Question

A car is traveling up a hill that is inclined at an angle θ above the horizontal. Determine the ratio of the magnitude of the normal force to the weight of the car when θ is equal to the following. (a) θ = 13°

Answer 1

Explanation:

The weight of the car is equal to, $W_c=m\times g$...........(1)

Where

m is the mass of car

g is the acceleration due to gravity

The normal or vertical component of the force is, $F_N=mg\ cos\theta$

or

$F_N=mg\ cos(13)$.............(2)

The horizontal component of the force is, $F_H=mg\ sin\theta$

Taking ratio of equation (1) and (2) as :

$\dfrac{F_N}{W_c}=\dfrac{mg\ cos\theta}{mg}$

$\dfrac{F_N}{W_c}=cos(13)$

$\dfrac{F_N}{W_c}=0.97$

or

$\dfrac{F_N}{W_c}=\dfrac{97}{100}$

Hence, this is the required solution.