Car A travels with speed v around curve number one, which has a radius r. Car B
travels with speed 2v around curve number two, which has a radius 2r. What is the ratio
of the two accelerations A/B?
A) 2
B) 4
C) 1/2
D) 1/4
E) 1
acceration1=v^2/r
acceleration2=4v^2/2r=2acceleration1
So it looks like a/B=1/2
To find the ratio of the two accelerations A/B, we need to compare the accelerations of car A and car B. The centripetal acceleration of an object moving in a circle can be calculated using the formula:
a = v^2 / r
Where:
a is the centripetal acceleration
v is the velocity of the object
r is the radius of the circle
For car A:
The speed of car A is v, and the radius of curve number one is r. So the centripetal acceleration of car A is given by:
a_A = v^2 / r
For car B:
The speed of car B is 2v, and the radius of curve number two is 2r. So the centripetal acceleration of car B is given by:
a_B = (2v)^2 / (2r) = 4v^2 / 2r = 2v^2 / r
Now, let's calculate the ratio of the two accelerations:
A/B = (a_A) / (a_B)
= (v^2 / r) / (2v^2 / r)
= (v^2 / r) * (r / 2v^2)
= 1/2
Therefore, the ratio of the two accelerations A/B is 1/2, which corresponds to option C.