A student weighing 700 N climbs at constant
speed to the top of an 8 m vertical rope in 10
s.
The average power expended by the student
to overcome gravity is most nearly
1. P = 560 W.
2. P = 87.5 W.
3. P = 5, 600 W
4. P = 1.1 W.
5. P = 875 W
mg h / time
= 700 * 8 /10 = 70 * 8 = 560
560 Watts
To find the average power expended by the student to overcome gravity, we can use the formula:
Power (P) = Work (W) / Time (t)
The work done against gravity can be calculated using the formula:
Work (W) = Force (F) x Distance (d)
In this case, the force is equal to the weight of the student, which is 700 N, and the distance is equal to the height climbed, which is 8 m. Therefore:
Work (W) = 700 N x 8 m = 5600 N·m
Given that the time taken to climb is 10 s, we can substitute these values into the power formula:
Power (P) = 5600 N·m / 10 s = 560 W
Therefore, the average power expended by the student to overcome gravity is most nearly 560 W, which corresponds to option 3.
To find the average power expended by the student to overcome gravity, we can use the formula:
Power = Work / Time
First, we need to determine the work done by the student to overcome gravity. The work done against gravity is given by:
Work = Force * Distance
In this case, the force is the weight of the student, which is 700 N, and the distance is the height climbed, which is 8 m.
Work = 700 N * 8 m = 5600 J
Next, we divide the work by the time taken, which is 10 s:
Power = 5600 J / 10 s = 560 W
Therefore, the average power expended by the student to overcome gravity is 560 W.
The correct answer is option 1: P = 560 W.