Work, Energy & Power: Essential Concepts for Exam Prep

Work, Energy & Power

Conservation of Energy Power Work Energy Theorem

Q. A roller coaster at the top of a hill has a height of 30 m. If it has a mass of 500 kg, what is its potential energy? (g = 9.8 m/s²)

A. 14700 J
B. 9800 J
C. 15000 J
D. 5000 J

Solution

Potential energy is given by PE = mgh. Here, PE = 500 * 9.8 * 30 = 14700 J.

Correct Answer: A — 14700 J

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Q. A roller coaster at the top of a hill has a height of 30 m. If it has a mass of 500 kg, what is its potential energy at the top?

A. 1500 J
B. 3000 J
C. 7500 J
D. 15000 J

Solution

Potential energy = mgh = 500 * 9.8 * 30 = 147000 J.

Correct Answer: D — 15000 J

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Q. A roller coaster at the top of a hill has a potential energy of 5000 J. If it descends to a height of 10 m, what is its speed at the bottom? (g = 9.8 m/s²)

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Using conservation of energy, initial PE + KE = final PE + KE. 5000 J = mgh + 0.5mv². Solving gives v = √(2(5000 - mgh)/m) = 30 m/s.

Correct Answer: C — 30 m/s

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Q. A roller coaster starts from rest at a height of 30 m. What is its speed at the lowest point? (g = 9.8 m/s²)

A. 10 m/s
B. 15 m/s
C. 20 m/s
D. 25 m/s

Solution

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = √(2gh) = √(2 * 9.8 * 30) = 24.5 m/s.

Correct Answer: C — 20 m/s

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Q. A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point? (g = 9.8 m/s²)

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Using conservation of energy, mgh = 0.5mv². Thus, v = sqrt(2gh) = sqrt(2 * 9.8 * 50) = 31.3 m/s, approximately 30 m/s.

Correct Answer: C — 30 m/s

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Q. A roller coaster starts from rest at a height of 50 m. What is its speed at the lowest point?

A. 10 m/s
B. 20 m/s
C. 30 m/s
D. 40 m/s

Solution

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv^2. Solving gives v = sqrt(2gh) = sqrt(2*9.8*50) = 31.3 m/s.

Correct Answer: C — 30 m/s

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Q. A spring with a spring constant of 200 N/m is compressed by 0.1 m. What is the potential energy stored in the spring?

A. 1 J
B. 2 J
C. 3 J
D. 4 J

Solution

Potential Energy = 0.5 × k × x² = 0.5 × 200 N/m × (0.1 m)² = 1 J.

Correct Answer: A — 1 J

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Q. A spring with a spring constant of 200 N/m is compressed by 0.1 m. What is the work done in compressing the spring?

A. 1 J
B. 2 J
C. 3 J
D. 4 J

Solution

Work done = 0.5 × k × x^2 = 0.5 × 200 N/m × (0.1 m)^2 = 1 J.

Correct Answer: A — 1 J

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Q. A spring with a spring constant of 200 N/m is compressed by 0.5 m. What is the potential energy stored in the spring?

A. 25 J
B. 50 J
C. 100 J
D. 200 J

Solution

Potential Energy in spring = 0.5 × k × x² = 0.5 × 200 N/m × (0.5 m)² = 25 J.

Correct Answer: B — 50 J

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Q. A spring with a spring constant of 200 N/m is compressed by 0.5 m. What is the work done in compressing the spring?

A. 25 J
B. 50 J
C. 100 J
D. 200 J

Solution

Work done = 0.5 × k × x² = 0.5 × 200 N/m × (0.5 m)² = 25 J.

Correct Answer: B — 50 J

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Q. An object is lifted to a height of 10 m. If the mass of the object is 5 kg, what is the gravitational potential energy gained?

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Potential Energy = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.

Correct Answer: B — 100 J

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Q. An object is lifted vertically 10 m against gravity. If the mass of the object is 5 kg, what is the work done against gravity?

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Work done = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.

