Introduction
To calculate the power of the motor lifting a body, we need to understand the concept of work done and how it relates to power.
Work Done
- Work is defined as the force applied to move an object over a distance.
- The formula for work done (W) is:
W = Force × Distance
- In this case:
- Mass (m) = 20 kg
- Distance (d) = 10 meters
- The force required to lift the object is equal to its weight:
Force (F) = m × g, where g (acceleration due to gravity) ≈ 9.81 m/s²
- Therefore:
F = 20 kg × 9.81 m/s² = 196.2 N
- Now, calculate the work done:
W = 196.2 N × 10 m = 1962 Joules
Time Taken
- The time taken to lift the body is given as 10 seconds.
Power Calculation
- Power (P) is defined as the rate of doing work. The formula for power is:
P = Work Done / Time
- Substituting the values:
P = 1962 Joules / 10 seconds = 196.2 Watts
Conclusion
The power of the motor lifting the 20 kg body up 10 meters in 10 seconds is 196.2 Watts. This calculation demonstrates the relationship between work, time, and power, essential concepts in physics.