Work and Energy: Master Calculus I Concepts with Interactive Quizzes

Question 1

A bicycle rider exerts a force of 500 N on the pedals while riding at a constant speed of 10 m/s. What is the power output of the rider?

Accepted Answer

5 kW

Answer

10 kW

Answer

15 kW

Answer

20 kW

Question 2

According to the conservation of energy principle, what happens to the total energy in an isolated system?

Accepted Answer

It can be transferred between different forms, but the total remains constant.

Answer

It can be created or destroyed.

Answer

It is always lost due to friction.

Answer

It decreases over time.

Question 3

A satellite orbits Earth in a circular path at a constant speed of 10,000 m/s. What is the centripetal force acting on the satellite if its mass is 1000 kg?

Accepted Answer

100,000 N

Answer

10,000 N

Answer

1,000,000 N

Answer

10,000,000 N

Question 4

A pendulum swings with a period of 5 seconds. What is the frequency of the pendulum?

Accepted Answer

0.5 Hz

Answer

0.2 Hz

Answer

1 Hz

Answer

2 Hz

Question 5

A force of 10 Newtons is applied to an object over a distance of 5 meters, and then an additional force of 5 Newtons is applied over a distance of 3 meters. Calculate the total work done.

Accepted Answer

75 Joules

Answer

50 Joules

Answer

65 Joules

Answer

85 Joules

Question 6

A spring with a spring constant of 100 Newtons per meter is stretched 5 centimeters. Determine the energy stored in the spring.

Accepted Answer

0.5 Joules

Answer

0.25 Joules

Answer

1 Joule

Answer

2 Joules

Question 7

A roller coaster car is positioned at the top of a hill with a height of 20 meters. Calculate the car's potential energy relative to the ground.

Accepted Answer

600 Joules

Answer

200 Joules

Answer

400 Joules

Answer

800 Joules

Question 8

A force of 100 Newtons acts on an object over a distance of 5 meters. If the action takes 2 seconds, calculate the power exerted by the force.

Accepted Answer

50 Watts

Answer

25 Watts

Answer

100 Watts

Answer

200 Watts

Question 9

Calculate the kinetic energy of a 10 kilogram object moving at a velocity of 5 meters per second.

Accepted Answer

25 Joules

Answer

12.5 Joules

Answer

50 Joules

Answer

100 Joules

Question 10

Which of the following is not considered a form of energy?

Accepted Answer

Velocity

Answer

Heat

Answer

Potential Energy

Answer

Kinetic Energy

Question 11

In the International System of Units (SI), the unit of energy is:

Accepted Answer

Joule

Answer

Newton

Answer

Watt

Answer

Kelvin

Question 12

A spring has a spring constant of 200 Newtons per meter and is compressed 0.1 meters. What is the potential energy stored in the spring?

Accepted Answer

2 Joules

Answer

1 Joule

Answer

3 Joules

Answer

4 Joules

Question 13

A block of mass 2 kilograms slides down a frictionless inclined plane that makes an angle of 30 degrees with the horizontal. What is the acceleration of the block?

Accepted Answer

14.7 meters per second squared

Answer

4.9 meters per second squared

Answer

9.8 meters per second squared

Answer

19.6 meters per second squared

Question 14

A 2 kg object is moving with a velocity of 10 m/s. What is its kinetic energy? Express your answer in Joules.

Accepted Answer

100 J

Answer

50 J

Answer

200 J

Answer

400 J

Question 15

An object with a mass of 10 kilograms is lifted vertically through a height of 10 meters. What is its potential energy at the final height?

Accepted Answer

100 Joules

Answer

98 Joules

Answer

980 Joules

Answer

1000 Joules

Question 16

What is the SI unit of energy?

Accepted Answer

Joule

Answer

Newton

Answer

Meter

Answer

Second

Question 17

Which of the following statements about energy is true?

Accepted Answer

Energy can be transferred from one form to another

Answer

Energy is always conserved in any process

Answer

Energy is only found in moving objects

Answer

Energy can be created or destroyed

Question 18

An object with a mass of 2 kilograms falls freely from a height of 5 meters. What is its kinetic energy at the moment it hits the ground?

Accepted Answer

49 joules

Answer

24.5 joules

Answer

196 joules

Answer

98 joules

Question 19

Which of the following energy forms is NOT mechanical?

