Q. 16

A car is going at a speed of 21.6 km/hr when it encounters a 12.8 m long slope of angle 30o (figure 6-E5). The friction coefficient between the road and the tyre is 1/2√3. Show that no matter how hard the driver applies the brakes; the car will reach the bottom with a speed greater than 36 km/hr. Take g = 10 m/s2.



Answer :


The maximum force of friction is developed between the surface of road and the car’s tyres when hard breaks are applied.


So, maximum frictional force = μR


From the free body diagram,


R mg cos θ = 0
R = mg cos θ (i)
and
μR + mamg sin θ = 0 (ii)
μ mg cos θ + mamg sin θ = 0


μg cos θ + a -10(12) =0


a=5- {1-(2)} ×10(/2)


a = -2.5 m/s2


When brakes are applied, car will deaccelerate by 2.5 m/s2


Distance s= 12.8 m
initial velocity u = 6 m/s
Velocity at the end of incline


ν=



v=10 m/s=36 km/h


Hence, the harder the driver applies the brakes, the lower will be the velocity of the car when it reaches the ground, i.e. at 36 km/h


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
HCV Objective Questions of FrictionHCV Objective Questions of FrictionHCV Objective Questions of Friction63 mins
Friction | Get the BasicsFriction | Get the BasicsFriction | Get the Basics53 mins
Friction ke kuch dhamakedaar questionsFriction ke kuch dhamakedaar questionsFriction ke kuch dhamakedaar questions46 mins
Interactive Quiz on Friction important questionsInteractive Quiz on Friction important questionsInteractive Quiz on Friction important questions47 mins
Friction ke kuch dhamakedaar questions | Check YourselfFriction ke kuch dhamakedaar questions | Check YourselfFriction ke kuch dhamakedaar questions | Check Yourself56 mins
Interactive Quiz of friction | Matering important chaptersInteractive Quiz of friction | Matering important chaptersInteractive Quiz of friction | Matering important chapters45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :