How much work would it take to push a # 25 kg # weight up a # 15 m # plane that is at an incline of # pi / 6 #?

Question

How much work would it take to push a #   25  kg  # weight up a # 15 m # plane that is at an incline of #  pi  /  6 #?

Benjamin Asiedu · Accepted Answer

#1800 "J"#

Let's look at the situation in terms of energy. At the bottom of the incline, the weight has zero potential energy. At the top, the weight will have gravitational potential energy #mgh#.

Assuming we have a fairly greasy weight or surface (such that friction is negligible) we can state that the work done by you in pushing the weight up the incline will be converted entirely into gravitational potential energy.

#mgh = 25 "kg" * 9.81 m/s^2 * 15 m * sin(pi/6) = 1839.375 "J"#

Considering that we should only have two significant digits our final answer will be

#1800 "J"#

Olivia Askew · Answer

undefined To calculate the work required to push a 25 kg weight up a 15 m plane at an incline of π/6, you can use the formula for work done against gravity on an inclined plane:

Work = force × distance × cos(angle)

First, find the force parallel to the incline, which is the weight of the object times the sine of the angle of inclination:

Force_parallel = weight × sin(angle)

Next, find the work done by multiplying the force parallel to the incline by the distance along the incline:

Work = Force_parallel × distance

Substitute the values given:

Force_parallel = 25 kg × 9.8 m/s² × sin(π/6)
Force_parallel ≈ 25 kg × 9.8 m/s² × 0.5
Force_parallel ≈ 122.5 N

Work = 122.5 N × 15 m × cos(π/6)
Work ≈ 122.5 N × 15 m × 0.866
Work ≈ 1584.75 J

So, it would take approximately 1584.75 Joules of work to push the 25 kg weight up the 15 m plane at an incline of π/6 radians.