# 2. Work, Energy and Conservation of Energy Tutori al 2

## Transcript Of 2. Work, Energy and Conservation of Energy Tutori al 2

EE1427 Engineering Science – Dr. Daniel Nankoo

Tutorial 2

2. Work, Energy and Conservation of Energy – Tutorial 2

2.1 A farmer pushes a 23-kg bale of hay 3.4 m across the floor of a barn. If he exerts a horizontal

force of 86 N on the hay, how much work has he done? (290J)

2.2 The coefficient of kinetic friction between a suitcase and the floor is 0.26. If the suitcase has a

mass of 70.0 kg, how far can it be pushed across the level floor with 640 J of work? (3.6m)

2.3 You pick up a 3.4-kg can of paint from the ground and lift it to a height of 1.8 m. (a) How

much work do you do on the can of paint? (b) You hold the can stationary for half a minute, waiting for a friend on a ladder to take it. How much work do you do during this time? (c) Your friend decides against the paint, so you lower it back to the ground. How much work do you do on the can as you lower it? (60J, 0, -60J)

2.4 A tow rope, parallel to the water, pulls a water skier directly behind the boat with constant

velocity for a distance of 65 m before the skier falls. The tension in the rope is 120 N. (a) Is the work done on the skier by the rope positive, negative, or zero? Explain. (b) Calculate the work done by the rope on the skier. (7.8kJ)

2.5 A child pulls a friend in a little red wagon with constant speed. If the child pulls with a force

of 16 N for 10.0 m, and the handle of the wagon is inclined at an angle of 25° above the horizontal, how much work does the child do on the wagon? (150J)

2.6 To clean a floor, a cleaner pushes on a mop handle with a force of 50.0 N. (a) If the mop

handle is at an angle of 55° above the horizontal, how much work is required to push the mop 0.50 m? (b) If the angle the mop handle makes with the horizontal is increased to 65°, does the work done by the cleaner increase, decrease, or stay the same? Explain. (14J)

2.7 A small plane tows a glider at constant speed and altitude. If the plane does 2.00 × 105 J of

work to tow the glider 145 m and the tension in the tow rope is 2560 N, what is the angle between the tow rope and the horizontal? (57.4°)

2.8

A

young r

woman

on

a

skateboard

is

pulled

by

a

rope

attached

to

a

bricycle.

The

velocity

of

the

skateboarder is v = (4.1 m s)x$ and the force exerted on her by the rope is F = (17 N)x$ + (12 N)y$. (a)

Find the work done on the skateboarder by the rope in 25 seconds. (b) Assuming the velocity of the

bike is the same as that of the skateboarder, find the work the rope does on the bicycle in 25 seconds.

(1700J, -1700J)

2.9 Water skiers often ride to one side of the centre line of a boat, as shown in Figure 2.9. In this

case, the ski boat is travelling at 15 m/s and the tension in the rope is 75 N. If the boat does 3500 J of work on the skier in 50.0 m, what is the angle θ between the tow rope and the centre line of the boat? (21°)

Figure 2.9

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EE1427 Engineering Science – Dr. Daniel Nankoo

Tutorial 2

2.10 When Skylab re-entered the Earth’s atmosphere on July 11, 1979, it broke into a myriad of

pieces. One of the largest fragments was a 1770-kg lead-lined film vault, and it landed with an estimated speed of 120 m/s. What was the kinetic energy of the film vault when it landed? (12.7MJ)

2.11 A 0.14-kg pinecone falls 16 m to the ground, where it lands with a speed of 13 m/s. (a) With

what speed would the pinecone have landed if there had been no air resistance? (b) Did air resistance do positive work, negative work, or zero work on the pinecone? Explain. (18m/s)

2.12 At t = 1.0 s, a 0.40-kg object is falling with a speed of 6.0 m/s. At t = 2.0 s, it has a kinetic

energy of 25 J. (a) What is the kinetic energy of the object at t = 1.0 s? (b) What is the speed of the object at t = 2.0 s? (c) How much work was done on the object between t = 1.0 s and t = 2.0 s? (7.2J, 11m/s, 18J)

