Work, Energy & Power: Essential Concepts for Exam Prep

Work, Energy & Power

Conservation of Energy Power Work Energy Theorem

Q. If a 10 kg object is moving with a velocity of 4 m/s, what is its kinetic energy?

A. 80 J
B. 40 J
C. 20 J
D. 160 J

Solution

Kinetic Energy (KE) = 1/2 * m * v^2 = 1/2 * 10 * (4^2) = 80 J

Correct Answer: A — 80 J

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Q. If a 1000 kg car accelerates from rest to a speed of 20 m/s in 10 seconds, what is the average power output of the car's engine?

A. 2000 W
B. 4000 W
C. 6000 W
D. 8000 W

Solution

First, calculate the work done: W = 0.5 * m * v^2 = 0.5 * 1000 kg * (20 m/s)^2 = 200000 J. Then, power is P = W/t = 200000 J / 10 s = 20000 W.

Correct Answer: C — 6000 W

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Q. If a 1000 W heater is used for 3 hours, how much energy does it consume in kilowatt-hours?

A. 3 kWh
B. 2 kWh
C. 1 kWh
D. 0.5 kWh

Solution

Energy consumed in kilowatt-hours is calculated as E = P (kW) * t (h). Here, P = 1000 W = 1 kW and t = 3 hours. Thus, E = 1 kW * 3 h = 3 kWh.

Correct Answer: A — 3 kWh

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Q. If a 1000 W heater runs for 2 hours, how much energy does it consume?

A. 7200 J
B. 14400 J
C. 20000 J
D. 3600000 J

Solution

Energy = Power × Time = 1000 W × (2 × 3600 s) = 7200000 J.

Correct Answer: D — 3600000 J

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Q. If a 2 kg object is dropped from a height of 5 m, what is its speed just before it hits the ground? (g = 10 m/s²)

A. 10 m/s
B. 5 m/s
C. 15 m/s
D. 20 m/s

Solution

Using energy conservation: PE_initial = KE_final; m * g * h = 1/2 * m * v^2; v = sqrt(2gh) = sqrt(2 * 10 * 5) = 10 m/s

Correct Answer: A — 10 m/s

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Q. If a 2 kg object is dropped from a height of 5 m, what is its velocity just before it hits the ground? (g = 10 m/s²)

A. 10 m/s
B. 5 m/s
C. 15 m/s
D. 20 m/s

Solution

Using energy conservation, v = sqrt(2gh) = sqrt(2 * 10 * 5) = 10 m/s

Correct Answer: A — 10 m/s

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Q. If a 3 kg object is moving with a speed of 4 m/s and comes to a stop, what is the work done by the friction?

A. -24 J
B. -48 J
C. -12 J
D. -36 J

Solution

Initial kinetic energy = 0.5 × 3 kg × (4 m/s)² = 24 J. Work done by friction = -24 J.

Correct Answer: B — -48 J

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Q. If a 3 kg object is moving with a speed of 4 m/s and comes to a stop, what is the work done by the friction force?

A. -24 J
B. -48 J
C. -72 J
D. -96 J

Solution

Initial kinetic energy = 0.5 × 3 kg × (4 m/s)² = 24 J. Work done by friction = -24 J.

Correct Answer: B — -48 J

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Q. If a 3 kg object is moving with a speed of 4 m/s and comes to a stop, what is the work done by friction?

A. -24 J
B. -48 J
C. 0 J
D. 24 J

Solution

Initial kinetic energy = 0.5 × m × v² = 0.5 × 3 kg × (4 m/s)² = 24 J. Work done by friction = -24 J.

Correct Answer: B — -48 J

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Q. If a 3 kg object is moving with a speed of 4 m/s, what is the total mechanical energy if it is at a height of 2 m?

A. 30 J
B. 40 J
C. 50 J
D. 60 J

Solution

Total mechanical energy = K.E + P.E = 0.5 × 3 kg × (4 m/s)² + 3 kg × 9.8 m/s² × 2 m = 24 J + 58.8 J = 82.8 J.

Correct Answer: C — 50 J

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Q. If a 3 kg object is moving with a velocity of 4 m/s, what is its momentum?

A. 12 kg m/s
B. 6 kg m/s
C. 8 kg m/s
D. 10 kg m/s

Solution

Momentum (p) = m * v = 3 kg * 4 m/s = 12 kg m/s

Correct Answer: A — 12 kg m/s

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Q. If a 5 kg object is lifted to a height of 10 m, what is the potential energy gained by the object? (g = 9.8 m/s²)

A. 490 J
B. 980 J
C. 245 J
D. 2450 J

Solution

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

Correct Answer: B — 980 J

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Q. If a 5 kg object is lifted to a height of 10 m, what is the work done against gravity? (g = 9.8 m/s²)

A. 49 J
B. 98 J
C. 490 J
D. 980 J

Solution

Work done = mgh = 5 kg × 9.8 m/s² × 10 m = 490 J.

Correct Answer: C — 490 J

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

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

Solution

Work done = mgh = 5 kg × 9.8 m/s² × 10 m = 490 J.

Correct Answer: D — 200 J

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Q. If a car engine has a power output of 150 kW, how much work can it do in 2 minutes?

