Physics problem! please help!?

Car travels with speed v around curve number one. which has a radius r. Car B travels with speed 2v around curve number 2, which has a radius 2 r. The acceleration will be...

zero for both cars

the same for both cars

greater for the car A

greater for the car B

Can you please show me how to do this problem? i need to see it step by step

Comments

  • You should have already met an equation for centripetal acceleration, a = v² /r

    [(v²/ r) is part of the centripetal force equ. .. F = m.v²/r .. .. it's the same equ. as .. F = m x a]

    Put in the values given for each car ..

    For car A .. a = v² / r

    For car B .. a = (2v)² / 2r .. .. = 4 v² / 2 r = 2 v² /r .. twice the accel. of car A

    Answer .. .. ►Greater for car B

  • the answer is greater for car B: as for how to do it...

    draw a semicircle for car A,

    label the radius "r".

    the velocity is "v". i know both of these b/c they are in the question...

    and the equation for acceleration is:

    A=(V^2)/R , so because we didnt mess around with our variable, (ie. no coefficients) the

    acceleration of car A is (v^2)/r. circle that...

    Draw a bigger semicircle for car B,

    label the radius 2R,

    Label the velocity as 2V. i know both of THOSE, because... they were also in the question. :)

    now, you know the equation of accelaration:

    A=(V^2)/R, but remember YOUR VELOCITY AND RADIUS ARE DIFFERENT FOR CAR B.

    so plug in:

    V =2v

    R=2r

    so if you follow rules of exponents, both parts of teh 2 and the V get squared in the numerator,

    leaving the answer as:

    A=(4v^2)/2r

    now you can simplify the 4 and the 2, leaving 2(v^2/r), circle that.

    realize that car B has twice the accelaration of car A... Tadaaa!

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