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Answer :
The x-component of the weight of the 135 kg crate on an 18.0° incline is calculated to be approximately 409 N.
To find the x-component of the weight of the crate, we need to decompose the weight along the inclined plane. First, we'll calculate the gravitational force (weight) acting on the crate:
Weight (W) = mass (m) × gravitational acceleration (g)
W = 135 kg × 9.8 m/s²
= 1323 N
Next, we will find the x-component of this weight. The x-component of the weight parallel to the incline can be calculated using the sine of the incline angle.
W_x = W × sin(θ)
W_x = 1323 N × sin(18.0°)
Using a calculator to find sin(18.0°):
sin(18.0°) ≈ 0.309
W_x = 1323 N × 0.309
≈ 409 N
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