Correct Answer: B — 100 J

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Q. An object is lifted vertically 3 m against gravity. If the mass of the object is 4 kg, what is the work done against gravity? (g = 9.8 m/s²)

A. 117.6 J
B. 39.2 J
C. 29.4 J
D. 19.6 J

Solution

Work done = mgh = 4 kg × 9.8 m/s² × 3 m = 117.6 J.

Correct Answer: A — 117.6 J

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Q. An object is lifted vertically to a height of 10 m. If the mass of the object is 5 kg, what is the work done against gravity?

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Work done = mass × g × height = 5 kg × 9.8 m/s² × 10 m = 490 J.

Correct Answer: B — 100 J

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Q. An object is moving in a circular path with a constant speed. What can be said about the work done by the centripetal force?

A. Positive work
B. Negative work
C. Zero work
D. Depends on speed

Solution

Centripetal force does no work as it acts perpendicular to the direction of motion.

Correct Answer: C — Zero work

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Q. An object is moving in a circular path with a constant speed. What type of energy is primarily involved?

A. Kinetic Energy
B. Potential Energy
C. Mechanical Energy
D. Thermal Energy

Solution

The object has Kinetic Energy due to its motion in the circular path.

Correct Answer: A — Kinetic Energy

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Q. An object is thrown vertically upwards with a speed of 15 m/s. What is the maximum height it reaches? (g = 10 m/s²)

A. 11.25 m
B. 22.5 m
C. 15 m
D. 20 m

Solution

Maximum Height (h) = v^2 / (2g) = (15^2) / (2 * 10) = 11.25 m

Correct Answer: B — 22.5 m

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Q. If 10^(2x) = 100, what is the value of x?

A. 0
B. 0.5
C. 1
D. 2

Solution

100 = 10^2, so 2x = 2, hence x = 1.

Correct Answer: B — 0.5

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Q. If 10^x = 0.01, what is the value of x?

A. -2
B. -1
C. 0
D. 1

Solution

Since 0.01 = 10^(-2), we have x = -2.

Correct Answer: A — -2

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Q. If 2^(x+1) = 16, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

16 = 2^4 => x + 1 = 4 => x = 3

Correct Answer: B — 3

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Q. If 3^(2x) = 81, what is the value of x?

A. 2
B. 3
C. 4
D. 1

Solution

Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.

Correct Answer: A — 2

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Q. If 4^x = 64, what is the value of x?

A. 2
B. 3
C. 4
D. 5

Solution

Since 64 = 4^3, we have x = 3.

Correct Answer: B — 3

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Q. If 5^(x+1) = 125, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

125 = 5^3, so x + 1 = 3, hence x = 2.

Correct Answer: B — 2

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Q. If 5^(x-1) = 25, what is the value of x?

A. 2
B. 3
C. 4
D. 1

Solution

Since 25 = 5^2, we have 5^(x-1) = 5^2, thus x - 1 = 2, giving x = 3.

Correct Answer: A — 2

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Q. If 5^x = 125, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

125 = 5^3 => x = 3

Correct Answer: C — 3

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Q. If 5^x = 25, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

Since 25 = 5^2, we have 5^x = 5^2, thus x = 2.

Correct Answer: B — 2

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Q. If 7^(x) = 49, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

49 = 7^2, so x = 2.

Correct Answer: B — 2

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Q. If 8^(x) = 64, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

64 = 8^2, so x = 2.

Correct Answer: B — 2

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Q. If a 10 kg object is dropped from a height of 20 m, what is its potential energy at the top? (1960)

A. 200 J
B. 1000 J
C. 500 J
D. 1500 J

Solution

Potential Energy (PE) = m * g * h = 10 kg * 9.8 m/s^2 * 20 m = 1960 J

Correct Answer: B — 1000 J

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Q. If a 10 kg object is dropped from a height of 5 m, what is the potential energy at that height?

A. 50 J
B. 100 J
C. 150 J
D. 200 J

Solution

Potential energy = mgh = 10 kg × 9.8 m/s² × 5 m = 490 J.

Correct Answer: B — 100 J

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Work, Energy & Power

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