A boy exerts a force of 4000 N to pull a cart at a constant speed of 30 m/s, calculate the power developed by the boy. (b) The power of a motor is 40 kW. At what speed can it raise a load of 20,000 Newton?
Answers
Question 1st
Provided that:
- Force = 4000 Newton
- Speed = 30 m/s
To calculate:
- The power
Solution:
The power = 120000 Watts or 120 kW
Using concept:
- Power formula
Using formula:
- Power = Force × Velocity
Knowledge required:
• 1 kilowatt = 1000 watts
Therefore,
- 1 watt = 1/1000 kilowatts
Required solution:
→ Power = Force × Velocity
→ Power = 4000 × 30
→ Power = 120000 Watts
→ Power = 120000/1000 kW
→ Power = 120 kW
_____________________
Question 2nd
Provided that:
- Power = 40 kW
- Force = 20,000 N
To calculate:
- The speed
Solution:
- The speed = 2 m/s
Using concept:
- Power formula
Using formula:
- Power = Force × Velocity
Knowledge required:
• 1 kilowatt = 1000 watts
• 1 watt = 1/1000 kilowatts
Required solution:
~ Firstly converting kW into W!
→ 1 kilowatt = 1000 watts
→ 40 × 1000
→ 40000 Watts
~ Now finding speed!
→ Power = Force × Velocity
→ 40000 = 20000 × Velocity
→ 40000 = 20000 × V
→ 40000 = 20000v
→ 40000/20000 = v
→ 4/2 = v
→ 2 = v
→ v = 2 m/s
→ Velocity = 2 m/s
→ Speed = 2 m/s
Answer:
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