Asked by Ember
A car of mass 1200 kg is traveling at 55.0 km/hour. It enters a banked turn covered in ice. The road is banked at 20.0 degrees and there is no friction between the road and the cars tires. Use g= 9.80 m/s throughout the problem
Find the radius given the 20 degree angle, assuming the car continues in uniform circular motion around the turn.
Find the radius given the 20 degree angle, assuming the car continues in uniform circular motion around the turn.
Answers
Answered by
R_scott
the horizontal component of the normal force (due to the road's banking)
... is equal to the centripetal acceleration
... n sin(20º) = m v^2 / r
the vertical component of the normal force
... is equal to the weight ... otherwise the car would slide vertically
... n cos(20º) = m g
[m g / cos(20º)] sin(20º) = m v^2 / r
r = v^2 / [g tan(20º)]
... is equal to the centripetal acceleration
... n sin(20º) = m v^2 / r
the vertical component of the normal force
... is equal to the weight ... otherwise the car would slide vertically
... n cos(20º) = m g
[m g / cos(20º)] sin(20º) = m v^2 / r
r = v^2 / [g tan(20º)]
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