a simpe wheel and axle is used to lift bucket of water out of a well. the radii of the wheel and axle are 20 cm and 4 cm, respectively. Determine,
1, velocity ratio
2, theoretical effort required to lift load of 30 N assuming no energy losses
3, the efficiency if the actual effort required is 10 N.
1. 20/4 = 5
2. 30/5 = 6 Newtons
3. 6/10 = 0.60 so 60%
To solve this problem, we need to understand the principles of a wheel and axle and use the formulae associated with it. Let's break down each question step by step:
1. Velocity Ratio:
The velocity ratio is the ratio of the distance traveled by the effort to the distance traveled by the load. In the case of a simple wheel and axle, the velocity ratio can be determined using the formula:
Velocity Ratio = Radius of Wheel / Radius of Axle
Therefore, substituting the values given:
Velocity Ratio = 20 cm / 4 cm = 5
So, the velocity ratio is 5.
2. Theoretical Effort:
The theoretical effort required to lift the load can be calculated using the formula:
Theoretical Effort = Load / Velocity Ratio
Substituting the values given:
Theoretical Effort = 30 N / 5 = 6 N
Therefore, the theoretical effort required to lift a load of 30 N is 6 N.
3. Efficiency:
The efficiency of a simple machine is the ratio of the useful work output to the total work input. Mathematically, efficiency is expressed as:
Efficiency = (Useful Work Output / Total Work Input) * 100
In this case, the useful work output is the work done in lifting the load, and the total work input is the product of the actual effort required and the distance it is applied over.
Useful Work Output = Load * Distance Lifted
Total Work Input = Actual Effort * Distance Moved
Efficiency = (Useful Work Output / Total Work Input) * 100
Efficiency = (Load * Distance Lifted) / (Actual Effort * Distance Moved) * 100
Substituting the given values:
Efficiency = (30 N * Distance Lifted) / (10 N * Distance Moved) * 100
The efficiency would be determined based on the specific values provided for the distances lifted and moved.
Note: To complete the calculation for efficiency, we would need to know the specific distances involved in lifting the load and applying the effort.
To determine the values, we can use the formulas related to wheel and axle systems.
1. Velocity Ratio:
The velocity ratio (VR) can be calculated using the formula:
VR = radius of wheel / radius of axle
Given that the radius of the wheel is 20 cm and the radius of the axle is 4 cm, we can substitute the values:
VR = 20 cm / 4 cm
VR = 5
Therefore, the velocity ratio of the wheel and axle system is 5.
2. Theoretical Effort:
The theoretical effort required to lift a load (TE) can be determined using the formula:
TE = load / VR
Given that the load is 30 N and the velocity ratio is 5, we can substitute the values:
TE = 30 N / 5
TE = 6 N
Therefore, the theoretical effort required to lift a load of 30 N is 6 N.
3. Efficiency:
Efficiency (E) of a machine can be calculated using the formula:
E = (MA / VR) * 100
Given that the actual effort required (AE) is 10 N, the mechanical advantage (MA) can be calculated using the formula:
MA = load / AE
Substituting the values:
MA = 30 N / 10 N
MA = 3
Using the calculated MA value and the previously calculated VR value of 5, we can calculate the efficiency:
E = (3 / 5) * 100
E = 60%
Therefore, the efficiency of the wheel and axle system is 60%.