Work, power & energy Questions and Answers

A 0 22 kg block is dropped on a vertical spring that has a spring constant of 280 N m The block attached to the spring compresses it by 11 cm before momentarily stopping Determine the height from which the block was dropped T

ces The force that must be exerted to drive a nail into a wall is roughly as shown in the graph The first 1 20 cm are through soft drywall then the nail enters the solid wooden stud How much work must be done to hammer the nail a horizontal distance of 6 21 cm into the wall Fx N 120 50 0 1 20 where K 6 21 cm 6 61 J K x cm

If friction is the only force acting on an object as it slows down which of the following assumptions can be made in regard to the object s kinetic energy The kinetic energy decreases The kinetic energy decreases and then increases The kinetic energy increases The kinetic energy remains the same

A 1500 kg car accelerates from 0 to 25 m s in 7 0 s What is the average power delivered by the engine 1 hp 746 W 90 hp 60 hp 50 hp 70 hp 80 hn

You throw a ball straight up Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down Work up is and the work down is Work up is and the work down is Work up is and the work down is Work up is and the work down is

A mass of 2 0 kg traveling at 3 0 m s along a smooth horizontal plane hits a relaxed spring The mass is slowed to zero velocity when the spring has been compressed by 0 15 m What is the spring constant of the spring 18 N m 9 0 N m 400 N m 20 N m 800 N m

A roller coaster car is moving at 20 m s along a straight horizontal track What will its speed be after climbing the 15 m hill shown in the figure if friction is ignored 17 m s 7 m s 5 m s 10 m s 14 m s 1 20 m s ww 15 m

9 The following situation may or may not be consistent with the principle of conservation of mechanical energy For the following examples state whether mechanical energy is conserved or not conserved 1 a An object moves up hill with a decreasing speed b An object moves downhill with a constant speed 00 Xion perved ccyserved noo not conser 0 5

A 48 kg child bounces on a pogo stick At the lowest point of one bounce the compressed spring in the stick has 120 J of elastic potential energy as it compresses 0 19 m Assume that the pogo stick is light enough that we can ignore its mass a Determine the child s maximum height during the jump following the bounce b Determine the child s maximum speed during the jump

1 A mass of 2 kg is attached to a horizontal spring with a spring constant of 70 N m The spring is stretched from equilibrium position by 5 cm and released a What is the maximum elastic potential energy b What is the maximum kinetic energy c What is the maximum speed of the mass d At which point the maximum speed will be nah

When the brake is applied to a car having a mass of 1500 kg its speed is reduced from 35 m s to 5 m s a How much work does the brake do on the car b If the brake is applied for a distance of 30 m what force does it exert on the car

A block of mass in 100 g is released from rest and slides down a frictionless track of height h 51 3 cin 4 the bottom of the track the black clides freely along horizontal table until it hits a a Spring attacked to a heavy immorable wall The spring compressed by 2 27 cm at the maximum Compression What is the value of the Spring Constant k

2 A 3 kg ball is thrown downward at 4 m s from a height of 1 5 m a What is the kinetic energy of the ball as it leaves the thrower s hand b What force is doing work on the ball as it falls c How much work is done on the ball as it falls d What is the final kinetic energy of the ball e What is the velocity of the ball as it strikes the ground

1 A 2 kg toy car moves at a speed of 5 m s a What is the kinetic energy of the car b If a child applies a 3 N force for 2 m in the same direction the car is already moving how much work is done on the car c What is the change in the car s kinetic energy from the applied force d What is the final kinetic energy of the car e What is the velocity of the car after the child applies the 3 N force

9 A mass spring system undergoes SHM The elastic potential energy at maximum stretch is 7 50 J the mass is 0 20 kg and the spring constant is 240 N m Calculate the frequency and amplitude of oscillation

A block of mass 2 5 kg is sliding across a smooth level surface at 3 0 m s when it hits a stationary spring bumper fixed at one end whose force constant is 360 N m By what amount does the block compress the spring before coming to rest

An ideal spring is compressed 10 cm by an applied force of 50 N This compressed spring is then used to project a 20 g marble straight up into the air To what maximum height does the marble rise

Given the force field F find the work required to move an object on the given orientated curve F y x on the parabola y 5x from 0 0 to 3 45 The amount of work required is Simplify your answer

p59 A constant force of magnitude 30 N makes an angle of 150 measured counterclockwise with the direction of increasing x as the force acts on a 18 kg object How much w one on the object by the force as the object moves from the origin to the point with position vector 3 5 m i 6 5 m j

4 A mass spring system undergoes SHM The elastic potential energy at maximum stretch is 7 50 J the mass is 0 20 kg and the spring constant is 240 N m Calculate The frequency of oscillation T2 C1

