91影视

A concrete highway curve of radius $70m$ is banked at a $15掳$ angle.

We need to draw a graph for analyze the situation.

From the graph we can obtain the expression for the horizontal direction;

$鈭�F_x:\frac{m{v}_m^2}{r}=N\sin 鈦�胃+F\cos 鈦�胃$

Where,

$v_m$: The maximum force required

$N$: Normal force

$r$ : Radius of the curve

$m$: mass of the car

role="math" localid="1648181750837" $胃$: Banking angle

Frictional force role="math" localid="1648181740479" $F={渭}_s\mathrm{N}$

Therefore,

$N\left(\sin 鈦�胃+{渭}_s\cos 鈦�胃\right)=\frac{m{v}_m^2}{r}$................(a)

Expression for vertical force:

$鈭�F_y:N\cos 鈦�胃=mg+F\sin 鈦�胃$

$鈬�N\left(\cos 鈦�胃鈭�{渭}_s\sin 鈦�胃\right)=mg$.................(b)

Dividing expression (a) by expression (b), we get

$\frac{v_m^2}{rg}=\frac{\sin 鈦�胃+{渭}_s\cos 鈦�胃}{\cos 鈦�胃鈭�{渭}_s\sin 鈦�胃}$

$鈬�v_m^2=\frac{rg\left(\sin 鈦�胃+{渭}_s\cos 鈦�胃\right)}{\cos 鈦�胃鈭�{渭}_s\sin 鈦�胃}$

$鈬�v_m^2=\frac{70脳9.8\left(\sin 鈦�{15}^{鈭�}+1脳\cos 鈦�{15}^{鈭�}\right)}{\cos 鈦�{15}^{鈭�}鈭�1脳\sin 鈦�{15}^{鈭�}}$

$鈬�v_m^2=1188.1868$

Therefore, the maximum speed the care can move without sliding is $34.47m/s$.