# Calculate the force to be applied, if a pulley system of an efficiency 80% and velocity ratio is 5 is used to lift a load of 200N.

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200/5 = 40N
40/0.80 = 50N

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## To calculate the force to be applied in a pulley system, we need to consider the efficiency and the velocity ratio of the system.

Step 1: Calculate the ideal mechanical advantage (IMA).
The ideal mechanical advantage (IMA) of a pulley system is equal to the number of supporting ropes or sections of rope that support the load.

In this case, the velocity ratio is given as 5, which means there are 5 sections of rope supporting the load. Therefore, the IMA is 5.

Step 2: Calculate the actual mechanical advantage (AMA) using the efficiency.
The actual mechanical advantage (AMA) takes into account the efficiency of the pulley system. It is calculated by dividing the IMA by the efficiency.

AMA = IMA / Efficiency

In this case, the efficiency is given as 80% or 0.8.

AMA = 5 / 0.8 = 6.25

Step 3: Calculate the force to be applied.
The force to be applied is equal to the load divided by the AMA.

Force to be applied = Load / AMA

In this case, the load is given as 200N.

Force to be applied = 200 / 6.25 ≈ 32N

So, the force to be applied to lift the load of 200N using the pulley system with an efficiency of 80% and a velocity ratio of 5 is approximately 32 Newtons.

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## To calculate the force to be applied, we need to understand the concepts of efficiency and velocity ratio in a pulley system.

Efficiency (η) is defined as the ratio of output work (Wo) to input work (Wi), expressed as a percentage:

Efficiency = (Wo / Wi) × 100%

The velocity ratio (VR) is defined as the ratio of the distance moved by the effort (De) to the distance moved by the load (Dl). In other words, it represents the mechanical advantage of the pulley system:

Velocity Ratio = De / Dl

Now, let's apply these concepts to solve the problem:

1. Calculate the input work (Wi):
The input work is equal to the product of the force (F) applied to the system and the distance moved by the effort (De):
Wi = F × De

2. Calculate the output work (Wo):
The output work is equal to the product of the force (F') needed to lift the load and the distance moved by the load (Dl):
Wo = F' × Dl

3. Calculate the efficiency (η):
The efficiency is given as 80% or 0.8 (80/100):
η = (Wo / Wi) × 100% = 0.8

4. Calculate the velocity ratio (VR):
The velocity ratio is given as 5:
VR = De / Dl = 5

5. Calculate the force to be applied (F):
We know that force (F') required to lift the load is equal to the weight of the load (Wl):
F' = Wl = 200N

Now, we can rearrange the efficiency equation to solve for the force (F):

η = (Wo / Wi) × 100%
0.8 = (F' × Dl) / (F × De) × 100%

Substitute the known values:
0.8 = (200N × Dl) / (F × De) × 100%

Simplify the equation:
0.8 = (2 × Dl) / (F × De)

Rearrange the equation to solve for F:
F = (2 × Dl) / (0.8 × De)

We know the velocity ratio (VR) is 5, so De = Dl × VR:
F = (2 × Dl) / (0.8 × Dl × VR)

Cancel out the common term (Dl):
F = 2 / (0.8 × VR)

Substitute the given velocity ratio (VR = 5):
F = 2 / (0.8 × 5)
F = 2 / 4
F = 0.5N

Therefore, the force to be applied to lift a load of 200N using a pulley system with an efficiency of 80% and a velocity ratio of 5 is 0.5N.