Final answer:
The mechanical advantage of the lever is 8, the weight of the load including water and the bucket is approximately 12.23 kg, and the load will move up by 1.57 meters after 5 rotations of the lever.
Step-by-step explanation:
Calculations for a Water Well Guide
Given a water well guide with a radius of 5 cm and a forearm with a diameter of 0.8 m, and an average force of 15N applied by a man to fetch water, we can calculate the following:
A. Mechanical Advantage of the Lever
The mechanical advantage (MA) of the lever is the ratio of the lever arm distance to the load arm distance. The diameter of the forearm is 0.8 meters, so the radius, which is the lever arm distance, is 0.4 meters (0.8 m / 2). The radius of the well guide is 5 cm, or 0.05 meters. Thus, the mechanical advantage (MA) is:
MA = lever arm distance/load arm distance = 0.4 m / 0.05 m = 8
B. Load Weight (Water + Bucket), Ignoring Cable Mass
The load weight can be calculated using the mechanical advantage and the force applied. The weight lifted (W) is the product of the force (F) and the mechanical advantage (MA).
W = F × MA = 15N × 8 = 120N
Assuming acceleration due to gravity is 9.81 m/s², the weight in kilograms is W/g, which gives:
Weight in kg = 120N / 9.81 m/s² ≈ 12.23 kg
C. Distance the Load Moves Up After 5 Rotations
If the man rotates the lever 5 times, the load will move a distance equal to the circumference of the well guide multiplied by the number of rotations. The circumference (C) of the well guide is 2πr, where r is the radius of the well guide.
C = 2π(5 cm) = 2π(0.05 m) ≈ 0.314 m
The load will therefore move up:
Distance = 5 × C = 5 × 0.314 m = 1.57 meters