find the mechanical advantage and hence the effort if the efficiency is 75%.a pulley system having 5 pulley is used to raise a 450N load
5 pulleys means a 5:1 mechanical advantage
effort = (load / mechanical advantage) / efficiency
To find the mechanical advantage and the effort when the efficiency is 75% and a pulley system with 5 pulleys is used to raise a 450N load, we need to apply the formulas for mechanical advantage, efficiency, and load.
First, let's define the variables:
Load (L) = 450N
Efficiency (η) = 75% = 0.75
Number of pulleys (Np) = 5
Mechanical Advantage (MA) is calculated using the formula:
MA = (Load / Effort)
Efficiency (η) is calculated using the formula:
η = (Output Work / Input Work) x 100
In this case, the Load is providing the Output Work, and the Effort applied is providing the Input Work. Since the Load and Effort are related to the mechanical advantage, we can rearrange the formulas to find the Effort.
Rearranging the efficiency formula:
Efficiency (η) = (Output Work / Input Work) x 100
Efficiency (η) = (Load x Load Distance) / (Effort x Effort Distance) x 100
Since the Load Distance is not given, we can assume it is equal to the Effort Distance.
Now, let's calculate the mechanical advantage:
MA = (Load / Effort)
MA = (450N / Effort)
To find the Effort, we need to calculate the Load Distance (LD) and Effort Distance (ED).
Since we know that the number of pulleys (Np) is 5 and assuming there are no frictional losses, we can apply the formula for the mechanical advantage of a pulley system:
Mechanical Advantage (MA) of pulley system = 2^Np
Substituting the value of Np:
MA = 2^5
MA = 32
Now we can find the Load Distance (LD) and Effort Distance (ED):
LD = (MA / (MA + 1)) x Effort Distance
ED = Effort Distance
Given that LD = ED:
LD = (MA / (MA + 1)) x LD
1 = (MA / (MA + 1))
Now we can calculate the Effort using the efficiency formula:
η = (Load x Load Distance) / (Effort x Effort Distance) x 100
0.75 = (450N x LD) / (Effort x ED) x 100
0.75 = (450N x LD) / (Effort x LD) x 100
0.75 = 450N / Effort x 100
0.0075 x Effort = 450N
Effort = 450N / 0.0075
Effort = 60000N
Therefore, the mechanical advantage of the pulley system is 32, and the effort required is 60000N.