Physics
Circular Motion Solutions
For a car traveling at a certain speed, it is possible to bank a curve at just the right angle so that no friction at
all is needed to maintain the car's turning radius. Then a can safely round the curve even on wet ice. Your
engineering firm built a curve so that a car moving at a speed v can safely make the turn even with no friction.
1) At what angle ß should the curve be banked? (Express it using v, free fall acceleration g, and radius of the
curve R.)
2) When the car travels in the banked curve with speed v, what's the direction of the net force (vector sum of
all the forces) applied to the car? (The curved is banked and the road on the is on the horizontal plane).
(a) Car rounding banked curve
B
R
O
B = arctan
u?
GR
: Net force points toward the center of the curvature
my²
9R
O B = arcsin ( moeite); Net force points toward the center of the curvature
B = arcsin (*): Net force points perpendicular to the surface of the road.
O
OR
O B = 0; Net force is zero,
O
B = arccos
mu
9R
Net force points perpendicular to the surface of the road.
