Three men using efforts of 600N 500N & 400N respectively push a drum up an inclined plane whose angle of inclination is 30° briefly calculate the efficiency of the plane
To calculate the efficiency of the inclined plane, we first need to find the work done by the men and the work done against gravity.
The work done by a force can be calculated using the formula:
Work = Force x Distance x cos(theta)
Where:
Force: The applied force on the drum
Distance: The distance covered along the inclined plane
theta: The angle between the direction of force and the direction of motion (in this case, 30°)
First, let's calculate the work done by each man:
Man 1:
Force = 600N
Distance = Hypotenuse of the inclined plane = √(height^2 + base^2)
= √(1^2 + 2^2) = √5
Work = 600N x √5 x cos(30°) = 600√15 J
Man 2:
Force = 500N
Distance = √5
Work = 500N x √5 x cos(30°) = 500√15 J
Man 3:
Force = 400N
Distance = √5
Work = 400N x √5 x cos(30°) = 400√15 J
The total work done by the men is:
Total work = 600√15 J + 500√15 J + 400√15 J = 1500√15 J
Now, let's calculate the work done against gravity:
Work against gravity = Weight x Distance x cos(theta)
Weight = mass x gravity
Since mass is not provided, we can assume a standard value, let's say 10 kg.
Weight = 10 kg x 9.8 m/s^2 = 98 N
Distance = √5
Work against gravity = 98N x √5 x cos(30°) = 98√15 J
Finally, we can calculate the efficiency of the inclined plane using the formula:
Efficiency = (Work done by the men / Total work) x 100
Efficiency = (1500√15 J / (1500√15 J + 98√15 J)) x 100 = (1500 / (1500 + 98)) x 100 = (1500 / 1598) x 100 ≈ 93.87%
Therefore, the efficiency of the inclined plane is approximately 93.87%.
To calculate the efficiency of the plane, we need to use the formula:
Efficiency = (output work / input work) * 100%
First, let's find the input work.
Input work = force * distance
The input work is the sum of the work done by the three men, so we add up their individual work:
Input work = (600N * distance) + (500N * distance) + (400N * distance)
Next, let's find the output work.
Output work = force * distance * cosine(angle)
The output work is the force required to move the drum up the inclined plane, which is equal to the sum of the three forces acting on the drum.
Output work = (600N + 500N + 400N) * distance * cosine(30°)
Now we can calculate the efficiency:
Efficiency = (Output work / Input work) * 100%
Efficiency = ((600N + 500N + 400N) * distance * cosine(30°)) / ((600N * distance) + (500N * distance) + (400N * distance)) * 100%