If the winch mine drum diameter is 6m, calculate how far the cage will drop for each single rotation of the drum, using the formula C =nr
You have the formula, though it is incorrect, so fix it and use it.
If you don't know why to use the formula, you just don't understand the problem.
One turn of the wheel uses up enough rope to wrap around the circumference of the drum.
The formula gives you that circumference.
And it’s not ‘n’ — it’s π (pi)
and it is pi D not pi r
To calculate how far the cage will drop for each single rotation of the drum, we need to use the formula C = nr.
In this formula:
- C represents the circumference of the drum,
- n represents the number of rotations, and
- r represents the radius of the drum.
Given that the drum diameter is 6m, we can determine the radius by dividing the diameter by 2:
Radius, r = 6m / 2 = 3m
Next, we need to find the circumference of the drum using the formula C = 2πr, where π is a constant equal to approximately 3.14159.
Circumference, C = 2 × 3.14159 × 3m = 18.84956m
Now that we know the circumference of the drum, we can calculate how far the cage will drop for each single rotation by multiplying the circumference by the number of rotations:
Distance dropped per rotation = Circumference × number of rotations
For example, if the number of rotations is 2, the distance dropped per rotation would be:
Distance dropped per rotation = 18.84956m/rotation × 2 rotations = 37.69912m