A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to maintain the circular motion at the same speed?
Practice Questions
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Q1
A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to maintain the circular motion at the same speed?
It doubles
It remains the same
It halves
It quadruples
Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for constant speed.
Questions & Step-by-step Solutions
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Q
Q: A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to maintain the circular motion at the same speed?
Solution: Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for constant speed.
Steps: 6
Step 1: Understand that centripetal force (F_c) is needed to keep an object moving in a circle.
Step 2: The formula for centripetal force is F_c = mv²/r, where m is mass, v is speed, and r is the radius of the circle.
Step 3: Identify that if the radius (r) is doubled, we replace r in the formula with 2r.
Step 4: Rewrite the formula with the new radius: F_c = mv²/(2r).
Step 5: Notice that dividing by 2r means the centripetal force is now half of what it was before.
Step 6: Conclude that if the radius is doubled, the centripetal force required to maintain the same speed is halved.
