I want to lift a 90kg box using an inclined plane, but I only have 30kg of strength. What does the length and height of the inclined plane need to be?

To determine the length and height of the inclined plane required to lift a 90kg box using your 30kg of strength, we can use the concept of mechanical advantage. Mechanical advantage is the ratio of the output force (the force you exert to lift the box) to the input force (your strength).

In this scenario, the output force is the weight of the box (90kg) and the input force is your strength (30kg). Therefore, the mechanical advantage can be calculated as:

Mechanical Advantage = Output Force / Input Force = Weight of the Box / Your Strength

Mechanical Advantage = 90kg / 30kg = 3

The mechanical advantage of an inclined plane is given by the formula:

Mechanical Advantage = Length of Inclined Plane / Height of Inclined Plane

Since we know that the mechanical advantage is 3, we can set up the equation:

3 = Length of Inclined Plane / Height of Inclined Plane

Now, we need to consider the specific angle of the inclined plane. Let's assume the angle is θ. The height of the inclined plane can be represented as Height = Length * sin(θ).

Substituting this expression into the mechanical advantage equation, we have:

3 = Length of Inclined Plane / (Length * sin(θ))

By rearranging the equation, we get:

3 = 1 / sin(θ)

To solve for θ, we can take the inverse sine (also known as arcsin) of both sides:

θ = arcsin(1/3)

Now that we know the angle θ, we can calculate the length and height of the inclined plane.

Please note that the range of arcsin is limited to -π/2 to π/2, meaning it only provides one of the possible angles. To find the other angles, subtract the value obtained from π.

Once you have the angle, you can determine the length and height based on your preferences and the available space.