How much work would it take to push a # 9 kg # weight up a # 2 m # plane that is at an incline of # pi / 6 #?

Question

How much work would it take to push a #   9  kg  # weight up a # 2 m # plane that is at an incline of #  pi  /  6 #?

Amelia Adams · Accepted Answer

#E_p=88,29" "J#

#E_p=m*g*h=9*9,81*1#
#E_p=88,29" "J#

Benjamin Asiedu · Answer

undefined To calculate the work done to push a 9 kg weight up a 2 m plane at an incline of π/6, we can use the equation for work done against gravity:

$$ W = F \cdot d \cdot \cos(\theta) $$

Where:
- $ W $ is the work done
- $ F $ is the force applied
- $ d $ is the distance along the plane
- $ \theta $ is the angle of the incline

First, let's find the force applied. The force acting against gravity can be calculated using the weight of the object:

$$ F = m \cdot g \cdot \sin(\theta) $$

Where:
- $ m $ is the mass of the object
- $ g $ is the acceleration due to gravity
- $ \theta $ is the angle of the incline

Given:
- $ m = 9 \, kg $
- $ g = 9.8 \, m/s^2 $
- $ \theta = \frac{\pi}{6} $

$$ F = 9 \, kg \cdot 9.8 \, m/s^2 \cdot \sin\left(\frac{\pi}{6}\right) $$
$$ F = 9 \cdot 9.8 \cdot \frac{1}{2} $$
$$ F = 44.1 \, N $$

Now, we can calculate the work done:

$$ W = 44.1 \, N \cdot 2 \, m \cdot \cos\left(\frac{\pi}{6}\right) $$
$$ W = 44.1 \cdot 2 \cdot \frac{\sqrt{3}}{2} $$
$$ W = 44.1 \cdot \sqrt{3} $$
$$ W \approx 76.27 \, J $$

So, it would take approximately 76.27 joules of work to push the 9 kg weight up the 2 m plane at an incline of π/6.