A machine has a velocity ratio of 6 and efficiency of 80%.What would be needed to lift a load of 80kg with the aid of the machine.
Answer
The aid of the machine is 4.80
To determine what would be needed to lift a load of 80 kg with the aid of the machine, we need to first understand the concepts of the "velocity ratio" and "efficiency" of the machine.
The velocity ratio (VR) is a measure of how much the machine amplifies the effort applied to it. It is calculated by dividing the distance the effort moves by the distance the load moves.
VR = distance moved by effort / distance moved by load
In this case, the velocity ratio is given as 6.
Efficiency (η) measures how well a machine converts input work into useful output work. It is expressed as a percentage and is calculated by dividing the useful output work by the input work and multiplying by 100.
Efficiency = (useful output work / input work) * 100
In this case, the efficiency is given as 80%.
Now, let's calculate what would be needed to lift the load of 80 kg with the aid of the machine.
1. First, determine the input work (Wi) required to lift the load.
Using the formula for work:
Work = Force * Distance
Wi = Force * Distance
Since we know the weight of the load is 80 kg, we can calculate the force needed to lift it using the formula:
Force = Mass * Gravity
Where gravity is approximately 9.8 m/s².
Force = 80 kg * 9.8 m/s² = 784 N
2. Next, we need to find the output work (Wo) done by the machine.
Output work (Wo) = input work (Wi) * efficiency (η)
Wo = Wi * η
Wo = 784 N * (80/100) = 627.2 N
3. Finally, we can calculate the distance the effort needs to move to lift the load.
Since the velocity ratio (VR) is the ratio of the distance moved by the effort to the distance moved by the load, we can calculate the distance moved by the effort using the formula:
Distance moved by effort = Distance moved by load / velocity ratio
Distance moved by effort = Unknown / 6
Since there is no specific distance mentioned for the load to move, we can assume it is a vertical lift. In that case, the distance moved by the load is the height it needs to be lifted.
Let's assume the height of the lift is h meters.
Thus,
Distance moved by effort = h / 6
Therefore, to lift the load of 80 kg with the machine:
- An input force of 784 N is required.
- The output work done by the machine is approximately 627.2 N.
- The distance the effort needs to move is h / 6, where h is the height of the lift.