Power

Step 1: Calculate work done Work = Force × distance Force = weight = mg = 500 kg × 10 m/s² = 5000 N Work = 5000 N × 20 m = 100,000 J

Step 2: Calculate power Power = Work / time P = 100,000 J / 10 s = 10,000 W = 10 kW

The crane outputs 10 kilowatts of power.

Given: Power = 750 W Time = 2 minutes = 120 s

Using: Power = Work / time Work = Power × time Work = 750 W × 120 s = 90,000 J = 90 kJ

The motor can do 90 kilojoules of work in 2 minutes.

Step 1: Calculate work done against gravity W = mgh W = 60 kg × 10 m/s² × 5 m = 3000 J

Step 2: Calculate average power P = W / t P = 3000 J / 4 s = 750 W

The student's average power output is 750 watts.

Note: This is just the power used to overcome gravity. The actual metabolic power would be higher due to inefficiency.

Step 1: Convert power to watts P = 150 hp × 746 W/hp = 111,900 W

Step 2: Use relationship between power, force, and velocity For constant velocity: P = F × v where F is the applied force, which equals resistive force at constant velocity

F = P / v F = 111,900 W / 30 m/s = 3730 N

The total resistive force is 3,730 N.

Physical insight: At constant velocity, the engine force equals resistive forces, and all engine power goes into overcoming resistance.

Step 1: Calculate work needed W = mgh W = 1000 kg × 10 m/s² × 15 m = 150,000 J

Step 2: Account for efficiency Only 70% of input power does useful work Useful power = 0.70 × 2500 W = 1750 W

Step 3: Calculate time t = W / P_useful t = 150,000 J / 1750 W ≈ 85.7 s

It will take approximately 86 seconds (about 1.4 minutes) to pump the water.

Note: The remaining 30% of power is lost as heat, noise, etc.