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 #?

Question

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 #?

Olivia Askew · Accepted Answer

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

#W = Delta U = mg Delta h#

Where #m# is the mass of the object, #g# is the acceleration due to gravity, and #Delta h# is the final height of the object. Notice that only the change in height matters, not the entire distance that the object travels. Since the plane is at an angle we can find the vertical component of the objects displacement using the #sin# function.

#Delta h = (6"m")sin(pi/3)#

# = 2sqrt3 "m"#

Using the work formula above, we can now obtain;

#W = (2 " kg")(9.8 " ms"^-2)(2sqrt3 " m")#

#=67.9 " J"#

Nathan Ashcroft · Answer

undefined 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)

Sebastian Acosta · Answer

undefined 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.