To find the minimum effort required to raise the load using a block tackle, we need to consider the efficiency and the velocity ratio.
Efficiency (η) is defined as the ratio of useful work output to the total work input. In this case, the efficiency is given as 80%, which can be expressed as 0.8.
The velocity ratio (VR) is the ratio of the distance moved by the effort to the distance moved by the load. In this case, the velocity ratio is given as 4.
To calculate the minimum effort required, we can use the formula:
Effort × Distance moved by effort = Load × Distance moved by load
Let's assume the distance moved by the effort and the load is the same, denoted by 'd'. The load is given as 50 kg.
From the velocity ratio definition, we know that:
Distance moved by effort = VR × d Distance moved by load = d
Using the given efficiency, we can rewrite the formula as:
Effort × (VR × d) = Load × d × η
Substituting the values, we have:
Effort × 4d = 50 kg × d × 0.8
Simplifying the equation, we get:
4Effort = 40 kg
Dividing both sides by 4, we find:
Effort = 10 kg
Therefore, the minimum effort required to raise the load is 10 kg.