A 50.7 kg student climbs a 6.35 m long rope and stops at the top. What must her average speed be in order to match the power output of a 130 W lightbulb
To find the average speed of the student, we can use the concept of work and power.
First, let's calculate the work done by the student to climb the rope. The work done is equal to the product of the force applied and the distance traveled. In this case, the force applied is equal to the weight of the student, which can be calculated using the formula:
Weight = mass × acceleration due to gravity
Weight = 50.7 kg × 9.8 m/s^2 = 496.86 N
Now, we can calculate the work:
Work = force × distance
Work = 496.86 N × 6.35 m = 3153.291 N·m or Joules
Next, we need to determine the time it took the student to climb the rope. Since we are looking for the average speed, we can use the formula:
Average speed = distance / time
In this case, the distance climbed is given as 6.35 m. We can rearrange the formula to solve for time:
Time = distance / average speed
Now, let's determine the time using the power output of a 130 W lightbulb, which is equivalent to the work done per unit time:
Power = Work / Time
Rearranging the formula, we find:
Time = Work / Power
Time = 3153.291 J / 130 W = 24.25947 s (approximately)
Finally, let's calculate the average speed:
Average speed = distance / time
Average speed = 6.35 m / 24.25947 s
Average speed = 0.2615 m/s (approximately)
Therefore, the student must have an average speed of approximately 0.2615 m/s in order to match the power output of a 130 W lightbulb.
m g h = gain in potential energy
50.7 * 9.81 * 6.35 = 3158 Joules
joules/t = power
so
power in Joules/second or Watts = 3158/t
so
3158/t = 130
t = 24.3 seconds