a pulley system having 5 pulleys is used to raise a 450N load. find the mechanical advantage and hence the effort if the efficiency is 75%
5 pulleys means 4 lines lifting the load ... a 4:1 mechanical advantage
ideally , the effort is ... 450N / 4
with 75% efficiency ... 450N / (4 * .75)
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Answer
Well, let's analyze the situation. If we have a pulley system with 5 pulleys, we need to consider the mechanical advantage it provides.
Each pulley contributes a mechanical advantage of 2, so with 5 pulleys, we have a total mechanical advantage of 2^5, which is 32.
Now, if the efficiency is 75%, it means that 75% of the input work is transformed into useful output work. So, the effort can be calculated as the load divided by the mechanical advantage multiplied by the efficiency.
Effort = (load / mechanical advantage) * efficiency
Effort = (450N / 32) * 0.75
Effort ≈ 8.83N
Therefore, the effort required to raise the load would be approximately 8.83 Newtons. But hey, don't worry! With this pulley system, you'll be lifting things like a superhero! Well, maybe not exactly like a superhero, but you get the idea.
To find the mechanical advantage of the pulley system, you need to count the number of ropes supporting the load. Each pulley increases the number of ropes supporting the load by a factor of 2. In this case, there are 5 pulleys, so the mechanical advantage is 2^5 = 32.
The mechanical advantage (MA) is calculated using the formula:
MA = Load (L) / Effort (E)
To find the effort, we rearrange the formula:
E = L / MA
Given that the load (L) is 450N and the efficiency is 75% (0.75), we can plug in these values to find the effort:
E = 450N / 32 = 14.06N
Therefore, the effort required to raise the load is approximately 14.06N.