What is the tangential acceleration (i.e., the acceleration parallel to the road) of car A?

SOMEONE ASKED ๐Ÿ‘‡

What is the tangential acceleration (i.e., the acceleration parallel to the road) of car A?

HERE THE ANSWERS ๐Ÿ‘‡

  • This problem has to do with the normal acceleration increasing/decreasing in the dips and bumps of the road. I would need the weight of the cars to get an exact answer so I will answer these in terms of the mass m.

    a) In this one we donโ€™t need to worry about the normal acceleration since there is no curve.

    at = uk*Fn

    Fn = mg = 9.81m

    at = 1*9.81m = -9.81*m

    this is considered negative since the forward motion of the car is in the positive direction.

    b) Now we will find the normal acceleration caused by the curve.

    an = v^2/r = 27^2/200 = 0.135 m/s^2

    Fn = m*(an+ag) = (9.81+0.135)m = 9.945m

    at = uk*Fn = 1*9.945m = -9.945m

    c) Since the velocity and the radius are the same the normal acceleration is the same, however this time it is in the opposite direction of gravity.

    an = 0.135

    Fn = (9.81 โ€“ 0.135)m = 9.675m

    at = uk*Fn = -9.675m

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