Normal Force and Static Frictional Force

[confounded]

Homework Statement

A car (m = 1710 kg) is parked on a road that rises 14.7 ° above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires?

Coefficient of static friction: rubber on dry concrete: 1.0

Homework Equations

F=ma
Fs max = coefficient of friction x normal force

The Attempt at a Solution

I drew some pictures, but I'm slightly computer illiterate so..sorry. Anyway, not really sure, but here's what I got:

F= (1710 kg)(9.8 m/s^2)
F= 16758 N

Attempt at solution of the normal force:

16758 N x sin (14.7) = 4252.48 N

Static Frictional Force:

(I'm really not sure of this, but I'll go ahead)

(4252.48 N)(1.0)= 4252.48


I'm just at my wit's end. I've been trying to figure out this problem for two hours straight. I have to enter my answers in online, and I can only have three significant digits, yet I can't enter in scientific notation, so...I just don't know! Help please!

 

[foxjwill]

You're thinking too hard about it. If you figure out the sum of forces you have

$$\begin{align*} \sum F_x &= f_s - mg\sin\theta = 0\\ \sum F_y &= F_N - mg\cos\theta = 0 \end{align*}$$​

 

[Moetasim]

I would approach this problem by using the fundamental equations of Newton's laws of motion. The normal force is the force exerted by the ground on the car perpendicular to the road surface. In this case, the normal force is equal to the weight of the car, which is calculated by multiplying the mass by the acceleration due to gravity (F=ma). So, the normal force would be 16758 N.

The static frictional force is the force that prevents the car from slipping down the road. It is equal to the coefficient of static friction (given as 1.0) multiplied by the normal force. So, the static frictional force would be 16758 N x 1.0 = 16758 N.

Since you are limited to three significant digits, your final answers would be:

(a) Normal force = 16800 N
(b) Static frictional force = 16800 N

I hope this helps! Remember to always use the fundamental equations and units when solving physics problems. Good luck with your homework!