Accepted Answer

Electrical energy

Answer

Kinetic energy

Answer

Potential energy

Answer

Elastic energy

Question 20

A constant force of 100 Newtons is applied to an object, causing its displacement to increase from 2 meters to 7 meters. What is the work done by the force?

Accepted Answer

500 Joules

Answer

300 Joules

Answer

200 Joules

Answer

400 Joules

Question 21

A force of 10 Newtons acts on an object, moving it 5 meters in the direction of the force. What is the work done by the force?

Accepted Answer

50 Joules

Answer

500 Joules

Answer

15 Joules

Answer

2 Joules

Question 22

A variable force F(x) = x² Newtons acts on an object moving along the x-axis from x = 1 meter to x = 3 meters. Calculate the work done by this force.

Accepted Answer

26/3 Joules

Answer

18/3 Joules

Answer

20/3 Joules

Answer

8 Joules

Question 23

A roller coaster car starts from rest at a height of 50 meters and rolls down a frictionless track. What is its speed at the bottom of the track? (Assume the acceleration due to gravity is 9.8 m/s²)

Accepted Answer

31.3 m/s

Answer

10 m/s

Answer

15 m/s

Answer

20 m/s

Question 24

A force F(x) = 3x² Newtons acts on an object moving along the x-axis from x = 0 meters to x = 2 meters. Calculate the work done by this force using integration.

Accepted Answer

8 Joules

Answer

2 Joules

Answer

4 Joules

Answer

16 Joules

Question 25

A constant force of 10 Newtons is applied to an object, causing it to move 5 meters in the direction of the force. What is the work done by the force?

Accepted Answer

50 Joules

Answer

2 Joules

Answer

25 Joules

Answer

15 Joules

Question 26

A variable force F(x) = x² Newtons acts on an object moving along the x-axis from x = 0 meters to x = 2 meters. What is the work done by the force?

Accepted Answer

8/3 Joules

Answer

2 Joules

Answer

16/3 Joules

Answer

4 Joules

Question 27

A spring with a spring constant of 20 N/m is stretched 0.5 meters from its equilibrium position. What is the potential energy stored in the spring?

Accepted Answer

2.5 Joules

Answer

5 Joules

Answer

10 Joules

Answer

1 Joules

Question 28

An object of mass 2 kg is moving with a velocity of 4 m/s. What is the kinetic energy of the object?

Accepted Answer

16 Joules

Answer

4 Joules

Answer

32 Joules

Answer

8 Joules

Question 29

A 10 kg object is lifted vertically 2 meters. What is the work done by gravity? (Assume the acceleration due to gravity is 9.8 m/s²)

Accepted Answer

-196 Joules

Answer

196 Joules

Answer

98 Joules

Answer

-98 Joules

Question 30

A roller coaster car with a mass of 500 kg is moving at 20 m/s at the top of a hill. If the car then descends to a point 10 meters below the top, ignoring friction, what is its speed at that point?

Accepted Answer

24.5 m/s

Answer

20 m/s

Answer

30 m/s

Answer

14.1 m/s

Question 31

A force F(x) = 3x² Newtons acts on an object moving along the x-axis from x = 1 meter to x = 3 meters. What is the change in kinetic energy of the object?

Accepted Answer

52 Joules

Answer

26 Joules

Answer

36 Joules

Answer

18 Joules

Question 32

A particle moves along a path defined by the equation y = x² from x = 0 to x = 2. A force of F = (2x, 4y) Newtons acts on the particle. What is the work done by the force?

Accepted Answer

32 Joules

Answer

64 Joules

Answer

8 Joules

Answer

16 Joules

Question 33

A satellite with a mass of 1000 kg is in a circular orbit around Earth at a height of 500 km. What is the gravitational potential energy of the satellite?

Accepted Answer

-5.88 x 10^10 Joules

Answer

1.18 x 10^10 Joules

Answer

5.88 x 10^10 Joules

Answer

-1.18 x 10^10 Joules

Question 34

A pendulum with a length of 1 meter is released from rest at an angle of 30 degrees from the vertical. What is the speed of the pendulum bob at the bottom of its swing?

Accepted Answer

1.71 m/s

Answer

0.85 m/s

Answer

3.42 m/s

Answer

2.57 m/s

Question 35

A constant force of 10 Newtons is applied to move an object 5 meters horizontally. What is the work done by the force?

