A student of mass 50 kg climbs a vertical ladder of 4.0 m in a time of 8.0 s. What is the average power developed by the student?
Understand the Problem
The question is asking for the average power developed by a student who climbs a vertical ladder. We'll need to apply the formula for power, which involves the work done against gravity over the time taken.
Answer
The average power developed by the student is \( 245.25 \, \text{W} \).
Answer for screen readers
The average power developed by the student is ( P = 245.25 , \text{W} ).
Steps to Solve
- Calculate the Work Done Against Gravity
The work done against gravity can be calculated using the formula: $$ W = m \cdot g \cdot h $$ where:
- ( m = 50 , \text{kg} ) (mass of the student)
- ( g = 9.81 , \text{m/s}^2 ) (acceleration due to gravity)
- ( h = 4.0 , \text{m} ) (height climbed)
Substituting these values: $$ W = 50 \cdot 9.81 \cdot 4.0 $$
- Calculate the Total Work Done
Perform the calculation: $$ W = 50 \cdot 9.81 \cdot 4.0 = 1962 , \text{Joules} $$
- Calculate Average Power Developed
Average power is given by the formula: $$ P = \frac{W}{t} $$ where ( t = 8.0 , \text{s} ) (time taken).
Substituting for power: $$ P = \frac{1962}{8.0} $$
- Perform the Calculation for Power
Now perform the division: $$ P = 245.25 , \text{Watts} $$
The average power developed by the student is ( P = 245.25 , \text{W} ).
More Information
This average power indicates how much work the student does against gravity per unit of time while climbing the ladder. The power output is a measurement of energy transfer, reflecting the effort required to perform the task.
Tips
- Misunderstanding Units: Ensure that all units are consistent (e.g., mass in kg, height in meters, and force in Newtons).
- Omitting Gravity: Remember to include the gravitational acceleration in the work calculation.
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