A 50kg student climbs a 5m long rope and stops at the top. (a) What must her average speed be in order to match the power output of a 200-W lightbulb? (b) HOw much work does she do?
power= work/time
how would I find time?
To answer these questions, we need to understand the concepts of power, speed, and work in physics.
(a) Power is the rate at which work is done or energy is transferred. It is given by the formula:
Power = Work / Time
In this case, we are told that the power output of a lightbulb is 200 watts. Since power is equal to work divided by time, we can rearrange the formula to solve for work:
Work = Power × Time
Now, to match the power output of the lightbulb, the student needs to do the same amount of work in the same amount of time. The work done by the student is equal to the gravitational potential energy gained while climbing the rope.
Gravitational Potential Energy = mass × gravity × height
In this case, the mass of the student is 50 kg, gravity is approximately 9.8 m/s², and the height is 5 meters. So, the work done by the student is:
Work = 50 kg × 9.8 m/s² × 5 m
Now, we have to find the time it takes for the student to climb the rope. To do that, we need to know the average speed of the student.
Average Speed = Distance / Time
In this case, the distance is the length of the rope, which is 5 meters. Rearranging the formula, we can solve for time:
Time = Distance / Average Speed
Now, we can substitute this expression for time in the formula for work:
Work = Power × (Distance / Average Speed)
Since the work done by the student must be equal to the power output of the lightbulb (200 watts), we can solve for the average speed:
200 watts = (50 kg × 9.8 m/s² × 5 m) / Average Speed
Simplifying, we get:
Average Speed = (50 kg × 9.8 m/s² × 5 m) / 200 watts
Calculating this expression will give us the average speed in meters per second.
(b) The work done by the student is equal to the gravitational potential energy gained while climbing the rope, as calculated earlier:
Work = 50 kg × 9.8 m/s² × 5 m
Evaluating this expression will give us the work done by the student in joules.