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January 30, 2015

January 30, 2015

Posted by **dmkp** on Wednesday, May 30, 2012 at 7:43am.

a) draw a free body diagram of the car

b)calculate the linear velocity of the car

c) Describe what will happen to a car that is travelling on the same track but with a higher linear velocity

- kinematics -
**Elena**, Wednesday, May 30, 2012 at 12:46pmLet the x-axis point toward the center of curvature and the y-axis point upward. Use Newton’s second law.

ΣFy = N• cos θ − mg − f •sin θ = 0

ΣFx = N• sin θ + f •cos θ = m•v²/R,

Solving the 1st equation for N, we obtain

N =( f •sin θ + m•g)/cos θ,

Substitute N to the 2nd equation and obtain friction force

f =m[(v²•cosθ/R) - g•sinθ].

f=0 =>

(v²•cosθ/R) - g•sinθ = 0,

v²•cosθ/R = g•sinθ,

v² /R•g = sinθ/cosθ = tanθ.

v =sqrt(R•g•tanθ) = sqrt (50•9.8•tan16º)=11.85 m/s

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