Three men using efforts of 600N 500N and 400N respectively push a drum of 240kg up an inclined plane whose angle of inclination is 30° calculate briefly and give answer to the question what is the efficiency of the plane
The efficiency of the plane can be calculated by comparing the work done by the plane to the work done by the three men.
Work = Force x Distance x cos(angle)
The work done by the plane would be the force of gravity acting on the drum (Weight) multiplied by the distance:
Work_plane = Weight x Distance_plane x cos(30°).
The work done by each man can be calculated as:
Work_man1 = Force_man1 x Distance_man1 x cos(30°)
Work_man2 = Force_man2 x Distance_man2 x cos(30°)
Work_man3 = Force_man3 x Distance_man3 x cos(30°)
The total work done by the three men would be the sum of their individual works:
Total_work_men = Work_man1 + Work_man2 + Work_man3
The efficiency of the plane is given by:
Efficiency = (Work_plane / Total_work_men) x 100
Plug in the given values and calculate to find the efficiency of the plane.
To calculate the efficiency of the inclined plane, we need to first determine the work done by the men and then calculate the input work and output work of the plane.
1. Calculate the work done by each man:
Work = force x distance
For the first man:
Force = 600 N
Distance = ?
Since the plane is inclined, we need to consider the vertical distance.
Vertical Distance = 240 kg x 9.8 m/s^2 x sin(30°) = 1176 J
Distance = Vertical Distance / sin(30°)
Distance = 1176 J / sin(30°)
For the second man:
Force = 500 N
Distance = ?
Vertical Distance = 240 kg x 9.8 m/s^2 x sin(30°) = 1176 J
Distance = Vertical Distance / sin(30°)
Distance = 1176 J / sin(30°)
For the third man:
Force = 400 N
Distance = ?
Vertical Distance = 240 kg x 9.8 m/s^2 x sin(30°) = 1176 J
Distance = Vertical Distance / sin(30°)
Distance = 1176 J / sin(30°)
2. Calculate the total work done by the men:
Total Work = Work1 + Work2 + Work3
3. Calculate the input work (W_in) of the inclined plane:
W_in = Total Work
4. Calculate the output work (W_out) of the inclined plane:
W_out = Weight x Distance
Weight = 240 kg x 9.8 m/s^2 = 2352 N
Distance = Horizontal Distance x cos(30°) = (Vertical Distance / sin(30°)) x cos(30°)
5. Calculate the efficiency (η) of the inclined plane:
Efficiency (η) = (W_out / W_in) x 100
Now, by plugging in the values, you can calculate the efficiency of the inclined plane.