To resolve this problem, we need to find the load that an applied force of 1200 N can lift using a wheel and axle with given radii and efficiency. Here is the step-by-step calculation process:
1. Determine the mechanical advantage (MA):
- Mechanical advantage (MA) is the ratio of the radius of the wheel to the radius of the axle.
- Formula: [tex]\[ MA = \frac{\text{radius of wheel}}{\text{radius of axle}} \][/tex]
- Substituting the given values:
[tex]\[ \text{radius of wheel} = 80 \; \text{cm} \][/tex]
[tex]\[ \text{radius of axle} = 10 \; \text{cm} \][/tex]
[tex]\[ MA = \frac{80 \; \text{cm}}{10 \; \text{cm}} = 8 \][/tex]
2. Calculate the theoretical load:
- The theoretical load is the load that can be lifted without taking the efficiency into account.
- Formula: [tex]\[ \text{Theoretical Load} = \text{Applied Force} \times MA \][/tex]
- Substituting the given values:
[tex]\[ \text{Applied Force} = 1200 \; \text{N} \][/tex]
[tex]\[ \text{Theoretical Load} = 1200 \; \text{N} \times 8 = 9600 \; \text{N} \][/tex]
3. Calculate the actual load considering the efficiency:
- The actual load considers the efficiency of the machine.
- Formula: [tex]\[ \text{Actual Load} = \text{Theoretical Load} \times \text{Efficiency} \][/tex]
- Substituting the given values:
[tex]\[ \text{Efficiency} = 0.85 \][/tex]
[tex]\[ \text{Actual Load} = 9600 \; \text{N} \times 0.85 = 8160 \; \text{N} \][/tex]
Therefore, with the given conditions, an applied force of 1200 N to the wheel will raise a load of 8160 N.
