A pulley system used to lift a load of 9600N using an effort of 2400N through a vertical distance of 20m.1)calculate the mechanical advantage, 2) velocity ratio,3)what is the efficiency of the pulley system, 4) calculate the distance moved by the effort
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Answers
To calculate the requested values, we'll need to use the formulas related to pulley systems:
1) Mechanical Advantage (MA) = Load / Effort
2) Velocity Ratio (VR) = Distance moved by effort / Distance moved by load
3) Efficiency = (MA / VR) x 100
4) Distance moved by the effort = Load distance / Velocity Ratio
Let's calculate each step-by-step:
1) Mechanical Advantage (MA) = Load / Effort
MA = 9600N / 2400N
MA = 4
2) Velocity Ratio (VR) = Distance moved by effort / Distance moved by load
Since the effort and load both move through the same vertical distance of 20m, the VR will be equal to 1.
3) Efficiency = (MA / VR) x 100
Efficiency = (4 / 1) x 100
Efficiency = 400%
4) Distance moved by the effort = Load distance / Velocity Ratio
Distance moved by the effort = 20m / 1
Distance moved by the effort = 20m
To summarize:
1) Mechanical Advantage (MA) = 4
2) Velocity Ratio (VR) = 1
3) Efficiency = 400%
4) Distance moved by the effort = 20m
To answer these questions, we need to understand the concepts of mechanical advantage, velocity ratio, efficiency, and the work done by the effort.
1) Mechanical advantage:
The mechanical advantage (MA) of a pulley system is the ratio of the load (L) to the effort (E). It can be calculated using the formula: MA = L / E.
Given that the load (L) is 9600N and the effort (E) is 2400N, we can substitute these values into the formula:
MA = 9600N / 2400N = 4
So, the mechanical advantage of the pulley system is 4.
2) Velocity ratio:
The velocity ratio (VR) of a pulley system is the ratio of the distance moved by the effort to the distance moved by the load. In this case, since the load is being lifted vertically, the distance moved by the load and the effort is the same.
The velocity ratio can be calculated using the formula: VR = distance moved by effort / distance moved by load.
Given that the distance moved by the effort and load is 20m, we can substitute these values into the formula:
VR = 20m / 20m = 1
So, the velocity ratio of the pulley system is 1.
3) Efficiency:
Efficiency is a measure of how well a machine (in this case, the pulley system) converts input work to useful output work. It is expressed as a percentage.
The efficiency (EFF) can be calculated using the formula: EFF = (output work / input work) x 100.
In this case, the output work is the work done against the load, which is the load multiplied by the distance moved by the load. The input work is the effort multiplied by the distance moved by the effort.
Output work = load x distance moved by load = 9600N x 20m = 192000 Nm
Input work = effort x distance moved by effort = 2400N x 20m = 48000 Nm
Now we can calculate efficiency:
EFF = (192000 Nm / 48000 Nm) x 100 = 400%
So, the efficiency of the pulley system is 400%.
4) Distance moved by the effort:
The distance moved by the effort is given in the problem as 20m. Hence, the distance moved by the effort is 20m.