Math Problem Statement
70 kg person climbs up 2 meter in 2.8 seconds. how much per did they gain?
Solution
To determine the power gained, we’ll calculate the work done by the person in climbing 2 meters and then divide it by the time taken.
Step 1: Calculate the Work Done (W)
The work done to lift a mass a height against gravity is given by: where:
- (mass),
- (acceleration due to gravity),
- (height).
So:
Step 2: Calculate the Power (P)
Power is the work done per unit time: where .
Thus:
Answer
The power gained is approximately 490.5 watts.
Would you like more details or have any questions?
Follow-up Questions:
- What would the power be if the height climbed was doubled?
- How would the power change if the person took twice as long to climb?
- What is the relationship between work, energy, and power?
- How does mass affect the power required for the same climb?
- Why is gravitational acceleration used in these calculations?
Tip: Power depends on both work done and time taken; reducing time increases power for the same amount of work.
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Math Problem Analysis
Mathematical Concepts
Physics
Work
Power
Energy
Formulas
Work done W = m * g * h
Power P = W / t
Theorems
Work-Energy Principle
Suitable Grade Level
Grades 9-11
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