Equations of problem 30
We express the braking force from relation (9): \[Fb = {m*v_0^2\over 2*Ss}\]
Equation 10 from problem 30
Note: The kinetic energy of a car at the beginning of its brakins is qual to the work done by the braking force: W=Ek
On a horitzontal surface it holds that:
\[Fb = {f*N = f*m*g}\]
Fb..frictional braking force
f..coeficient of static friction
N..force wich the car acts upon the road
m..the mass of the object
g..the acceleration of gravity
Equation 11 from problem 30
The coefficient of friction f will be the sabe in both scenarios
We substitute for Fb from relation (10)
Equation 12 from problem 30
Forces acting upon a car moving uphill:
Fg.. gravitational force
N1..normal force with which the road upon the car
Fb1..braking force
Equation of motion a car going uphill:
\[Fb_1 + Fg + N_1 = {m * a_1}\]
We rewrite the equation using scalars and choose a coordinate system such that the x axis is parallel to the movement of the car.
The y axis is perpendicular to the x axis. We split the gravitational force into two components in the directions of the axes: