Banked Curve
Track curves on race courses are steeply banked, which allow race car drivers to taken them at very fast speeds. If a particular course has a 125 m radius curve banked at 50°, what is the max allowable speed if the road is frictionless?
Expand Hint
$$$tan\theta =\frac{v^2}{rg}$$$
where
$$\theta$$
is the banked angle,
$$v$$
is the velocity,
$$g$$
is the acceleration due to gravity, and
$$r$$
is the radius.
Hint 2
Use the equation to solve for velocity,
$$v$$
.
Start with:
$$$tan\theta =\frac{v^2}{rg}$$$
where
$$\theta$$
is the banked angle,
$$v$$
is the velocity,
$$g$$
is the acceleration due to gravity, and
$$r$$
is the radius. Thus,
$$$tan50^{\circ} =\frac{v^2}{(125m)(9.8m/s^2)}$$$
Solving for velocity,
$$$v=\sqrt{(125m)(9.8m/s^2)\times tan50^{\circ}}=\sqrt{(1.19)(1,225)m^2/s^2}$$$
$$$v=\sqrt{1,457.75m^2/s^2}=38.2\:m/s$$$
38.2 m/s
Time Analysis
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