Suppose your car is on a 5% grade, meaning that for every 100 m you travel along the road you raise or lower only 5 m in elevation. If your car weighs 1500 kg, what is the component of its weight parallel to the road?
A) 15000 N
B) 1500 N
C) 7500 N
D) 750 N

Question

Quizplus · Accepted Answer

The component of the car's weight parallel to the road can be calculated using the formula: $W_{\text{parallel}} = W \sin(\theta)$, where $W$ is the weight of the car and $\theta$ is the angle of the incline. Since the grade is 5%, this means the tangent of the angle $\theta$ is 0.05 (5/100). For small angles, $\tan(\theta) \approx \sin(\theta)$, so we can use 0.05 as an approximation for $\sin(\theta)$. The weight of the car is $1500 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 14700 \, \text{N}$. Therefore, $W_{\text{parallel}} = 14700 \, \text{N} \times 0.05 = 735 \, \text{N}$, which rounds to 750 N, making D the correct answer.

Suppose Your Car Is on a 5% Grade, Meaning That