Physics · Dynamics of uniform circular motion, centripetal force and its applications: vehicle on a level circular road, vehicle on a banked road
A circular road of radius r is banked for a speed A car of mass attempts to go o
A circular road of radius r is banked for a speed \( \mathbf{v}=40 \mathrm{km} / \mathrm{hr} . \) A car of mass \( \mathrm{m} \) attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible.
- A. The car cannot make a turn without skidding
- B. if the car turns at a speed less than \( 40 \mathrm{km} / \mathrm{hr} \), it will slip down.
- C. If the car turns at the correct speed of \( 40 \mathrm{km} / \mathrm{hr} \), the force by the road on the car is equal to \( m v^{2} / r \)
- D. If the car turns at the correct speed of \( 40 \mathrm{km} / \mathrm{hr} \), the force by the road on the car is greater than mg as well as greater than \( m v^{2} / r \)
Step-by-step solution
For a banked road without friction, at the design speed v, the normal force N provides the centripetal force. From equilibrium, N cosθ = mg and N sinθ = mv²/r. Since cosθ < 1 and sinθ < 1, N > mg and N > mv²/r.
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