Accepted Answer

50 J

Answer

2 J

Answer

100 J

Answer

15 J

Question 36

A force of F(x) = x² Newtons acts on an object moving along the x-axis from x = 1 meter to x = 3 meters. What is the work done by the force?

Accepted Answer

26/3 J

Answer

18 J

Answer

8 J

Answer

16/3 J

Question 37

A 2 kg object is lifted vertically 4 meters. What is the potential energy gained by the object?

Accepted Answer

78.4 J

Answer

39.2 J

Answer

8 J

Answer

156.8 J

Question 38

A 10 kg object is moving at a speed of 5 m/s. What is its kinetic energy?

Accepted Answer

125 J

Answer

5 J

Answer

50 J

Answer

250 J

Question 39

A spring with a spring constant of 20 N/m is stretched 0.5 meters from its equilibrium position. What is the potential energy stored in the spring?

Accepted Answer

2.5 J

Answer

1 J

Answer

5 J

Answer

10 J

Question 40

A 5 kg object is initially at rest. A force acts on the object, causing it to accelerate to a speed of 10 m/s. What is the work done by the force?

Accepted Answer

250 J

Answer

100 J

Answer

125 J

Answer

50 J

Question 41

A roller coaster car starts at rest at the top of a 20-meter-high hill. Ignoring friction, what is its speed at the bottom of the hill?

Accepted Answer

20 m/s

Answer

40 m/s

Answer

10 m/s

Answer

30 m/s

Question 42

A 1 kg object is thrown vertically upward with an initial velocity of 10 m/s. What is the maximum height the object reaches?

Accepted Answer

5.1 m

Answer

10 m

Answer

15 m

Answer

2.5 m

Question 43

A 2 kg object is attached to a spring with a spring constant of 100 N/m. The object is pulled 0.2 meters from its equilibrium position and released. What is the maximum speed of the object?

Accepted Answer

2 m/s

Answer

1 m/s

Answer

4 m/s

Answer

0.5 m/s

Question 44

A 1000 kg car is traveling at 20 m/s. The driver applies the brakes, bringing the car to a stop in 5 seconds. What is the average power dissipated by the brakes?

Accepted Answer

80 kW

Answer

20 kW

Answer

160 kW

Answer

40 kW

Question 45

A constant force of 100 N is applied to an object, moving it from rest over a distance of 5 meters. How much work is done on the object?

Accepted Answer

500 J

Answer

250 J

Answer

1000 J

Answer

100 J

Question 46

A 5 kg object is moving at 10 m/s. What is its kinetic energy?

Accepted Answer

250 J

Answer

1000 J

Answer

500 J

Answer

125 J

Question 47

A spring has a spring constant of 100 N/m and is stretched by 0.2 meters. How much potential energy is stored in the spring?

Accepted Answer

2 J

Answer

4 J

Answer

8 J

Answer

1 J

Question 48

A force of 20 N acts over a distance of 5 meters along a displacement of 3 meters. Calculate the work done by the force.

Accepted Answer

60 J

Answer

150 J

Answer

100 J

Answer

200 J

Question 49

An object with a mass of 10 kg is lifted vertically through a height of 2 meters. What is its change in gravitational potential energy?

Accepted Answer

200 J

Answer

400 J

Answer

100 J

Answer

300 J

Question 50

A roller coaster car with a mass of 200 kg is at the top of a 30-meter-high hill. What is its potential energy at the top of the hill?

Accepted Answer

58.8 kJ

Answer

29.4 kJ

Answer

117.6 kJ

Answer

88.2 kJ

Question 51

A pendulum swings back and forth with a period of 2 seconds. What is its frequency?

Accepted Answer

0.5 Hz

Answer

2 Hz

Answer

4 Hz

Answer

1 Hz

Question 52

A wave has a wavelength of 10 meters and a frequency of 2 Hz. What is its speed?

Accepted Answer

20 m/s

Answer

10 m/s

Answer

40 m/s

Answer

30 m/s

Question 53

A sound wave has a frequency of 440 Hz. What is its period?

Accepted Answer

0.0023 s

Answer

0.0046 s

Answer

0.0035 s

Answer

0.0011 s

Question 54

A light wave has a wavelength of 500 nm. What is its frequency?

Accepted Answer

6 x 10^14 Hz

Answer

9 x 10^14 Hz

Answer

3 x 10^14 Hz

Answer

12 x 10^14 Hz