Step-by-step explanation:
To determine the effort needed to lift a load of 200N, given a velocity ratio of 5 and an efficiency of 80%, we can use the formula:
Efficiency = (Output Work / Input Work) * 100
Efficiency can also be calculated as the ratio of the output force to the input force. In this case, the output force is the load being lifted (200N), and the input force is the effort required.
Given that the velocity ratio is 5, it means that for every 5 units of distance the effort moves, the load moves 1 unit of distance. This implies that the effort is exerted over a greater distance than the load.
Let's denote the effort force as "E" and the distance moved by the effort as "dE." Similarly, the load force is "L," and the distance moved by the load is "dL."
Using the velocity ratio, we have the following relationship:
dE / dL = 5
Now, we can calculate the input work (Wi) and the output work (Wo):
Input Work (Wi) = Effort (E) * Distance moved by the effort (dE)
Output Work (Wo) = Load (L) * Distance moved by the load (dL)
Given that the efficiency is 80%, we can rewrite the formula for efficiency as:
0.80 = (Wo / Wi) * 100
Now, let's solve for the effort (E) using the given values:
Load (L) = 200N
Efficiency = 0.80
Velocity Ratio = 5
First, calculate the output work (Wo):
Wo = Load (L) * Distance moved by the load (dL)
Since the velocity ratio is 5, the distance moved by the load (dL) will be 1/5 of the distance moved by the effort (dE):
dL = (1/5) * dE
Wo = L * (1/5) * dE
Wo = 200N * (1/5) * dE
Wo = 40N * dE
Next, calculate the input work (Wi):
Wi = Effort (E) * Distance moved by the effort (dE)
Wi = E * dE
Now, substitute the values into the efficiency formula:
0.80 = (Wo / Wi) * 100
0.80 = (40N * dE) / (E * dE) * 100
0.80 = 40 / E * 100
0.80 * E = 40
E = 40 / 0.80
E = 50N
Therefore, the effort needed to lift a load of 200N with a velocity ratio of 5 and an efficiency of 80% is 50N.