A block and tackle system of pulley s consisting of four pulleys used to raise a load of 800N through a height of 20m . if the total work done against friction in the pulley is equivalent to 800, calculate (a) total work done by the effort (b) efficiency of the system (c)
effort applied
To calculate the total work done by the effort and the efficiency of the system, we'll need to consider the principles of work, mechanical advantage, and efficiency.
First, let's calculate the work done against friction in the pulley system. We are given that the work done against friction is equivalent to 800 Joules.
Work is calculated as the product of force and distance, so the work done against friction can be represented as:
Work against friction = Force against friction x Distance = 800 J
Next, let's calculate the mechanical advantage (MA) of the system. The mechanical advantage of a pulley system is determined by the number of supporting ropes. In this case, we have four pulleys, so the MA is 4.
Mechanical Advantage (MA) = 4
Now, we can calculate the total work done by the effort (W):
Total Work = Force x Distance
Given that the load being raised is 800 N and the distance is 20 m, we can use the formula:
Total Work = Load x Distance = 800 N x 20 m
Total Work = 16,000 Joules
Therefore, the total work done by the effort is 16,000 Joules (W = 16,000 J).
Next, let's calculate the efficiency of the system:
Efficiency (η) = Output work / Input work
Since the input work is the total work done by the effort (16,000 J) and the output work is the work done against friction (800 J):
Efficiency (η) = 800 J / 16,000 J = 0.05
The efficiency of the system is 0.05, which is equivalent to 5% efficiency.
Finally, to calculate the effort applied, we can use the formula:
Effort = Load/ Mechanical Advantage
In this case, the load is 800 N, and the mechanical advantage is 4:
Effort = 800 N / 4 = 200 N
Therefore, the effort applied is 200 Newtons.