2.13 A 1300-kg car coasts on a horizontal road with a speed of 18 m/s. After crossing an unpaved,

sandy stretch of road 30.0 m long, its speed decreases to 15 m/s. (a) Was the net work done on the car positive, negative, or zero? Explain. (b) Find the magnitude of the average net force on the car in the sandy section. (2.1kN)

2.14 A 65-kg cyclist rides his 8.8-kg bicycle with a speed of 14 m/s. (a) How much work must be

done by the brakes to bring the bike and rider to a stop? (b) How far does the bicycle travel if it takes 4.0 s to come to rest? (c) What is the magnitude of the braking force? (-7.2kJ, 28m, 260N)

2.15 A spring with a force constant of 3.5 × 104 N m is initially at its equilibrium length. (a) How

much work must you do to stretch the spring 0.050 m? (b) How much work must you do to compress it 0.050 m? (44J, 44J)

2.16 Initially sliding with a speed of 2.2 m/s, a 1.8-kg block collides with a spring and compresses

it 0.31 m before coming to rest. What is the force constant of the spring? (91N/m)

2.17 The force shown in Figure 2.17 moves an object from x = 0 to x = 0.75 m. (a) How much

work is done by the force? (b) How much work is done by the force if the object moves from x = 0.15 m to x = 0.60 m? (0.45J, 0.24J)

Figure 2.17

2.18 It takes 160 J of work to compress a certain spring 0.14 m. (a) What is the force constant of

this spring? (b) To compress the spring an additional 0.14 m, does it take 160 J, more than 160 J, or less than 160 J? Verify your answer with a calculation. (16kN/m, 480J)

2.19 A block is acted on by a force that varies as (2.0 × 104 N m)x for 0 ≤ x ≤ 0.21 m, and then

remains constant at 4200 N for larger x. How much work does the force do on the block in moving it (a) from x = 0 to x = 0.30 m, or (b) from x = 0.10 m to x = 0.40 m? (0.82kJ, 1.1kJ)

2.20 Calculate the power output of a 1.3-g fly as it walks straight up a windowpane at 2.5 cm/s.

(0.32mW)

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EE1427 Engineering Science – Dr. Daniel Nankoo

Tutorial 2

2.21 You raise a bucket of water from the bottom of a deep well. If your power output is 108 W,

and the mass of the bucket and the water in it is 5.00 kg, with what speed can you raise the bucket? Ignore the weight of the rope. (2.20m/s)

2.22 A kayaker paddles with a power output of 50.0 W to maintain a steady speed of 1.50 m/s. (a)

Calculate the resistive force exerted by the water on the kayak. (b) If the kayaker doubles her power output, and the resistive force due to the water remains the same, by what factor does the kayaker’s speed change? (33.3N, 2)

2.23 A grandfather clock is powered by the descent of a 4.15-kg weight. (a) If the weight descends

through a distance of 0.720 m in 3.25 days, how much power does it deliver to the clock? (b) To increase the power delivered to the clock, should the time it takes for the mass to descend be increased or decreased? Explain. (0.104mW)

2.24 A certain car can accelerate from rest to the speed v in T seconds. If the power output of the

car remains constant, (a) how long does it take for the car to accelerate from v to 2v? (b) How fast is the car moving at 2T seconds after starting? (3T, v√2)

2.25 Calculate the work done by friction as a 3.2-kg box is slid along a floor from point A to point

B in Figure 2.25 along paths 1, 2, and 3. Assume that the coefficient of kinetic friction between the box and the floor is 0.21. (-73J, -33J, -46J)

Figure 2.25

2.26 (a) Calculate the work done by gravity as a 5.2-kg object is moved from A to B in Figure

2.26 along paths 1 and 2. (b) How do your results depend on the mass of the block? Specifically, if you increase the mass, does the work done by gravity increase, decrease, or stay the same? (51J, 51J)

