Expand your horizons with the diverse and informative answers found on IDNLearn.com. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.
Sagot :
To solve for the [tex]\( y \)[/tex]-component of the weight of a 150 kg crate on a ramp inclined at [tex]\( 18.0^\circ \)[/tex], let's follow these steps:
1. Calculate the weight of the crate:
- The weight ([tex]\( w \)[/tex]) is determined by the mass ([tex]\( m \)[/tex]) and gravitational acceleration ([tex]\( g \)[/tex]).
- Given: [tex]\( m = 150 \)[/tex] kg and [tex]\( g = 9.81 \)[/tex] m/s[tex]\(^2\)[/tex].
Formula for weight:
[tex]\[ w = m \cdot g \][/tex]
Substituting the given values:
[tex]\[ w = 150 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1471.5 \, \text{N} \][/tex]
2. Convert the angle to radians:
- The angle given is [tex]\( 18.0^\circ \)[/tex].
- We convert degrees to radians using the formula:
[tex]\[ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) \][/tex]
Substituting the given angle:
[tex]\[ \text{radians} = 18.0 \times \left( \frac{\pi}{180} \right) = 0.3141592653589793 \, \text{radians} \][/tex]
3. Calculate the [tex]\( y \)[/tex]-component of the weight:
- The [tex]\( y \)[/tex]-component of the weight ([tex]\( w_y \)[/tex]) is found by multiplying the weight by the sine of the angle in radians.
Formula for the [tex]\( y \)[/tex]-component of the weight:
[tex]\[ w_y = w \cdot \sin(\text{angle in radians}) \][/tex]
Substituting the given values:
[tex]\[ w_y = 1471.5 \, \text{N} \times \sin(0.3141592653589793) \][/tex]
- Using a calculator to find the sine value (assuming a pre-calculated value):
[tex]\[ w_y = 1471.5 \, \text{N} \times 0.30901699437494745 = 454.71850722273507 \, \text{N} \][/tex]
So, the [tex]\( y \)[/tex]-component of the weight of the crate is approximately:
[tex]\[ w_y = 454.72 \, \text{N} \][/tex]
1. Calculate the weight of the crate:
- The weight ([tex]\( w \)[/tex]) is determined by the mass ([tex]\( m \)[/tex]) and gravitational acceleration ([tex]\( g \)[/tex]).
- Given: [tex]\( m = 150 \)[/tex] kg and [tex]\( g = 9.81 \)[/tex] m/s[tex]\(^2\)[/tex].
Formula for weight:
[tex]\[ w = m \cdot g \][/tex]
Substituting the given values:
[tex]\[ w = 150 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1471.5 \, \text{N} \][/tex]
2. Convert the angle to radians:
- The angle given is [tex]\( 18.0^\circ \)[/tex].
- We convert degrees to radians using the formula:
[tex]\[ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) \][/tex]
Substituting the given angle:
[tex]\[ \text{radians} = 18.0 \times \left( \frac{\pi}{180} \right) = 0.3141592653589793 \, \text{radians} \][/tex]
3. Calculate the [tex]\( y \)[/tex]-component of the weight:
- The [tex]\( y \)[/tex]-component of the weight ([tex]\( w_y \)[/tex]) is found by multiplying the weight by the sine of the angle in radians.
Formula for the [tex]\( y \)[/tex]-component of the weight:
[tex]\[ w_y = w \cdot \sin(\text{angle in radians}) \][/tex]
Substituting the given values:
[tex]\[ w_y = 1471.5 \, \text{N} \times \sin(0.3141592653589793) \][/tex]
- Using a calculator to find the sine value (assuming a pre-calculated value):
[tex]\[ w_y = 1471.5 \, \text{N} \times 0.30901699437494745 = 454.71850722273507 \, \text{N} \][/tex]
So, the [tex]\( y \)[/tex]-component of the weight of the crate is approximately:
[tex]\[ w_y = 454.72 \, \text{N} \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.