To calculate the Mechanical Advantage (MA), Velocity Ratio (VR), and efficiency of an inclined plane, let's work through each step:
### Given:
- Height (h) = 8 meters
- Length (l) = 32 meters
- Load (L) = 1200 N
- Effort (E) = 400 N
### Step-by-Step Solution
#### Step 1: Calculate the Mechanical Advantage (MA)
Mechanical Advantage is the ratio of the load to the effort.
[tex]\[ MA = \frac{\text{Load}}{\text{Effort}} \][/tex]
Substituting the given values:
[tex]\[ MA = \frac{1200 \, \text{N}}{400 \, \text{N}} = 3.0 \][/tex]
#### Step 2: Calculate the Velocity Ratio (VR)
Velocity Ratio is the ratio of the length of the inclined plane to its height.
[tex]\[ VR = \frac{\text{Length}}{\text{Height}} \][/tex]
Substituting the given values:
[tex]\[ VR = \frac{32 \, \text{m}}{8 \, \text{m}} = 4.0 \][/tex]
#### Step 3: Calculate the Efficiency
Efficiency can be determined using the Mechanical Advantage and Velocity Ratio. It is given by the formula:
[tex]\[ \text{Efficiency} (\%) = \left( \frac{MA}{VR} \right) \times 100 \][/tex]
Substituting the values from the previous steps:
[tex]\[ \text{Efficiency} (\%) = \left( \frac{3.0}{4.0} \right) \times 100 = 75.0 \% \][/tex]
### Summary of Results
- Mechanical Advantage (MA): 3.0
- Velocity Ratio (VR): 4.0
- Efficiency: 75.0%
Thus, the Mechanical Advantage of the inclined plane is 3.0, the Velocity Ratio is 4.0, and the efficiency is 75.0%.