Figure 2.26

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EE1427 Engineering Science – Dr. Daniel Nankoo

Tutorial 2

2.27 In the system shown in Figure 2.27, suppose the block has a mass of 2.7 kg, the spring has a

force constant of 480 N/m, and the coefficient of kinetic friction between the block and the floor is 0.16. (a) Find the work done on the block by the spring and by friction as the block is moved from point A to point B along path 2. (b) Find the work done on the block by the spring and by friction if the block is moved directly from point A to point B. (-0.096J, -0.25J, -0.096J, -0.085J)

Figure 2.27

2.28 Find the gravitational potential energy of an 83-kg person standing atop Mt. Everest at an

altitude of 8848 m. Use sea level as the location for y = 0. (7.2MJ)

2.29 A vertical spring stores 0.962 J in spring potential energy when a 3.0-kg mass is suspended

from it. (a) By what multiplicative factor does the spring potential energy change if the mass attached to the spring is doubled? (b) Verify your answer to part (a) by calculating the spring potential energy when a 6.0-kg mass is attached to the spring. (4, 3.85J)

2.30 Pushing on the pump of a soap dispenser compresses a small spring. When the spring is

compressed 0.50 cm, its potential energy is 0.0025 J. (a) What is the force constant of the spring? (b) What compression is required for the spring potential energy to equal 0.0084 J? (200N/m, 0.92cm)

2.31 The work required to stretch a certain spring from an elongation of 4.00 cm to an elongation

of 5.00 cm is 30.5 J. (a) Is the work required to increase the elongation of the spring from 5.00 cm to 6.00 cm greater than, less than, or equal to 30.5 J? Explain. (b) Verify your answer to part (a) by calculating the required work. (37.3J)

2.32 A 0.33-kg pendulum bob is attached to a string 1.2 m long. What is the change in the

gravitational potential energy of the system as the bob swings from point A to point B in Figure 2.32? (-0.70J)

Figure 2.32

2. Work, Energy and Conservation of Energy

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Tutorial 2

2. Work, Energy and Conservation of Energy – Tutorial 2

2.1 A farmer pushes a 23-kg bale of hay 3.4 m across the floor of a barn. If he exerts a horizontal

force of 86 N on the hay, how much work has he done? (290J)

2.2 The coefficient of kinetic friction between a suitcase and the floor is 0.26. If the suitcase has a

mass of 70.0 kg, how far can it be pushed across the level floor with 640 J of work? (3.6m)

2.3 You pick up a 3.4-kg can of paint from the ground and lift it to a height of 1.8 m. (a) How

much work do you do on the can of paint? (b) You hold the can stationary for half a minute, waiting for a friend on a ladder to take it. How much work do you do during this time? (c) Your friend decides against the paint, so you lower it back to the ground. How much work do you do on the can as you lower it? (60J, 0, -60J)

2.4 A tow rope, parallel to the water, pulls a water skier directly behind the boat with constant

velocity for a distance of 65 m before the skier falls. The tension in the rope is 120 N. (a) Is the work done on the skier by the rope positive, negative, or zero? Explain. (b) Calculate the work done by the rope on the skier. (7.8kJ)

2.5 A child pulls a friend in a little red wagon with constant speed. If the child pulls with a force

of 16 N for 10.0 m, and the handle of the wagon is inclined at an angle of 25° above the horizontal, how much work does the child do on the wagon? (150J)

2.6 To clean a floor, a cleaner pushes on a mop handle with a force of 50.0 N. (a) If the mop

handle is at an angle of 55° above the horizontal, how much work is required to push the mop 0.50 m? (b) If the angle the mop handle makes with the horizontal is increased to 65°, does the work done by the cleaner increase, decrease, or stay the same? Explain. (14J)

2.7 A small plane tows a glider at constant speed and altitude. If the plane does 2.00 × 105 J of

work to tow the glider 145 m and the tension in the tow rope is 2560 N, what is the angle between the tow rope and the horizontal? (57.4°)

2.8

A

young r

woman

on

a

skateboard

is

pulled

by

a

rope

attached

to

a

bricycle.

