A big truck of mass 2000-kg travels along a straight 700-m portion of highway (f

Question

A big truck of mass 2000-kg travels along a straight 700-m portion of highway (from A to B) at a constant speed of 10 m/s. At B, the truck encounters an unbanked curve of radius 50m. The Jeep follows the road from B to C travelling at a constant speed of 10 m/s while the direction of the Jeep changes from east to south. i. Calculate the magnitude of the acceleration of the truck as it travels from A to B? ii. What is the magnitude of the acceleration of the truck as it travels from B to C? iii. Find the magnitude of the frictional force between the tires and the toad as the truck negotiates the curve from B to C?

Explanation / Answer

i)

acceleration is given as

a = (Vf - Vi)/t

where Vf = final velocity , Vi = initial velocity , t = time

for A to B motion :

Vf = 10 m/s    towards east

Vi = initial velocity = 10 m/s towards east

a = (10 - 10)/t = 0 m/s2

ii)

for B to C

the truck moves in a curve of radius 50 m at constant speed , hence it experience centripetal acceleration which is given as

a = V2/r = 102/50 = 2 m/s2

iii)

for B to C , the frictional force provides the necessary centripetal force to move in curve

hence , frictional force = f = centripetal force = m a = 2000 x 2 = 4000 N

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