Worked Example | Calculate Optimal Bank Angle for a Car to Travel Around a Curve

In this application of centripetal force; given the velocity of a vehicle as well as the radius of a corner, calculate the optimal bank angle of the road so that the car can travel around the corner without any friction or traction necessary between the tires and the road.
This problem reduces down to an analysis of the free body diagram of the vehicle while traveling around the corner. The vertical component of the normal force cancels out the force of gravity. However the horizontal component of the normal force is unbalanced and acts as the centripetal force, causing the vehicle to travel in a circle.
This problem commonly comes up in introductory physics courses such as high school physics, AP Physics 1, AP Physics C as well as early college physics.

[@INTEGRALPHYSICS]

In the end when I rearranged for theta, the equation shows 'tan' but it should in fact be 'invtan'... Sorry!

[@josepires_pmp]

No problem. To be more precise, it should be:
Theta = invtan(10^2/(30*9.8))

[@mirabdulsamad5171]

Sir while finding apparent acceleration due to gravity due to earth's speed on a body ,we take the frame of body so that the force is centrifugal (outwards) and we get a reduced net acceleration.
But on viewing from outside inertial frame of refrence we have to take a centripetal force(inwards) thereby getting an increase in net acceleration. But the net acceration can't be different in different frames. Plz tell me where am i wrong ?

[@INTEGRALPHYSICS]

When at all possible, avoid a non-inertial reference frame. Something is wrong with how you are calculating the centrifugal force.

[@mirabdulsamad5171]

​@@INTEGRALPHYSICS But sir books use centrifugal force.

[@MIZANURRAHMAN-my1rx]

Nice presentation

[@INTEGRALPHYSICS]

thanks!

[@eprohoda]

salut-gorgeous uploading-

[@INTEGRALPHYSICS]

Thanks!