Answer to Question #198923 in Mechanical Engineering for Sello

Question #198923

The speed of a vehicle is reduced with a constant acceleration from 72km/h

72km/h to 18 km/h

km/h over 250m

250m directly down an incline of 1in25

1in25. The mass of the vehicle is 1.9 Mg

Mg and it has a constant resistance to motion of 350N

350N. 

Calculate the magnitude of the braking Force


1
Expert's answer
2021-05-28T02:26:27-0400

Given as:

V1=72 km/hrs=20m/s

V2=18 km/hrs=5m/s

Distance(d)=250 m

Slope of the road ("\\theta")=1/25

Mass(m)=1900kg

Resistance force(F)=350 N

Solution:

Let "F_b" be the braking force

Resolving weight (m×g) along the inclined road as "m\\times g\\times sin\\theta"

Considering dynamic equilibrium along the inclined road,

"m\\times g\\times sin\\theta -F-F_b=m\\times(a)"

By kinematical equation

"(V_2)^2=(V_1)^2+2\u00d7a\u00d7d"

"a=0.75 \\:m\/s^2"

Substitute,

"1900\\times 9.8\\times sin(1\/25) -350-F_b=1900\\times(0.75)"

Breaking force(Fb)=1030.40 N


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