A. 18000 J
B. 9000 J
C. 30000 J
D. 180000 J

Solution

Power is the rate of doing work. Work done can be calculated as W = P * t. Here, P = 150 kW = 150000 W and t = 2 minutes = 120 seconds. Thus, W = 150000 W * 120 s = 18000000 J.

Correct Answer: D — 180000 J

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Q. If a cyclist is moving at a constant speed and exerts a force of 200 N, what is the power output if the speed is 5 m/s?

A. 1000 W
B. 500 W
C. 200 W
D. 400 W

Solution

Power can be calculated using P = F * v. Here, F = 200 N and v = 5 m/s. Thus, P = 200 N * 5 m/s = 1000 W.

Correct Answer: A — 1000 W

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Q. If a force of 10 N is applied to move an object 5 m in the direction of the force, what is the work done?

A. 50 J
B. 30 J
C. 20 J
D. 10 J

Solution

Work Done (W) = Force * Distance = 10 N * 5 m = 50 J

Correct Answer: A — 50 J

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Q. If a force of 10 N is applied to move an object 5 m, what is the work done?

A. 50 J
B. 25 J
C. 10 J
D. 5 J

Solution

Work Done (W) = Force * Distance = 10 N * 5 m = 50 J

Correct Answer: A — 50 J

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Q. If a force of 12 N is applied at an angle of 30 degrees to the horizontal while moving an object 3 m, what is the work done by the force?

A. 18 J
B. 24 J
C. 30 J
D. 36 J

Solution

Work done = F × d × cos(θ) = 12 N × 3 m × cos(30°) = 12 N × 3 m × (√3/2) = 18 J.

Correct Answer: B — 24 J

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Q. If a force of 15 N acts on an object and moves it 4 m in the direction of the force, what is the work done?

A. 30 J
B. 60 J
C. 75 J
D. 90 J

Solution

Work done = Force × Distance = 15 N × 4 m = 60 J.

Correct Answer: B — 60 J

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Q. If a force of 15 N is applied at an angle of 60 degrees to the horizontal while moving an object 4 m, what is the work done by the force?

A. 30 J
B. 60 J
C. 120 J
D. 180 J

Solution

Work done = F × d × cos(θ) = 15 N × 4 m × cos(60°) = 15 N × 4 m × 0.5 = 30 J.

Correct Answer: C — 120 J

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Q. If a force of 15 N is applied at an angle of 60° to the horizontal while moving an object 4 m, what is the work done by the force?

A. 30 J
B. 60 J
C. 120 J
D. 180 J

Solution

Work done = F × d × cos(θ) = 15 N × 4 m × cos(60°) = 15 N × 4 m × 0.5 = 30 J.

Correct Answer: C — 120 J

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Q. If a force of 15 N is applied to move an object 3 m in the direction of the force, what is the work done?

A. 45 J
B. 30 J
C. 15 J
D. 60 J

Solution

Work done = Force × Distance = 15 N × 3 m = 45 J.

Correct Answer: A — 45 J

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Q. If a force of 15 N is applied to move an object 4 m in the direction of the force, what is the work done?

A. 30 J
B. 60 J
C. 45 J
D. 75 J

Solution

Work done = Force × Distance = 15 N × 4 m = 60 J.

Correct Answer: B — 60 J

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Q. If a force of 5 N acts on an object and moves it 4 m in the direction of the force, what is the work done?

A. 10 J
B. 15 J
C. 20 J
D. 25 J

Solution

Work done = Force × Distance = 5 N × 4 m = 20 J.

Correct Answer: C — 20 J

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Q. If a force of 5 N is applied at an angle of 60 degrees to the horizontal while moving an object 3 m, what is the work done by the force?

A. 7.5 J
B. 15 J
C. 12.99 J
D. 10 J

Solution

Work done = Force × Distance × cos(θ) = 5 N × 3 m × cos(60°) = 5 N × 3 m × 0.5 = 7.5 J.

Correct Answer: C — 12.99 J

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Q. If a force of 5 N is applied at an angle of 60 degrees to the horizontal while moving an object 4 m, what is the work done by the force?

A. 10 J
B. 20 J
C. 5 J
D. 15 J

Solution

Work done = Force × Distance × cos(θ) = 5 N × 4 m × cos(60°) = 5 N × 4 m × 0.5 = 10 J.

Correct Answer: A — 10 J

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Q. If a machine does 200 J of work in 5 seconds, what is its power output?

A. 20 W
B. 40 W
C. 50 W
D. 60 W

Solution

Power = Work / Time = 200 J / 5 s = 40 W.

Correct Answer: B — 40 W

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Q. If a machine does 2000 J of work in 5 seconds, what is its power output?

A. 200 W
B. 400 W
C. 500 W
D. 600 W

Solution

Power = Work / Time = 2000 J / 5 s = 400 W.

Correct Answer: B — 400 W

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Q. If a machine does 500 J of work in 10 seconds, what is its power output?

A. 50 W
B. 100 W
C. 200 W
D. 500 W

Solution

Power is calculated using the formula P = W/t. Here, W = 500 J and t = 10 s. Thus, P = 500 J / 10 s = 50 W.

Correct Answer: B — 100 W

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Work, Energy & Power

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