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Answer :
To find the [tex]\( x \)[/tex]-component of the weight of the car on the hill, we can follow these steps:
1. Understand the Situation:
- The weight of the car acts vertically downward.
- The car is on a hill inclined at an angle of [tex]\( 37.0^\circ \)[/tex] with the horizontal.
2. Determine the Weight of the Car:
- First, calculate the weight of the car using the formula:
[tex]\[
\text{Weight (W)} = \text{mass} \times \text{gravitational acceleration}
\][/tex]
- The mass of the car is [tex]\( 115 \, \text{kg} \)[/tex].
- The gravitational acceleration is [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
3. Calculate the Weight in Newtons:
[tex]\[
W = 115 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1128.15 \, \text{N}
\][/tex]
4. Find the [tex]\( x \)[/tex]-Component of the Weight:
- The [tex]\( x \)[/tex]-component of the weight is the component of the gravitational force parallel to the incline.
- To find it, we use the sine of the incline angle because this component acts along the slope.
- The formula for the [tex]\( x \)[/tex]-component is:
[tex]\[
w_x = W \times \sin(\text{angle of incline})
\][/tex]
5. Calculate the Angle in Radians:
- The angle in degrees is given as [tex]\( 37.0^\circ \)[/tex].
- First, convert this angle to radians because trigonometric calculations typically use radian measure.
- Conversion from degrees to radians:
[tex]\[
\text{radians} = 37.0^\circ \times \left(\frac{\pi}{180}\right) = 0.6458 \text{ radians}
\][/tex]
6. Compute the [tex]\( x \)[/tex]-Component of the Weight:
[tex]\[
w_x = 1128.15 \, \text{N} \times \sin(0.6458) = 678.94 \, \text{N}
\][/tex]
Therefore, the [tex]\( x \)[/tex]-component of the weight of the car is approximately [tex]\( 678.94 \, \text{N} \)[/tex].
1. Understand the Situation:
- The weight of the car acts vertically downward.
- The car is on a hill inclined at an angle of [tex]\( 37.0^\circ \)[/tex] with the horizontal.
2. Determine the Weight of the Car:
- First, calculate the weight of the car using the formula:
[tex]\[
\text{Weight (W)} = \text{mass} \times \text{gravitational acceleration}
\][/tex]
- The mass of the car is [tex]\( 115 \, \text{kg} \)[/tex].
- The gravitational acceleration is [tex]\( 9.81 \, \text{m/s}^2 \)[/tex].
3. Calculate the Weight in Newtons:
[tex]\[
W = 115 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1128.15 \, \text{N}
\][/tex]
4. Find the [tex]\( x \)[/tex]-Component of the Weight:
- The [tex]\( x \)[/tex]-component of the weight is the component of the gravitational force parallel to the incline.
- To find it, we use the sine of the incline angle because this component acts along the slope.
- The formula for the [tex]\( x \)[/tex]-component is:
[tex]\[
w_x = W \times \sin(\text{angle of incline})
\][/tex]
5. Calculate the Angle in Radians:
- The angle in degrees is given as [tex]\( 37.0^\circ \)[/tex].
- First, convert this angle to radians because trigonometric calculations typically use radian measure.
- Conversion from degrees to radians:
[tex]\[
\text{radians} = 37.0^\circ \times \left(\frac{\pi}{180}\right) = 0.6458 \text{ radians}
\][/tex]
6. Compute the [tex]\( x \)[/tex]-Component of the Weight:
[tex]\[
w_x = 1128.15 \, \text{N} \times \sin(0.6458) = 678.94 \, \text{N}
\][/tex]
Therefore, the [tex]\( x \)[/tex]-component of the weight of the car is approximately [tex]\( 678.94 \, \text{N} \)[/tex].
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