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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