How much work would it take to push a # 1 kg # weight up a # 1 m # plane that is at an incline of # pi / 4 #?

The gain in potential energy equals the work required to push the object up the plane.

The plane's height is

Potential energy is

To calculate the work required to push the 1 kg weight up a 1 m plane at an incline of π/4, you can use the formula:

Work = Force × Distance

First, determine the force required to overcome gravity acting on the weight along the incline. The force can be calculated using the component of the weight parallel to the incline:

Force = Weight × sin(θ)

Where θ is the angle of the incline (π/4 in this case), and the weight is the mass multiplied by the acceleration due to gravity (9.8 m/s^2).

Then, calculate the distance along the incline, which is the hypotenuse of the right triangle formed by the incline and the horizontal surface:

Distance = hypotenuse = 1 m

Plug the values into the formula to find the work:

Work = Force × Distance

Work = (Weight × sin(θ)) × Distance

Work = (1 kg × 9.8 m/s^2 × sin(π/4)) × 1 m

After calculating this expression, you will get the work required to push the 1 kg weight up the 1 m incline.