meters high a ball of mass 0 4 kilogram is launched horizontally with a fekty of 30 meters per second at time 1 0 as shown above The potential energy of the ball is zero at the bottom of the cliff Use g 10 meters per second squared a Calculate the potential kinetic and total energies of the ball at time t 0 b On the axes below sketch and label graphs of the potential kinetic and total energies of the call as functions of the distance fallen from the top of the cliff Energy joules 500 400 300 Energy joules 200 100 30 m s 200 0 100 0 Top of diff 20 30 Distance Fallen m 50 c On the axes below sketch and label the kinetic and potential energies of the ball as functions of time until the ball hits 600 500 60 5 70 6 Bottom of cliff 8

2 M Before Collision a v the speed of the blocks immediately after impact b x the maximum distance the spring is compressed MA xo I 1 2M Xo wwww M After Collision 1983B2 A block of mass M is resting on a horizontal frictionless table and is attached as shown above to a relaxed spring of spring constant k A second block of mass 2M and initial speed v collides with and sticks to the first block Develop expressions for the following quantities in terms of M k and vo

45 Figure I Figure li C1981M2 A swing seat of mass M is connected to a fixed point P by a massless cord of length L A child also of mass M sits on the seat and begins to swing with zero velocity at a position at which the cord makes a 60 angle with the vertical is shown in Figure I The swing continues down until the cord is exactly vertical at which time the child jumps off in a horizontal direction The swing continues in the same direction until its cord makes a 45 angle with the vertical as shown in Figure II at that point it begins to swing in the reverse direction a Determine the speed of the child and seat just at the lowest position prior to the child s dismount from the seat b Determine the speed if the seat immediately after the child dismounts c Determine the speed of the child immediately after he dismounts from the swing

1kWw 3 kg J 77777 1981B2 A massless spring is between a 1 kilogram mass and a 3 kilogram mass as shown above but is not attached to either mass Both masses are on a horizontal frictionless table In an experiment the 1 kilogram mass is held in place and the spring is compressed by pushing on the 3 kilogram mass The 3 kilogram mass is then released and moves off with a speed of 10 meters per second Determine the minimum work needed to compress the spring in this experiment

100m 1990B1 A bullet of mass m is moving horizontally with speed v when it hits a block of mass 100m that is at rest on a horizontal frictionless table as shown above The surface of the table is a height h above the floor After the impact the bullet and the block slide off the table and hit the floor a distance x from the edge of the table Derive expressions for the following quantities in terms of m h Vo and appropriate constants a the speed of the block as it leaves the table b the change in kinetic energy of the bullet block system during impact c the distance x Suppose that the bullet passes through the block instead of remaining in it d State whether the time required for the block to reach the floor from the edge of the table would now be greater less or the same Justify your answer e State whether the distance x for the block would now be greater less or the same Justify your answer

1984M1 modified An amusement park ride consists of a rotating vertical cylinder with rough canvas walls The floor is initially about halfway up the cylinder wall as shown above After the rider has entered and the cylinder is rotating sufficiently fast the floor is dropped down yet the rider does not slide down The rider has mass of 50 kilograms The radius R of the cylinder is 5 meters the frequency of the cylinder when rotating is 1 revolutions per second and the coefficient of static friction between the rider and the wall of the cylinder is 0 6 a 0 00 b C 044 On the diagram above draw and identify the forces on the rider when the system is rotating and the floor has dropped down Calculate the centripetal force on the rider when the cylinder is rotating and state what provides that force Calculate the upward force that keeps the rider from falling when the floor is dropped down and state what provides that force d At the same rotational speed would a rider of twice the mass slide down the wall Explain your answer

O R 8m 1975B1 A 2 kilogram block is released from rest at the top of a curved incline in the shape of a quarter of a cir of radius R The block then slides onto a horizontal plane where it finally comes to rest 8 meters from the beginn of the plane The curved incline is frictionless but there is an 8 newton force of friction on the block while it slic horizontally Assume g 10 meters per second a Determine the magnitude of the acceleration of the block while it slides along the horizontal plane b How much time elapses while the block is sliding horizontally C Calculate the radius of the incline in meters

Z a R e Side View 2001B1 A ball of mass M is attached to a string of length R and negligible mass The ball moves clockwise in a vertical circle as shown above When the ball is at point P the string is horizontal Point Q is at the bottom of the circle and point Z is at the top of the circle Air resistance is negligible Express all algebraic answers in terms of the given quantities and fundamental constants On the figures below draw and label all the forces exerted on the ball when it is at points P and Q respectively Q b Derive an expression for Vmin the minimum speed the ball can have at point Z without leaving the circular path The maximum tension the string can have without breaking is Tmax Derive an expression for Vmax the maximum speed the ball can have at point Q without breaking the string C d Suppose that the string breaks at the instant the ball is at point P Describe the motion of the ball immediately after the string breaks

Ground 1984B1 A ball of mass M attached to a string of length L moves in a circle in a vertical plane as shown above At the top of the circular path the tension in the string is twice the weight of the ball At the bottom the ball just clears the ground Air resistance is negligible Express all answers in terms of M L and g a b Determine the magnitude and direction of the net force on the ball when it is at the top Determine the speed v of the ball at the top The string is then cut when the ball is at the top C Determine the time it takes the ball to reach the ground d Determine the horizontal distance the ball travels before hitting the ground

Which one has larger kinetic energy a 20 kg object moving at 40 m s or a 40 kg object moving at 20 m s The 40 kg object The 20 kg object Both have the same kinetic energy

5 A ball rolls down a straight ramp During the motion which of the following quantities change and how do they change distance from the starting point speed ve locity

A cart with a box of books is pulled 10m horizontally with a constant force of 150 N acting at 40 to the horizontal and then pulled up a 5m long ramp at an angle of 0 with the same force If the total amount of work done is 1860J determine the angle 0 ramp is inclined at Include diagram in your solution

Both the KE and PE of a block freely sliding down no friction and air resistance a ramp are shown below only at the bottom position in the sketch a 10 points Fill in the missing values for the other positions 1 At the top when KE 0 PE 2 At the point where PE 50 J KE 3 At the point where KE 50 J PE b 10 points If the mass of the block is 5 kg what is the height of the block relative to the bottom of the ramp at the point where its PE is 50 J Show calculation s PE 50J KE KE 50 J PESO KE 75 J

C A total of 490 J of work is done on a pin when a 5 0 kg sledgehammer strikes it bringing the to rest Calculate the initial speed of the sledgehammer K U 5 sledgehammer

A diagram of the forces being applied to a box is provided below If the net force acting on the box is 10 N to the right what is the magnitude of the force applied by the boy pulling to the left Record your answer in the grid below Show all work eeee00 0 080 60600 eee00 0 e 0 099 eese a Object Object A Object B Object C Object D Newtons eeee eeeee 9800 e 000000000 Left 0 Which of the following objects requires the greatest amount of force to produce the acceleration shown Show work here eeee 00 eeeo 11 Newtons Work Math Answer with units A student applies 2 Newtons of force to a toy car causing it to accelerate at a rate of 10 m s What is the mass of the toy car in kg Record your answer in the grid below Show all work Acceleration m s 2 5 1 2 4 9 0 7 Equation 8 Newtons Work Math Right Mass kg 5 7 3 14 21 Newtons

A boy and a girl pu horizontal surface moving it 13 m at a constant speed The boy exerts 75 N of force at an angle of 32 above the horizontal and the girl exerts a force of 75 N at an angle of 22 above the horizontal Calculate the total work done by the boy and girl together

8 Two identical tiny balls of highly compressed matter are 1 50 m apart When released in an orbiting space station they accelerate toward each other at 2 00 cm s2 What is the mass of each of them G 6 67 x 10 11 N m2 kg2 8 points E