2 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 content is 1250 N m a Calculate the maximum distance the spring is compressed T2 C1 b Determine the speed and acceleration of the block who the spring is compressed a distance of 14 cm T4 C2

16 20 11 THINKING AND COMMUNICATION Answer using G R A S S for full marks Organize your solution neatly Marks for communication will be given for proper significant figures units and statement 1 A police car of mass 2 4 x 10 kg is travelling on the highway when the officers receive an emergency call They increase the speed of the car to 33 m s The increase in speed results in 3 1 x 105 J of work done on the car Determine the initial speed of the police car T4 C2

First 8c8p4 In the figure a frictionless roller coaster of mass 1000 kg tops the first hill at height h 40 m with speed 6 85 m s How much work does its weight do on it from that point point A Submit Answer Tries 0 8 How much work does its weight do on it from that point to point B Submit Answer How much work h 2 Tries 0 8 does its weight do on it from that point to point C Submit Answer Tries 0 8 If the gravitational potential energy of the coaster Earth system is taken to be zero at point C what is its value when the coaster is at point B Submit Answer Tries 0 8 If the gravitational potential energy of the coaster Earth system is taken to be zero at point C what is its value when the coaster is at point A

the force on a 5 00kg object as it is moved a through a displacement 22 0m A How much work is done in the following graph as an object is moved from 16 0m to 18 Force N 80 0 60 0 40 0 20 0 0 0 20 0 40 0 60 0 0 0 2 0 4 0 6 0 Force vs Displacement 8 0 10 0 12 0 14 0 16 0 Displacement m 18 0 20 0 22 0 6 60 10 B If the object was originally moving at 3 50m s when it had reached 16 0m how fast was it going at 22 0m W Y 2mv 12mv V 2

Bc7p26 During spring semester at MIT residents of the parallel buildings of the East Campus dorms battle one another with large catapults that are made with surgical hose mounte on a window frame A balloon filled with dyed water is placed in a pouch attached to the hose which is then stretched through the width of the room Assume that the stretching of th nose obeys Hooke s law and has a spring constant of 102 N m If the hose is stretched by 4 7 m and then released how much work does the force from the hose do on the balloon in pouch by the time the hose reaches its relaxed length

5 3 When you crushed the chalk with a block you released the 5 kg block from a height of 1 m above the chalk a What is the gravitational potential energy of the block Earth system before you released it Be sure to mention what you set as your reference level b How much kinetic energy did the block have the instant before colliding with the chalk

H Submit Answer Tries 0 8 A h hrw8c11p11 A homogeneous sphere starts from rest at the upper end of the track shown in the figure and rolls without slipping until it rolls off the right hand end If H 13 0 m and h 3 0 m and the track is horizontal at the right hand end how far horizontally from point A does the sphere land on the floor Send Feedback

38 An adult pulls a sled forward with a force of 89 N The sled moves a distance of 37 m in 1 8 min What is the average power generated by the adult O 18 W O 20 W O 30 W O 23 W

39 What is the height h of the ramp A 2 6 m BI O 11 cm O 1 5 m Smooth B Rough The diagram shows a 0 74 kg square block at four positions along a track The track is frictionless between points A and B Elsewhere the coefficient of static friction on the block is 0 36 C Initially the block is held in place against a spring by a horizontal external force of magnitude 29 N Then the external force is removed and the block is projected forward V 1 2 m s V3 1 4 m s V2 1 9 m s The block stops at point D The block descends a ramp and has speed with speed at the bottom At point C its speed is DE

Calculate the torque magnitude and direction about point Q due to the force F in each of the cases sketched In each case the force F and the rod both lie in the plane of the page the rod has fength 4 00 m and the force has magnitude F 10 0 N 60 0 00 a 90 0 d 2 00 m b 120 0 e 60 0 c 30 0 F

33 Which unit is equivalent to the joule J the unit of work meter per second squared m s O kilogram meter kg m O kilogram meter per second kg m s newton meter Nm

32 A car s engine performs 4 80 x 105 J of work as it on accelerates from O 43 2 m s O 29 7 m s O 23 1 m s O 18 3 m s 10 0 m s to speed vf The mass of the car is 1230 kg car What is vf

15 km h 24 A 1200 kg car is traveling at O 96 km h 68 km h O 82 km h O 54 km h 2400 kg truck has 41 times the kinetic energy of the car How fast is the truck moving

18 A battery powered train travels in a complete circle of radius 1 82 m The coefficient of friction between the train and the track is 0 12 and the train s weight is 65 0 N the train do against friction with the track O 1800 J O 89 2 J O OJ O 370 J All changes sa How much work d

