Question

The driver of an automobile, travelling along a straight level highway, suddenly applies the brakes so that the car slides for 2 s, covering a distance 9.66 m, before coming to a stop. Assuming that during this time the car moved with constant deceleration; find the coefficient of friction between the tyres and pavement

Answer 1

By using D'Alembertz principle we can solve this question very easily.
 given   s=9.66; v=0; t=2sec;
∑fx=0 ⇒  -f-ma=0                    ------------------------------------------------ let it be (i)
∑fy=0 ⇒ N-mg=0 ⇒ N=mg     ------------------------------------------------ let it be (ii)
we know that f=frictional force= MN
here M=coefficient of friction between the tyres and pavement
N=Normal reaction
therefore  (i) ⇒ -MN-mg=0
substitute (ii) in (i)
⇒  -M(mg)-ma=0
 Mg+a=0   
M= -a/g                         -------------------------------------------------------- let it be (iii)
 s=u×t+1/2×a×t²
9.66=u(2)+1/2×a×2²
u+a=4.83                       ------------------------------------------------------- let it be (iv)
v=u+a×t
⇒ u= -2×a                      ------------------------------------------------------- let it be (v)
substitute (v) in (iv)
-2×a+a=4.83
⇒ a=-4.83
substitute 'a' value in (iii)
⇒  M= -(-4.83)/9.81
      M=0.49235474
           

Answer 2

The balloon has a total mass of 400 kg including the passengers and ballast. The ballon s rising at a constant velocity of 18 km/hr when h=10 m. If the man drops the 40-kg sand bag, determine the velocity of the balloon when the bag strikes the ground Neglect air resistance.