A 2,000 kg car runs around a track at 10 m/s with a centripetal acceleration of 4 m/s². What is the radius of the track?

Question

A 2,000 kg car runs around a track at 10 m/s with a centripetal acceleration of 4 m/s². What is the radius of the track??  
A. 1,000 m  
B. 400 m  
C. 25 m  
D. 12 m

Accepted Answer

Correct Answer: (C)25 m. 
Rationale: The radius of the track is 25 m.In uniform circular motion, centripetal acceleration depends on the speed of the object and the radius of the circular path. The relationship is given by:centripetal acceleration = speed squared ÷ radiuswhere a is the centripetal acceleration, v is the speed, and r is the radius. Rearranging this equation allows the radius to be calculated directly from the given speed and acceleration. The mass of the car does not affect the radius in this kinematic relationship.A) 1,000 mThis value might result from incorrectly including the mass of the car in the calculation. In centripetal motion, mass cancels out when determining radius from speed and acceleration, so using mass here leads to an exaggerated and incorrect value.B) 400 mThis option reflects an incorrect manipulation of the formula, such as inverting the relationship to radius = acceleration ÷ speed squared, or mishandling units. Applying the correct formula does not produce this result.C) 25 mUsing the centripetal acceleration formula:radius = speed squared ÷ centripetal accelerationradius = (10 m per second) squared ÷ 4 m per second squaredradius = 100 ÷ 4radius = 25 mThis calculation correctly applies the physics of circular motion and shows that the radius depends only on speed and centripetal acceleration.D) 12 mThis value appears to be an arbitrary reduction of the correct radius without any basis in the formula for centripetal acceleration. It does not follow from the given data.ConclusionCentripetal acceleration is related to speed and radius by centripetal acceleration = speed squared ÷ radius. Substituting the given values yields a radius of 25 m, demonstrating that the mass of the car is irrelevant in this calculation.

A 2,000 kg car runs around a track at 10 m/s with a centripetal acceleration of 4 m/s². What is the radius of the track?

A
1,000 m

B
400 m

C
25 m

D
12 m

The radius of the track is 25 m.

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Related Questions

A 2,000 kg car runs around a track at 10 m/s with a centripetal acceleration of 4 m/s². What is the radius of the track?

A 1,000 m B 400 m C 25 m D 12 m

The radius of the track is 25 m.

Topic Flashcards

Mini Quiz

Related Questions

A
1,000 m

B
400 m

C
25 m

D
12 m