A car going around a certain curve at a speed of 25 km/h has a centripetal force acting on it of 100 N. If the speed of the car is doubled, the centripetal force:
Correct answer: A. Is quadrupled
- A. Is quadrupled
- B. Is doubled
- C. Is multiplied by the √2
- D. Is reduced to ½ of the original value
- E. Is reduced to ⅙ of the original value
Explanation
The centripetal force acting on an object moving in athe circular path is given by the equation: F = (mv^2) / r where F is the centripetal force, m is the mass of theobject, v is the velocity of the object, and r is the radius of the circularpath. If the speed of the car is doubled while maintaining thethe same radius of the curve, the velocity term (v) in the centripetal forcethe equation will become twice its original value. Doubling the velocity will result in the centripetal forceequation becoming: F' = (m(2v)^2) / r = 4(mv^2) / r Therefore, the centripetal force will quadruple (become fourtimes) when the speed of the car is doubled.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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