Question

Why are mountain roads generally made winding upwards rather than going straight up?

Answer 1

Here, ${\theta }^{\prime }=$ Angle made by the slope of the mountain with the ground
$\theta =$ Angle made by each turn with the ground.
As it is clear that ${\theta }^{\prime }>\theta$.

The mountain roads are generally constructed in a winding fashion to increase friction and thereby reduce skidding of vehicles. This comes from the definition of friction for an object placed at a slope of angle 𝜃.
$f=\mu N=\mu \text{mgcos}\theta$

Here, $f$ is the frictional force, $\mu$ is the coefficient of friction, $m$ is the mass of the object, $g$ is the acceleration due to gravity and $\theta$ is the angle made by the object with the surface.

Now, winding the road means decreasing the $\theta$ with respect to ground. This will increase friction as cosine will increase. Hence the frictional force increases so there is a less chance of skidding.
Going straight up means going at a larger angle so the friction will decrease. So there is a high chance of skidding.
Final Answer: $f=\mu R=\mu mgcos\theta$ is the force of friction, if $\theta$ is angle made by the slope. If $\theta$ is small, force of friction is high and there is less chance of skidding.