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%.
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
1 answer