Mechanics - Work, Energy & Power

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Q1. A 10 kg block slides down a frictionless incline of height 5 m. What is its speed at the bottom? (g = 10 m/s²) (2020)

Solution:

Using conservation of energy, PE at top = KE at bottom: mgh = 1/2 mv²; v = sqrt(2gh) = sqrt(2 * 10 m/s² * 5 m) = 10 m/s

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Q2. A 3 kg object is lifted to a height of 4 m. What is the gravitational potential energy gained? (2023)

Solution:

Potential Energy (PE) = m * g * h = 3 kg * 9.8 m/s^2 * 4 m = 117.6 J (approximately 120 J)

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Q3. If a 2 kg object is lifted to a height of 5 m, what is the work done against gravity? (g = 10 m/s²) (2019)

Solution:

Work Done = mgh = 2 kg * 10 m/s² * 5 m = 100 J

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Q4. A 2 kg object is lifted to a height of 3 m. What is the work done against gravity? (2020)

Solution:

Work Done (W) = m * g * h = 2 kg * 9.8 m/s^2 * 3 m = 58.8 J (approx. 60 J)

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Q5. A 3 kg object is thrown upwards with a velocity of 15 m/s. What is its maximum height? (2020)

Solution:

Using the formula v^2 = u^2 - 2gh, we find h = u^2 / (2g) = (15 m/s)^2 / (2 * 9.8 m/s²) = 11.5 m.

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Q6. A spring is compressed by 0.2 m and has a spring constant of 500 N/m. What is the potential energy stored in the spring? (2023)

Solution:

Potential Energy in Spring (PE) = 1/2 kx^2 = 1/2 * 500 N/m * (0.2 m)^2 = 10 J

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Q7. A 3 kg object is moving with a velocity of 2 m/s. What is its kinetic energy? (2021)

Solution:

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 3 kg * (2 m/s)^2 = 6 J

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Q8. If a 5 kg object is dropped from a height of 20 m, what is its potential energy at the top? (2021)

Solution:

Potential Energy (PE) = m * g * h = 5 kg * 9.8 m/s^2 * 20 m = 980 J (approx. 1000 J)

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Q9. A spring is compressed by 0.1 m and has a spring constant of 200 N/m. What is the potential energy stored in the spring? (2019)

Solution:

Potential Energy (PE) = 1/2 * k * x^2 = 1/2 * 200 N/m * (0.1 m)^2 = 1 J

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Q10. A 1 kg object is moving with a velocity of 4 m/s. What is its kinetic energy? (2021)

Solution:

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 1 kg * (4 m/s)^2 = 8 J.