When an automobile moving with a speed of 36

Asked by admin @ 20/08/2021 in Physics viewed by 344 People

When an automobile moving with a speed of 36 km/hr reaches an upward inclined road of angle 30 degree, its engine is switched off. If the coefficient of friction is 0.1, how much distance will the automobile move before coming to rest?

Answered by admin @ 20/08/2021

F = normal force by the incline

f = kinetic frictional force

perpendicular to incline, force equation is given as

F = mg Cos30 eq-1

μ = coefficient of friction = 0.1

kinetic frictional force is given as

f = μF

using eq-1

f = μmg Cos30 eq-2

parallel to incline force equation is given as

mg Sin30 + f = ma

using eq-2

mg Sin30 + μmg Cos30 = ma

a = g (Sin30 + μCos30)

a = (9.8) (Sin30 + (0.1)Cos30)

a = 5.75 m/s²

consider the upward parallel to incline direction as positive

v₀ = initial velocity = 36 km/h = 10 m/s

v = final velocity when it comes to stop = 0 m/s

a = acceleration = - 5.75 m/s²

d = distance travelled before stopping

using the equation

v² = v²₀ + 2 a d

0² = 10² + 2 (- 5.75) d

d = 8.7 m

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