An inclined plane is used to raise a 100 kg box to a height of 5 m. How long must the inclined plane be if a force of 250 N is used to push the box up the inclined plane?
you want a mechanical advantage of 100*9.8/250
MA= length/height = 9800/250
solve for lenght
To solve this problem, we need to apply the principles of work and energy.
First, let's recall the formula for work: work = force × distance × cos(θ), where θ is the angle between the force and the displacement.
In this case, the force is the force applied to push the box up the inclined plane, which is 250 N. The distance is the height the box has to be raised, which is 5 m. And since the inclined plane is at an angle, the angle between the force and the displacement is the angle of the inclined plane.
Now, let's calculate the angle of the inclined plane. The inclined plane forms a right triangle with the vertical line. The height is 5 m, and the length of the inclined plane is the hypotenuse of the triangle. Using the Pythagorean theorem, we can find the length of the inclined plane.
The formula for the Pythagorean theorem is a² + b² = c², where a and b are the two shorter sides of the right triangle, and c is the hypotenuse. In this case, a is the height (5 m), b is the length of the inclined plane, and c is the unknown hypotenuse.
So, the equation becomes 5² + b² = c².
Simplifying the equation, we have 25 + b² = c².
Now, we need to solve for b (the length of the inclined plane). Rearranging the equation, we have b² = c² - 25.
Taking the square root of both sides, we get b = √(c² - 25).
Now that we have the length of the inclined plane, we can calculate the work done to raise the box.
Using the work formula, work = force × distance × cos(θ), where force = 250 N, distance = 5 m, and θ is the angle of the inclined plane (which can be found by using sin⁻¹(a/c), where a is the height and c is the length of the inclined plane).
Let's calculate θ: θ = sin⁻¹(5/c).
Now, we can calculate the work: work = 250 N × 5 m × cos(θ).
Finally, to find the required length of the inclined plane, we need to solve for c in the equation b = √(c² - 25).
By substituting the resulting value of b and solving the equation, we can find the length of the inclined plane.