A bucket of weight 72 N is lifted from a well by the wheel and axle system shown below:
If the diameter of the circle of the crank handle (diameter of the wheel) is 120 cm and the diameter of the shaft that the rope is wrapped around (diameter of the axle) is 10 cm,
What is the mechanical advantage of this machine?
What effort would be required to lift the bucket out of the well?
Over what distance would the handle of the crank have to be turned in order for the bucket to be lifted 6 m out of the well?
If an effort of 200 N is the largest that could be exerted in turning the handle, what would be the largest weight that could be lifted out of the well?
MA=120/10
effort= 72/MA
distance= 6m*MA
max lift= 200*MA
To find the mechanical advantage of the wheel and axle system, we need to calculate the ratio of the radius of the wheel (crank handle) to the radius of the axle.
The radius of the wheel is half the diameter, so the radius of the wheel (r1) is 120 cm / 2 = 60 cm = 0.6 m.
The radius of the axle is half the diameter, so the radius of the axle (r2) is 10 cm / 2 = 5 cm = 0.05 m.
The mechanical advantage (MA) is calculated by dividing the radius of the wheel by the radius of the axle: MA = r1 / r2.
In this case, MA = 0.6 m / 0.05 m = 12.
So, the mechanical advantage of this machine is 12.
To find the effort required to lift the bucket out of the well, we need to divide the weight of the bucket by the mechanical advantage. The weight of the bucket is given as 72 N.
Effort = Weight / Mechanical Advantage.
Effort = 72 N / 12 = 6 N.
Therefore, an effort of 6 N would be required to lift the bucket out of the well.
To determine the distance the handle of the crank would have to be turned to lift the bucket 6 m out of the well, we need to use the formula:
Effort × Distance of effort = Load × Distance of load.
We know the Effort (6 N), the Load (72 N), and the Distance of load (6 m).
6 N × Distance of effort = 72 N × 6 m.
Therefore, Distance of effort = (72 N × 6 m) / 6 N.
Distance of effort = 72 m.
So, the handle of the crank would have to be turned a distance of 72 m to lift the bucket 6 m out of the well.
If the largest effort that can be exerted is 200 N, we need to calculate the largest weight that can be lifted using the formula:
Effort × Distance of effort = Load × Distance of load.
In this case, Effort = 200 N, Distance of effort = ?, Load = ?, Distance of load = ?
We need to find the Load.
200 N × Distance of effort = Load × Distance of load.
Dividing both sides of the equation by Distance of load, we get:
Load = (200 N × Distance of effort) / Distance of load.
Since we don't have the value of the Distance of load, we cannot calculate the largest weight that can be lifted without further information.