Question

A plane inclined at an angle theta with the horizontals is used to overcome a load of 500 Newton by applying an effort of 200 Newton if the efficiency is 80% calculate the theta

Answer 1

To determine the angle \(\theta\) of the inclined plane, we can use the relationship between load, effort, efficiency, and the mechanical advantage (MA).

1. **Mechanical Advantage (MA)**:
\[
\text{Efficiency} = \frac{\text{MA}}{\text{Velocity Ratio (VR)}}
\]
Knowing the efficiency is 80%, we express it as a decimal:
\[
\text{Efficiency} = 0.8
\]

2. **Expressing MA**:
The mechanical advantage can be defined as:
\[
\text{MA} = \frac{\text{Load}}{\text{Effort}} = \frac{500 \, \text{N}}{200 \, \text{N}} = 2.5
\]

3. **Calculating the Velocity Ratio (VR)**:
Rearranging the efficiency formula, we have:
\[
\text{MA} = \text{Efficiency} \times \text{VR}
\]
Thus,
\[
\text{VR} = \frac{\text{MA}}{\text{Efficiency}} = \frac{2.5}{0.8} = 3.125
\]

4. **Finding the Angle \(\theta\)**:
The Velocity Ratio for an inclined plane is given by:
\[
\text{VR} = \frac{1}{\sin(\theta)}
\]
Therefore,
\[
\sin(\theta) = \frac{1}{\text{VR}} = \frac{1}{3.125}
\]
\[
\sin(\theta) ≈ 0.32
\]

5. **Calculating \(\theta\)**:
Now, to find \(\theta\), we take the inverse sine (arcsin):
\[
\theta ≈ \arcsin(0.32)
\]
Using a calculator, we find:
\[
\theta ≈ 18.75^\circ
\]

Thus, the angle \(\theta\) of the inclined plane is approximately **18.75 degrees**.