How much work would it take to push a # 2 kg # weight up a # 6 m # plane that is at an incline of # pi / 3 #?

The net change in the object's potential energy equals the amount of work that has been done on it.

Using the work formula above, we can now obtain;

To calculate the work required to push the 2 kg weight up the 6 m plane at an incline of π/3 radians, you can use the formula:

Work = Force × Distance × cos(θ)

First, find the force required to overcome the gravitational force acting on the weight along the incline:

Force = Weight × sin(θ) = m × g × sin(θ)

Where: m = mass of the weight (2 kg) g = acceleration due to gravity (approximately 9.8 m/s²) θ = angle of the incline (π/3 radians)

Then, calculate the distance along the incline:

Distance = hypotenuse of the triangle = 6 m

Finally, calculate the work:

Work = Force × Distance × cos(θ)

The work done to push a 2 kg weight up a 6 m plane inclined at an angle of $\frac{\pi}{3}$ radians can be calculated using the formula:

$\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)$

Where:

• Force = $m \times g$, where $m$ is the mass and $g$ is the acceleration due to gravity (approximately $9.81 \, \text{m/s}^2$)
• Distance = 6 m (the length of the plane)
• $\theta$ = $\frac{\pi}{3}$ radians (the angle of incline)

Substitute the given values into the formula and calculate the work.