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 keep the stone moving in a circle 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 keep the stone moving in a circle 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 the same 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 keep the stone moving in a circle at the same speed?
Solution: Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for the same 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 when we double the radius, the formula shows that 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 keep the stone moving at the same speed is halved.
