Question

a car is travelling on with speed v=72 km/h around a banked cure of diameter d= 190 m calculate the following:

a. the centripetal acceleration of the car.

b.the banked angle to keep the car from sliding assume no friction.

c.assume the curve is leveled horizontally , determine the coefficient of static friction to keep the car from sliding

d.Calculate the centeripetal force at the given spedd on a car of mass, m=1000 kg and a truck of mass m=12500 kg if static frictions is decreasesed due to rain, determine which of the vehicles will skid

Answer 1

a)

Speed of car

V=72*(1000/3600)=20 m/s

radius

r=d/2 =190/2 =95 m

Centripetal acceleration

a_c=V²/r =20²/95

a_c =4.21 m/s²

b)

Banking angle

o=tan^-1(V²/rg) =tan^-1(20²/95*9.8)

o=23.25^o

c)

For a leveled curve

centripetal force =frictional force

MV²/r =uMg

=>u=V²/rg =20²/(95*9.8)

u=0.43

d)

Centripetal force of car

F=Ma_c =1000*4.21

F=4210 N

Centripetal force of truck

F=12500*4.21=52,625 N