Mechanics - Work, Energy & Power

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Q1. A 2 kg ball is dropped from a height of 20 m. What is its speed just before it hits the ground? (g = 10 m/s²) (2023)

Solution:

Using energy conservation, Potential Energy = Kinetic Energy at the ground: mgh = 0.5 mv^2; v = sqrt(2gh) = sqrt(2 * 10 m/s² * 20 m) = 20 m/s

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Q2. A cyclist is moving with a speed of 10 m/s. If he doubles his speed, how much more kinetic energy will he have? (2023)

Solution:

Kinetic Energy is proportional to the square of the speed. If speed is doubled, KE increases by a factor of 2^2 = 4.

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Q3. A 1 kg ball is thrown upwards with a speed of 20 m/s. What is the maximum height it reaches? (g = 10 m/s²) (2021)

Solution:

Maximum Height (h) = v^2 / (2g) = (20 m/s)^2 / (2 * 10 m/s²) = 20 m

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Q4. If a machine does 2000 J of work in 5 seconds, what is its power? (2022)

Solution:

Power (P) = Work Done / Time = 2000 J / 5 s = 400 W

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Q5. A 2 kg object is moving with a velocity of 4 m/s. What is its momentum? (2020)

Solution:

Momentum (p) = m * v = 2 kg * 4 m/s = 8 kg m/s

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Q6. If a machine does 200 J of work in 5 seconds, what is its power? (2022)

Solution:

Power (P) = Work Done (W) / Time (t) = 200 J / 5 s = 40 W

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Q7. A cyclist is moving at a speed of 10 m/s. If he doubles his speed, how much more kinetic energy will he have? (2023)

Solution:

Kinetic Energy is proportional to the square of the speed. If speed is doubled, KE increases by a factor of 2^2 = 4.

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Q8. A 10 kg block slides down a frictionless incline of height 5 m. What is its speed at the bottom? (2020)

Solution:

Using conservation of energy, PE at top = KE at bottom. mgh = 1/2 mv^2. 10 kg * 9.8 m/s^2 * 5 m = 1/2 * 10 kg * v^2. Solving gives v = 10 m/s.

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Q9. If a machine does 200 J of work in 10 seconds, what is its power? (2022)

Solution:

Power (P) = Work / Time = 200 J / 10 s = 20 W

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Q10. 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