The

velocity

of

the

skateboarder is v = (4.1 m s)x$ and the force exerted on her by the rope is F = (17 N)x$ + (12 N)y$. (a)

Find the work done on the skateboarder by the rope in 25 seconds. (b) Assuming the velocity of the

bike is the same as that of the skateboarder, find the work the rope does on the bicycle in 25 seconds.

(1700J, -1700J)

2.9 Water skiers often ride to one side of the centre line of a boat, as shown in Figure 2.9. In this

case, the ski boat is travelling at 15 m/s and the tension in the rope is 75 N. If the boat does 3500 J of work on the skier in 50.0 m, what is the angle θ between the tow rope and the centre line of the boat? (21°)

Figure 2.9

2. Work, Energy and Conservation of Energy

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EE1427 Engineering Science – Dr. Daniel Nankoo

Tutorial 2

2.10 When Skylab re-entered the Earth’s atmosphere on July 11, 1979, it broke into a myriad of

pieces. One of the largest fragments was a 1770-kg lead-lined film vault, and it landed with an estimated speed of 120 m/s. What was the kinetic energy of the film vault when it landed? (12.7MJ)

2.11 A 0.14-kg pinecone falls 16 m to the ground, where it lands with a speed of 13 m/s. (a) With

what speed would the pinecone have landed if there had been no air resistance? (b) Did air resistance do positive work, negative work, or zero work on the pinecone? Explain. (18m/s)

2.12 At t = 1.0 s, a 0.40-kg object is falling with a speed of 6.0 m/s. At t = 2.0 s, it has a kinetic

energy of 25 J. (a) What is the kinetic energy of the object at t = 1.0 s? (b) What is the speed of the object at t = 2.0 s? (c) How much work was done on the object between t = 1.0 s and t = 2.0 s? (7.2J, 11m/s, 18J)

2.13 A 1300-kg car coasts on a horizontal road with a speed of 18 m/s. After crossing an unpaved,

sandy stretch of road 30.0 m long, its speed decreases to 15 m/s. (a) Was the net work done on the car positive, negative, or zero? Explain. (b) Find the magnitude of the average net force on the car in the sandy section. (2.1kN)

2.14 A 65-kg cyclist rides his 8.8-kg bicycle with a speed of 14 m/s. (a) How much work must be

done by the brakes to bring the bike and rider to a stop? (b) How far does the bicycle travel if it takes 4.0 s to come to rest? (c) What is the magnitude of the braking force? (-7.2kJ, 28m, 260N)

2.15 A spring with a force constant of 3.5 × 104 N m is initially at its equilibrium length. (a) How

much work must you do to stretch the spring 0.050 m? (b) How much work must you do to compress it 0.050 m? (44J, 44J)

2.16 Initially sliding with a speed of 2.2 m/s, a 1.8-kg block collides with a spring and compresses

it 0.31 m before coming to rest. What is the force constant of the spring? (91N/m)

2.17 The force shown in Figure 2.17 moves an object from x = 0 to x = 0.75 m. (a) How much

work is done by the force? (b) How much work is done by the force if the object moves from x = 0.15 m to x = 0.60 m? (0.45J, 0.24J)

Figure 2.17

2.18 It takes 160 J of work to compress a certain spring 0.14 m. (a) What is the force constant of

this spring? (b) To compress the spring an additional 0.14 m, does it take 160 J, more than 160 J, or less than 160 J? Verify your answer with a calculation. (16kN/m, 480J)

2.19 A block is acted on by a force that varies as (2.0 × 104 N m)x for 0 ≤ x ≤ 0.21 m, and then

remains constant at 4200 N for larger x. How much work does the force do on the block in moving it (a) from x = 0 to x = 0.30 m, or (b) from x = 0.10 m to x = 0.40 m? (0.82kJ, 1.1kJ)

