Question

An object travels with a constant speed v in a circular path of radius r .
1. If v is double, how is acceleration affected?
2.if r is doubled, how is a affected?
3. Why is it impossible for an object to travel around a perfectly sharp angular turn?

Answer 1

Do you know the formula for centripetal acceleration ?

Answer 2

v^2/r ?

Answer 3

yes

Answer 4

Is acceleration doubled?

Answer 5

that gives you the ans to first 2 questions

Answer 6

wait centripital acceleration formula?

Answer 7

yes

Answer 8

Ok so doubling V makes a/2? and doubling r makes 2a?

Answer 9

i. a becomes 4 times
ii. a becomes halved

Answer 10

Whoa whoa How?

Answer 11

a is proportional to square of v ; and inverselt proportional to r. The formula says so.

Answer 12

Ohh okk I read the proportional part somewhere. But why 4x ?

Answer 13

because v doubled means new v = 2 times old v

Answer 14

(2v)^2?

Answer 15

yes

Answer 16

Help with part 3 now?

Answer 17

sure

Answer 18

I f you try to visualize you'll see that as the turn becomes sharper, the associated radius of curvature
\[r \rightarrow 0\]
that means, the centripetal acceleration blows off i.e, infinite force would be required in such a scenario, which of course isn't possible.

Answer 19

So r becomes zero so its just f = v^2/0 ?

Answer 20

@kappa007

Answer 21

ya

Answer 22

actually, \[F = \frac{ mv ^{2} }{ r }\]

Answer 23

ohhh yeah sorry sorry :P

Answer 24

:P

Answer 25

wait how would require infinite force if mv^2 is divided by zero?

Answer 26

Btw thanks for the pic @Algebraic!