Water is taken from a well 11m deep in a bucket, the good winding on to a drum 35 cm in diameter. Through what angle dies the handle turn in winding up 1 metre of rope.

Question

How many revolutions of the handle does it take to bring the bucket up from the bottom.
If the arm of the handle.is 42cm long bow far does the hand of the winder travel when bringing the bucket up from the bottom

Answer 1

To wind up 1 meter of rope, the handle must turn a distance equal to the circumference of the drum. The circumference of a circle is given by the formula C = πd, where d is the diameter of the circle. In this case, the diameter is 35 cm, so the circumference is:

C = π(35) = 110 cm = 1.1 meters

Therefore, to wind up 1 meter of rope, the handle must turn a total of 1.1 meters.

To calculate how many revolutions of the handle it takes to bring the bucket up from the bottom, we need to find the total distance the handle needs to turn. Since the bucket is 11 meters deep, the handle must turn a total distance of 11 meters. Therefore, the number of revolutions is:

Revolutions = Total distance / Circumference = 11 / 1.1 = 10 revolutions

Finally, to calculate how far the hand of the winder travels when bringing the bucket up from the bottom, we can use the formula for the length of the arc of a circle:

Arc length = θr

where θ is the angle in radians and r is the radius of the circle (in this case, the length of the arm of the handle). Since the handle turns a total distance of 11 meters, we can find the angle θ with the formula:

11 meters = θ(42 cm)

Converting the length of the arm to meters:

42 cm = 0.42 meters

Therefore, the angle θ is:

θ = 11 / 0.42 ≈ 26.19 radians

Finally, we can calculate the distance the hand of the winder travels:

Arc length = 26.19 * 0.42 ≈ 11 meters

So, when bringing the bucket up from the bottom, the hand of the winder travels approximately 11 meters.