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Answer :
To find the y-component of the weight of a car on an incline, we follow these steps:
1. Calculate the Weight of the Car:
The weight [tex]\( W \)[/tex] of the car is determined using the formula:
[tex]\[
W = m \times g
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the car, which is 115 kg.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
So, [tex]\( W = 115 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1127 \, \text{N} \)[/tex].
2. Understand the Inclined Plane:
On an incline, the weight of the car can be broken down into two components: one parallel to the incline (x-component) and one perpendicular to the incline (y-component).
3. Calculate the Y-component of the Weight:
The y-component of the weight is found using the sine of the angle of the incline:
[tex]\[
W_y = W \times \sin(\theta)
\][/tex]
where [tex]\( \theta \)[/tex] is the angle of the incline, given as [tex]\( 37.0^{\circ} \)[/tex].
4. Convert the Angle from Degrees to Radians:
Because many mathematical functions use radians, we convert degrees to radians for calculation:
[tex]\[
\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}
\][/tex]
5. Substitute the Values:
Calculate the sine of [tex]\( 37.0^{\circ} \)[/tex] and then find [tex]\( W_y \)[/tex]:
[tex]\[
W_y = 1127 \, \text{N} \times \sin(37.0^{\circ}) = 678.25 \, \text{N} \, (\text{approximately})
\][/tex]
Therefore, the y-component of the weight of the car is approximately [tex]\( 678.25 \, \text{N} \)[/tex].
1. Calculate the Weight of the Car:
The weight [tex]\( W \)[/tex] of the car is determined using the formula:
[tex]\[
W = m \times g
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the car, which is 115 kg.
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].
So, [tex]\( W = 115 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1127 \, \text{N} \)[/tex].
2. Understand the Inclined Plane:
On an incline, the weight of the car can be broken down into two components: one parallel to the incline (x-component) and one perpendicular to the incline (y-component).
3. Calculate the Y-component of the Weight:
The y-component of the weight is found using the sine of the angle of the incline:
[tex]\[
W_y = W \times \sin(\theta)
\][/tex]
where [tex]\( \theta \)[/tex] is the angle of the incline, given as [tex]\( 37.0^{\circ} \)[/tex].
4. Convert the Angle from Degrees to Radians:
Because many mathematical functions use radians, we convert degrees to radians for calculation:
[tex]\[
\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}
\][/tex]
5. Substitute the Values:
Calculate the sine of [tex]\( 37.0^{\circ} \)[/tex] and then find [tex]\( W_y \)[/tex]:
[tex]\[
W_y = 1127 \, \text{N} \times \sin(37.0^{\circ}) = 678.25 \, \text{N} \, (\text{approximately})
\][/tex]
Therefore, the y-component of the weight of the car is approximately [tex]\( 678.25 \, \text{N} \)[/tex].
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