Calculation of Power Required for a Body Moving Up an Inclined Plane

Given parameters:
- Mass of the body (m) = 4 kg
- Inclined plane angle (θ) = 1/40
- Velocity of the body (v) = 40 m/s
- Efficiency (η) = 50%

Step 1: Calculation of the Inclined Plane Height
The height (h) of the inclined plane can be calculated using the formula:
h = (1/40) * L
where L is the distance covered by the body on the inclined plane.

Step 2: Calculation of the Distance Covered on the Inclined Plane
The distance covered by the body on the inclined plane can be calculated using the formula:
L = v^2 / 2gh
where g is the acceleration due to gravity (9.8 m/s^2).

Step 3: Calculation of the Power Required
The power (P) required to move the body up the inclined plane can be calculated using the formula:
P = mgh/t
where t is the time taken to cover the distance on the inclined plane.

Step 4: Calculation of the Time Taken to Cover the Distance
The time taken to cover the distance on the inclined plane can be calculated using the formula:
t = L/v

Step 5: Substitution of Values in the Formulas
Substituting the values in the above formulas, we get:
- h = (1/40) * L = (1/40) * (40^2 / 2 * 9.8) = 20 m
- L = v^2 / 2gh = 40^2 / 2 * 9.8 * 20 = 408.16 m
- t = L/v = 408.16 / 40 = 10.204 s
- P = mgh/t = 4 * 9.8 * 20 / 10.204 = 38.4 W

Answer: The power required to move the body up the inclined plane is 38.4 W.

Explanation: The power required to move the body up the inclined plane can be calculated using the formulas mentioned above. We need to calculate the height of the inclined plane, distance covered by the body on the inclined plane, time taken to cover the distance and finally the power required to move the body up the inclined plane. Substituting the given values in the formulas, we get the answer as 38.4 W.