Question

1.A block accelerates at 3.1 m/s2 down a plane inclined at an angle 24.0◦. Find μk between the block and the in- clined plane. The acceleration of gravity is 9.81 m/s2 . 2.A 1200 kg car moves along a horizontal road at speed v0 = 20.1 m/s. The road is wet, so the static friction coefficient between the tires and the road is only μs = 0.189 and the kinetic friction coefficient is even lower, μk = 0.1323. The acceleration of gravity is 9.8 m/s2 . What is the shortest possible stopping dis- tance for the car under such conditions? Use g = 9.8 m/s2 and neglect the reaction time of the driver. Answer in units of m. Thank you for the help!

Answer 1

1.  Fp = Mg*sin24 = 0.407Mg. 
Fn = Mg*Cos24 = 0.914Mg. 
Fk = u*0.914Mg. 

Fp-Fk = M*a. 
0.407Mg-u*0.914Mg = M*a.
Divide by Mg: 
0.407-0.914u = a/g = 3.1/-9.81, 
0.407-.914u = -0.316, uk = 0.791.

2.  M*g = 1200*9.8 = 11,760 N. = Wt. of car. = Normal force(Fn). 
Fp = Mg*sin 0 = 0. 
Fk = uk*Fn = 0.1323*11,760 = 1556 N. 

Fp-Fk = M*a. 
0-1556 = 1200a, a = -1.30 m/s^2. 

V^2 = Vo^2 + 2a*d. 
0 = (20.1)^2 - 19.6d