Brake or turn? Figure 6-44 depicts an overhead view of a car\'s path as the car
ID: 1431530 • Letter: B
Question
Brake or turn? Figure 6-44 depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is d = 107 m, and take the car's mass as m = 1400 kg, its initial speed as v0 = 35.0 m/s, and the coefficient of static friction as ?s = 0.50. Assume that the car's weight is distributed evenly on the four wheels, even during braking. (a) What magnitude of frictional force is needed (between tires and road) to stop the car just as it reaches the wall? (b) What is the maximum possible static friction fs, max? (c) If the coefficient of kinetic friction between the (sliding) tires and the road is ?k = 0.40, at what speed will the car hit the wall? To avoid the crash, a driver could elect to turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of frictional force would be required to keep the car in a circular path of radius d and at the given speed v0, so that the car moves in a quarter circle and then parallel to the wall? (e) Is the required force less than Fs(max) so that a circular path is possible?
4) i, Mail File Edit View Mailbox Message Format Window Help 0 , 68% CI, Mon 2:20 AM MP The TRUE Story Behind An x (SugarSync x Untitled 2 Chegg.com Li file:///Users/linaisasad/Downloads/P221%20L05%20force%20and%20motion%20problem5%20(1).pdf 58 Brake or rn? Figure 6-44 depicts an overhead view of a car's path as the car travels toward a wall. Assume that the driver begins to brake the car when the distance to the wall is d= 107 m, and take the car's mass as m= 1400 kg, its initial speed as v 35 m/s, and the coefficient of static friction as 0.50. Assume that the car's weight is distributed evenly on the four wheels, even during braking. (a) What magnitude of static friction is needed (between tires and road) to stop the car just as it reaches the wall? (b) What is the maximum pos- sible static friction mas? (c) If the coefficient of kinetic friction between the (sliding) tires and the road is * = 0.40, at what speed will the car hit the wall? To avoid the crash, a driver could elect to turn the car so that it just barely misses the wall, as shown in the figure. (d) What magnitude of fric- tional force would be required to keep the car in a circular path of radius d and at the given speed vo. so that the car moves in a quar ter circle and then parallel to the wall? (e) Is the required force less than fso that a circular path is possible? Fig. 6-43 Problem 57 Car path Wall Fig. 6-44 Problem 58 21765 2Explanation / Answer
a) u = 35 m/s
final speed v have to zero within 107 m .
using v^2 - u^2 = 2ad
0^2 - 35^2 = 2(a)(107)
a = - 5.72 m/s^2
f = ma
f = 1400 x 5.72 = 8014 N .....Ans
b) maximum static friction = us N and N = mg
f max = us mg = 0.50 x 1400 x 9.8 = 6860 N .....Ans
c) a = f/m = umg /m
a = uk g = 0.4 x 9.8 = 3.92 m/s^2
using v^2 - u^2 = 2ad
v^2 - 35^2 = 2(3.92)(107)
v = 19.65 m/s
d) f = mv^2 / r
f = 1400 x 35^2 / 107
f = 16028.04 N
e) fmax = 6860 N
to keep in circular path, required force is greater.
so it is not possible.