Centripetal Force: Speed Change w/ Doubled Radius & Force

In summary, when the centripetal force acting on an object is doubled and the radius is also doubled, the speed of the object increases by a factor of 2. This can be calculated by substituting the values in the equation F = mv2/r, where F is the force, m is the mass, v is the velocity, and r is the radius. The correct answer is (B) increases by a factor of 2.
  • #1
brake4country
216
7

Homework Statement


The centripetal force acting on an object is doubled. The radius is also doubled. The speed of the object:

(a) increases by a factor of 4
(b) increases by a factor of 2
(c) decreases by a factor of 2
(d) The change in the object's speed depends on its mass

Homework Equations


F = mv2/r

The Attempt at a Solution


So if I substitute 2's in for F and r in the above equation, my 2's cancel but the correct answer is a. ?
 
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  • #2
Do a numerical example...
 
  • #3
brake4country said:
The centripetal force acting on an object is doubled.
So if I substitute 2's in for F and r in the above equation, my 2's cancel but the correct answer is a. ?
Not happy with the wording of the question. Centripetal force does not act. It is the force required to be supplied by forces which do act in order to produce a certain motion.
Anyway, I don't get how the 2's would cancel. (Not that I necessarily agree with the supposed answer.). Please post detailed working.
 
  • #4
I am sorry; an erroneous math calculation. By substituting 2 for both the force and the radius, I get 4 which is (a). Thank you!
 
  • #5
Can you still show your calculation ? It doesn't fit at all.
 
  • #6
brake4country said:
I am sorry; an erroneous math calculation. By substituting 2 for both the force and the radius, I get 4 which is (a). Thank you!
As I hinted, I disagree with that answer. Looks like BvU disagrees with it too.
 
  • #7
Sorry everyone! That's what happens when you don't read the answer choices correctly! Okay here is the original question: the centripetal force acting on an object is doubled. The radius of the object's motion is also doubled. The speed of the object is:
(A) increases by a factor of
(B) increases by a factor of 2
(C) decreases by a factor of 2
(D) the change in the object's speed depends on its mass.

Fc = mv2/r. If I plug in 2 for F and r, I get 2 = mv2/2 = 4 = mv2. Therefore, the correct answer is (B) increases by a factor of 2! Thanks everyone!
 

FAQ: Centripetal Force: Speed Change w/ Doubled Radius & Force

What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary to maintain the object's direction and speed.

How does doubling the radius affect the speed of an object?

Doubling the radius of a circular path will decrease the speed of the object. This is because the centripetal force required to keep the object in motion is directly proportional to the square of the velocity and inversely proportional to the radius.

What happens to the force required to maintain the speed when the radius is doubled?

If the radius of a circular path is doubled, the force required to maintain the speed will decrease by a factor of four. This is because the centripetal force is inversely proportional to the radius squared.

How does the mass of an object affect the centripetal force?

The mass of an object has a direct effect on the amount of centripetal force required to maintain its circular motion. The greater the mass of the object, the greater the centripetal force needed to keep it in its path.

Can an object maintain a constant speed with a changing radius and force?

Yes, as long as the centripetal force and the radius are changing proportionally, the object can maintain a constant speed. This is known as uniform circular motion, where the object moves in a circular path at a constant speed.

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