2.20 Calculate the power output of a 1.3-g fly as it walks straight up a windowpane at 2.5 cm/s.

(0.32mW)

2. Work, Energy and Conservation of Energy

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EE1427 Engineering Science – Dr. Daniel Nankoo

Tutorial 2

2.21 You raise a bucket of water from the bottom of a deep well. If your power output is 108 W,

and the mass of the bucket and the water in it is 5.00 kg, with what speed can you raise the bucket? Ignore the weight of the rope. (2.20m/s)

2.22 A kayaker paddles with a power output of 50.0 W to maintain a steady speed of 1.50 m/s. (a)

Calculate the resistive force exerted by the water on the kayak. (b) If the kayaker doubles her power output, and the resistive force due to the water remains the same, by what factor does the kayaker’s speed change? (33.3N, 2)

2.23 A grandfather clock is powered by the descent of a 4.15-kg weight. (a) If the weight descends

through a distance of 0.720 m in 3.25 days, how much power does it deliver to the clock? (b) To increase the power delivered to the clock, should the time it takes for the mass to descend be increased or decreased? Explain. (0.104mW)

2.24 A certain car can accelerate from rest to the speed v in T seconds. If the power output of the

car remains constant, (a) how long does it take for the car to accelerate from v to 2v? (b) How fast is the car moving at 2T seconds after starting? (3T, v√2)

2.25 Calculate the work done by friction as a 3.2-kg box is slid along a floor from point A to point

B in Figure 2.25 along paths 1, 2, and 3. Assume that the coefficient of kinetic friction between the box and the floor is 0.21. (-73J, -33J, -46J)

Figure 2.25

2.26 (a) Calculate the work done by gravity as a 5.2-kg object is moved from A to B in Figure

2.26 along paths 1 and 2. (b) How do your results depend on the mass of the block? Specifically, if you increase the mass, does the work done by gravity increase, decrease, or stay the same? (51J, 51J)

Figure 2.26

2. Work, Energy and Conservation of Energy

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EE1427 Engineering Science – Dr. Daniel Nankoo

Tutorial 2

2.27 In the system shown in Figure 2.27, suppose the block has a mass of 2.7 kg, the spring has a

force constant of 480 N/m, and the coefficient of kinetic friction between the block and the floor is 0.16. (a) Find the work done on the block by the spring and by friction as the block is moved from point A to point B along path 2. (b) Find the work done on the block by the spring and by friction if the block is moved directly from point A to point B. (-0.096J, -0.25J, -0.096J, -0.085J)

Figure 2.27

2.28 Find the gravitational potential energy of an 83-kg person standing atop Mt. Everest at an

altitude of 8848 m. Use sea level as the location for y = 0. (7.2MJ)

2.29 A vertical spring stores 0.962 J in spring potential energy when a 3.0-kg mass is suspended

from it. (a) By what multiplicative factor does the spring potential energy change if the mass attached to the spring is doubled? (b) Verify your answer to part (a) by calculating the spring potential energy when a 6.0-kg mass is attached to the spring. (4, 3.85J)

2.30 Pushing on the pump of a soap dispenser compresses a small spring. When the spring is

compressed 0.50 cm, its potential energy is 0.0025 J. (a) What is the force constant of the spring? (b) What compression is required for the spring potential energy to equal 0.0084 J? (200N/m, 0.92cm)

2.31 The work required to stretch a certain spring from an elongation of 4.00 cm to an elongation

of 5.00 cm is 30.5 J. (a) Is the work required to increase the elongation of the spring from 5.00 cm to 6.00 cm greater than, less than, or equal to 30.5 J? Explain. (b) Verify your answer to part (a) by calculating the required work. (37.3J)

2.32 A 0.33-kg pendulum bob is attached to a string 1.2 m long. What is the change in the

gravitational potential energy of the system as the bob swings from point A to point B in Figure 2.32? (-0.70J)

Figure 2.32

2. Work, Energy and Conservation of Energy

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