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Answer :
To find the x-component of the weight of the crate on an inclined ramp, follow these steps:
1. Determine the weight of the crate:
The weight ([tex]\( W \)[/tex]) is the force due to gravity acting on the crate. It can be calculated using the formula:
[tex]\[
W = m \times g
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the crate (135 kg)
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.81 m/s[tex]\(^2\)[/tex])
Substituting the values:
[tex]\[
W = 135 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1324.35 \, \text{N}
\][/tex]
2. Calculate the x-component of the weight:
The x-component of the weight ([tex]\( w_x \)[/tex]) is found by decomposing the weight into components parallel and perpendicular to the inclined plane. The x-component can be found using the sine of the angle of inclination ([tex]\( \theta \)[/tex]):
[tex]\[
w_x = W \times \sin(\theta)
\][/tex]
where:
- [tex]\( W \)[/tex] is the weight (1324.35 N)
- [tex]\( \theta \)[/tex] is the angle of inclination (18.0°)
Since we need to use the sine function with degrees, we convert the angle to radians first. However, for simplicity in this step-by-step outline, we'll use the sine value directly in degrees.
Therefore, substituting the values:
[tex]\[
w_x = 1324.35 \, \text{N} \times \sin(18.0^\circ)
\][/tex]
3. Compute the sine value and complete the calculation:
The sine of [tex]\( 18.0^\circ \)[/tex] is approximately 0.309. Thus,
[tex]\[
w_x = 1324.35 \, \text{N} \times 0.309 \approx 409.25 \, \text{N}
\][/tex]
Therefore, the x-component of the weight of the crate on the ramp is:
[tex]\[
w_x \approx 409.25 \, \text{N}
\][/tex]
1. Determine the weight of the crate:
The weight ([tex]\( W \)[/tex]) is the force due to gravity acting on the crate. It can be calculated using the formula:
[tex]\[
W = m \times g
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the crate (135 kg)
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.81 m/s[tex]\(^2\)[/tex])
Substituting the values:
[tex]\[
W = 135 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1324.35 \, \text{N}
\][/tex]
2. Calculate the x-component of the weight:
The x-component of the weight ([tex]\( w_x \)[/tex]) is found by decomposing the weight into components parallel and perpendicular to the inclined plane. The x-component can be found using the sine of the angle of inclination ([tex]\( \theta \)[/tex]):
[tex]\[
w_x = W \times \sin(\theta)
\][/tex]
where:
- [tex]\( W \)[/tex] is the weight (1324.35 N)
- [tex]\( \theta \)[/tex] is the angle of inclination (18.0°)
Since we need to use the sine function with degrees, we convert the angle to radians first. However, for simplicity in this step-by-step outline, we'll use the sine value directly in degrees.
Therefore, substituting the values:
[tex]\[
w_x = 1324.35 \, \text{N} \times \sin(18.0^\circ)
\][/tex]
3. Compute the sine value and complete the calculation:
The sine of [tex]\( 18.0^\circ \)[/tex] is approximately 0.309. Thus,
[tex]\[
w_x = 1324.35 \, \text{N} \times 0.309 \approx 409.25 \, \text{N}
\][/tex]
Therefore, the x-component of the weight of the crate on the ramp is:
[tex]\[
w_x \approx 409.25 \, \text{N}
\][/tex]
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