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°

Respuesta :

Explanation:

The weight of the car is equal to, [tex]W_c=m\times g[/tex]...........(1)

Where

m is the mass of car

g is the acceleration due to gravity

The normal or vertical component of the force is, [tex]F_N=mg\ cos\theta[/tex]

or

[tex]F_N=mg\ cos(13)[/tex].............(2)

The horizontal component of the force is, [tex]F_H=mg\ sin\theta[/tex]

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

[tex]\dfrac{F_N}{W_c}=\dfrac{mg\ cos\theta}{mg}[/tex]

[tex]\dfrac{F_N}{W_c}=cos(13)[/tex]

[tex]\dfrac{F_N}{W_c}=0.97[/tex]

or

[tex]\dfrac{F_N}{W_c}=\dfrac{97}{100}[/tex]

Hence, this is the required solution.