Click to see additional instructions Questions 18 19 A particular kitchen blender delivers 1100 watts of mechanical power while blending the mixed fruit in its carafe to make a smoothie Assume that 100 of this power is absorbed by the food as the blades spin 18 If the blender runs for 23 seconds what is the total energy in kilojoules delivered to the food kj

How high did rocks ejected from a volcano reach into the atmosphere that hit the ground at 350 m s ignoring air resistance The rocks went x 10 meters into the air

Find the numeric value of the work done on the gas in the following figures Enter your answers in J Pay attention to the units scale on the axis and the negative signs of your answers HINT a b P 105Pa 9 00 6 00 3 00 P 10 Pa 9 00 6 00 1 00 2 00 3 00 3 00 1 00 2 00 3 00 V m

2 A person is pulling a wagon with a force of 36 pounds at an angle of 40 above the horizontal and moves it for 220 feet 6 points Find the amount of work done in foot pound

m Spring is released from a position s hown in figure Find the maximum elongation in the spring in it s subs equent action

tically upward When you let go of the ball it has a kinetic energy Ko assume the ball has zero gravitational potential energy at the point where you let go Without air drag the ball reaches a maximum height h above the point where you let go You throw the ball again this time giving it a kinetic energy of 16 Ko What will be the maximum height of the ball again without air drag Note that the square root of 2 is approximately 1 4 16 h h 256 h 4 h 1 4 O 2h Oh 2 4 h Oh 16 O 1 4 h O 256 h

The blue curved line represents some potential energy as a function of position x At which position is the force in the x direction U O A only O Conly O A and C OB and C A B C X

A 0 8 kg mass is placed on a ramp at a height h 0 79 m above the ground as shown The mass is given a push so it has an initial velocity of 3 3 m s The mass travels down the ramp which is frictionless upon reaching the bottom the mass travels along the horizontal surface where friction is present The coefficient of friction is 0 4 How far along the horizontal surface does the mass travel before coming to a stop in units of m h Note if you need to enter a number in scientific notation use e For example 1200 1 2e3 and 0 0012 1 2e 3 Include several decimal places in your calculations and your answer to avoid rounding error Do not include units with your answer

All changes saved 25 A model rocket with a mass of 0 212 kg is launched into the air with an initial speed of 84 m s How much kinetic energy will the rocket have at a height of 214 m Assume there is no wind resistance O 303 J O 747 J O 634 J O 444 J

3 A toy airplane ejects its 8 4 g pilot using a spring with a spring constant of 5 2 X 102 N m The spring is initially compressed 5 2 cm T a Calculate the elastic potential energy of the compressed spring b Calculate the speed of the pilot as it ejects upward from the airplane c Determine the maximum height that the pilot will reach

4 In a pinball game a compressed spring with spring constant 1 2 X 102 N m fires an 82 g pinball The pinball first travels horizontally and then travels up an inclined plane in the machine before coming to rest The ball rises up the ramp through a vertical height of 3 4 cm Determine the distance of the

D A tennis coach uses a machine to help with tennis practice The machine uses a compressed spring to launch tennis balls The spring constant is 440 N m and the spring is initially compressed 45 cm A 57 g tennis ball leaves the machine horizontally at a height of 1 2 m Calculate the horizontal distance that the tennis ball can travel before hitting the ground T

A wooden box of mass 6 0 kg slides on a frictionless tabletop with a speed of 3 0 m s It is brought to rest by a compressing spring The spring constant is 1250 N m TA a Calculate the maximum distance the spring is compressed b Determine the speed and acceleration of the block when the spring is compressed a distance of 14 cm

2 A mass rests against a spring on a horizontal frictionless table The spring constant is 520 N m and the mass is 4 5 kg The mass is pushed against the spring so that the spring is compressed by 0 35 m and then it is released Determine the velocity of the mass when it leaves the spring T