To determine the mechanical advantage (MA) of moving a 5 g box up a 25° incline, you can use the concept of mechanical advantage related to inclined planes. The mechanical advantage of an inclined plane is given by the formula:
[tex]\[ \text{MA} = \frac{1}{\sin(\theta)} \][/tex]
where [tex]\(\theta\)[/tex] is the angle of the incline in degrees.
Let's go step-by-step through this calculation:
1. Identify the angle of the incline: The angle [tex]\(\theta\)[/tex] given is 25°.
2. Convert the angle from degrees to radians: Since trigonometric functions in many contexts (including manual calculations) use radians, we need to convert the angle from degrees to radians. Noting that π radians is equivalent to 180 degrees, the conversion is performed using the equation:
[tex]\[ \theta_\text{radians} = \theta_\text{degrees} \times \frac{\pi}{180} \][/tex]
3. Calculate the sine of the angle in radians: Using the angle in radians, compute the sine of the angle.
4. Find the mechanical advantage (MA): Substitute the sine value into the mechanical advantage formula.
Let’s summarize the process:
- The angle is 25°.
- Converting 25° to radians:
[tex]\[ 25° \times \frac{\pi}{180} \approx 0.43633 \text{ radians} \][/tex]
- Next, take the sine of this angle:
[tex]\[ \sin(0.43633) \approx 0.4226 \][/tex]
- Finally, calculate the mechanical advantage:
[tex]\[ \text{MA} = \frac{1}{0.4226} \approx 2.366 \][/tex]
Thus, the mechanical advantage of moving a 5 g box up a 25° incline is approximately:
[tex]\[ 2.366 \][/tex]
Therefore, the mechanical advantage for this scenario is about 2.366.
