A machine has a velocity ratio of 6and an efficiency of 80 efficiency calculate the effort needed to raise a load of 90N
Efficiency is calculated using the formula: efficiency = (output work / input work) * 100
Since the machine has an efficiency of 80%, we can set up the equation as follows:
80 = (output work / input work) * 100
To find the effort needed, we can rearrange the equation:
output work / input work = 80 / 100
Simplifying the equation:
output work / input work = 0.8
The velocity ratio of the machine is 6. This means that for every 1 unit of input distance, the machine moves the load 6 units of output distance.
We can use the formula for velocity ratio: velocity ratio = output distance / input distance
To find the input distance, we can rearrange the equation:
input distance = output distance / velocity ratio
Since the output distance is the input distance multiplied by the velocity ratio, we can substitute this into the efficiency equation as follows:
(output work / (output distance / velocity ratio)) = 0.8
Simplifying the equation:
(output work * velocity ratio) / output distance = 0.8
Given that the load is 90N, we can substitute this into the equation as the output work and 90 / output distance is equal to the load.
(90 * velocity ratio) / output distance = 0.8
Substituting the velocity ratio of 6, we get:
(90 * 6) / output distance = 0.8
540 / output distance = 0.8
To find the output distance, we can rearrange the equation:
output distance = 540 / 0.8
Simplifying the equation:
output distance = 675
Now that we have the output distance, we can use the velocity ratio to find the input distance:
input distance = output distance / velocity ratio
input distance = 675 / 6
input distance = 112.5
The effort needed to raise a load of 90N is equal to the input force. Since force = load / velocity ratio, we can calculate the effort as follows:
effort = load / velocity ratio
effort = 90 / 6
effort = 15N
Therefore, the effort needed to raise a load of 90N is 15N.
To solve this problem, we need to use the formula for calculating effort (E) based on the load (L), velocity ratio (VR), and efficiency (η):
Effort (E) = Load (L) / (velocity ratio * efficiency)
Given:
Load (L) = 90N
Velocity ratio (VR) = 6
Efficiency (η) = 80% or 0.8 (in decimal form)
Plugging in the values into the formula:
Effort (E) = 90N / (6 * 0.8)
Effort (E) = 90N / 4.8
Effort (E) = 18.75N
Therefore, the effort needed to raise a load of 90N is approximately 18.75N.