All changes 16 A mountain hiker and his gear have mass 110 kg He walks a distance of 156 m on a hill that slants 30 with the horizontal How much work did the mountain climber do against gravity O9 830 J O 84 100 J O 48 100 J

F is applied to the car the car slows down to a halt The work performed on the car is 1 A car is traveling along a straight highway When a constant force O positive O zero O negative

8 Force N 10 9 8 3 3 2 2 3 4 5 6 7 Distance of displacement m 8 ta 10x The graph shows the relationship between a force acting on an object and the displacement of the object Approximately how much work does the force perform on the object as the ob displaced from x 1 m to x 4 m O 0 5 J 02J O 6J O 10 J

9 110 y 100 90 80 70 60 Force F 8 8 8 8 8 8 50 30 20 10 5 10 15 Displacement m 20 25 All change The graph plots the force needed to stretch a very large elastic band against the displacement of the elastic band from rest How much work is required to stretch the band from its rest pos to a displacement of 20 m O 1600 J O 400 J O 1200 J O 800 J

Work A force of 4 pounds is required to hold a spring stretched 0 6 feet beyond its natural length How much work in foot pounds is done in stretching the spring from its natural length to 0 8 feet beyond its natural length

Force N 13 124 11 10 8 9 10 11 12 13 14 15 16 Distance of displacement m A non uniform force is applied to an object as it travels across a linear axis The graph shows how the magnitude of the force changes with the object s displacement To which m situation does the graph best apply pushing a box across the floor at constant speed O stretching a spring O twirling a ball at the end of a rope launching a cannonball

All changes save 7 A block slides from rest down the 26 0 m length of a frictionless ramp The ramp angle is 23 0 to the horizontal What is the speed of the block as it reaches the bottom of the ramp O 14 1 m s O 21 9 m s O 199 m s O 9 97 m s

2 A 0 500kg ball is placed on a ramp that is 3 00m tall and has a length of 11 0m The ball is given a slight shove so that it starts with a velocity of 2 00m down the ramp A What is it initial mechanical energy of the ball ME 1 m v m g h 12 500 2 00 500 9 8 3 00 1 14 7 15 70 e 15 700 J B What is the velocity of the ball at the bottom of the ramp assuming no energy is lost to friction C The ball runs into a spring and compresses it 0 250m as it comes to a stop What is the spring constant of the spring

Figure shows a partial profile of a roller coaster ride Friction and air resistance are negligible The speed at the top of the highest hill A is 70 0 m s a Determine the speed of the coaster at position C Solve using conservation of energy principles 3 b Will the coaster be able to reach a hill which is 40 m high Explain using calculations 3 37 8 m B 128 m 17 8 m

5 3 00 m A B 6 00 m C A 10 0 kg block is released from point A The track is frictionless except for the portion between B and C which has a length of 6 00 m The block travels down the track hits a spring of force constant k 2250 N m and compresses the spring 0 300m from its equilibrium position before coming to rest momentarily a Calculate the energy lost due to friction b Determine the coefficient of friction between B and C

3 A smooth 0 16 kg hockey puck slides across a smooth gym floor experiences a frictional force of 0 36 N and stops in a distance of 2 3 m Calculate the work done by the normal force that the floor exerts upward on the puck 0 0 J a b 3 60 J gravitational potential energy the string c 1 6 J d 0 56 J e 0 13 J 4 A 80 0 kg skydiver falls straight downward with an open parachute through a vertical height of 300 0 m The skydiver s velocity remains constant What is the work done by the non conservative force of air resistance which is the only non conservative force acting a 2 3 105 b 2 35x105 J c 2 35x105 J d 0 0 J

The graph below represents the force on a 5 00kg object as it is moved a through a displacement A How much work is done in the following graph as an object is moved from 16 0m to 22 0m Force N 80 0 60 0 40 0 20 0 0 0 20 0 40 0 60 0 0 0 2 0 4 0 Force vs Displacement 6 0 8 0 10 0 12 0 Displacement m 14 0 16 0 18 0 20 0 22 0

A student in a lab exerts a 25 N force to pull a block a distance of 0 48 m If a total of 11 J of work is done the angle between the force and the displacement is

A 80 0 kg skydiver falls straight downward with an open parachute through a vertical height of 300 0 m The skydiver s velocity remains constant What is the work done by the non conservative force of air resistance which is the only non conservative force acting

35 2 5m m 60kg Find the final speed of the initial speed is 7 5 y 9 Find y she can reach a 3 0m hill the initial Speed remain the same

Roger Federer tosses the ball 2 0 m straight up from his hand for his first serve Solve using conservation of energy principles a Calculate the speed of the ball as it leaves Federer s hand 3 b On his second serve he tosses the ball at 1 2 the speed Is the height reached halved Explain using calculations 3