Correct Answer - Option 1 : Brake sharply
CONCEPT:
Work-Energy Theorem:
-
The work-energy theorem states that the net work done by the forces on an object is equal to the change in its kinetic energy.
⇒ W = ΔKE
Where W = work done and ΔKE = change in kinetic energy
Kinetic Energy:
- The energy possessed by a particle by the virtue of its motion is called kinetic energy.
- It is given by,
\(⇒ KE=\frac{1}{2}m× v^{2}\)
where m = mass and v = velocity
Centripetal force:
- The force which is responsible for circular motion and acts towards the axis of rotation is called centripetal force.
\(⇒ F_{c}=\frac{mv^{2}}{r}\)
CALCULATION:
Given v = velocity of the car, a = distance of the car from the wall
Case 1:(When the driver applies brake)
- Let the distance covered by the car after applying the brake be x.
- Since after applying brake the car will stop so the final kinetic energy of the car will be zero.
Let F = Braking force
- So work done on the car by braking force,
⇒ W = Fx -----(1)
- The change in kinetic energy is given as,
\(\Rightarrow \Delta KE=\frac{1}{2}mv^2\) -----(2)
⇒ W = ΔKE
\(\Rightarrow Fx=\frac{1}{2}mv^2\)
\(\Rightarrow x=\frac{mv^2}{2F}\) -----(3)
Case 2:(When the driver takes a sharp turn)
- Let the radius of the turn be r.
Let F = centripetal force
So centripetal force is given as,
\(⇒ F=\frac{mv^{2}}{r}\)
\(⇒ r=\frac{mv^{2}}{F}\) -----(4)
- By equation 3 and equation 4 it is clear that by the same retarding force the car can be stopped at a less distance when the driver applies brakes.
- Hence, option 1 is correct.
