Question

Which statement is true for a car that first goes around a curve of radius r at a constant speed v, and then goes around the same curve at half the original speed?
The centripetal force is twice as big the second time around.

The centripetal force is four times as big the second time around.

The centripetal force is one-half as big the second time around.

The centripetal force is one-fourth as big the second time around.

Answer 1

Centripetal force is equal to (mv^2)/r
The way I use to answer these question is to set every variable to 1
m=1
v=1
r=1
so centripetal force =1
then change the variable we're looking at
and since we're find when it's half we could either change it to 1/2 or 2, but 2 is easier to use
m=1
v=2
r=1
((1)×(2)^2)/1=4
So the velocity in the 1st part is half the velocity in the 2nd part and the centripetal force is 4× less
The answer is the centripetal force is 1/4 as big the second time around