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Difficulty: MediumSpeed on Curves and Downgrades

If a commercial motor vehicle doubles its travel speed when rounding a highway curve, the centrifugal force acting upon the vehicle increases by a factor of four, requiring four times as much tire traction to avoid skidding or rolling over.

Answer: Answer

Answer

True: doubling vehicle speed quadruples the centrifugal force acting on the vehicle, requiring four times as much tire traction to stay on the road.
Centrifugal force varies directly with the square of the vehicle's velocity (Fc=mv2rF_c = \frac{m v^2}{r}). When a driver doubles vehicle speed from vv to 2v2v, the outward lateral force increases by a factor of (2)2=4(2)^2 = 4. Consequently, the vehicle requires four times greater tire-to-pavement friction to counteract the force and prevent a fatal rollover or skid.

Step-by-Step Solution

1
Identify the physical relationship governing speed and centrifugal force on curved roadways.
Centrifugal force is proportional to the square of velocity (Fc=mv2rF_c = \frac{m v^2}{r}).
Vehicle mass and curve radius remain constant while velocity changes.
2
Calculate the factor by which centrifugal force increases when speed is doubled.
Substituting 2v2v into the velocity term yields (2v)2=4v2(2v)^2 = 4v^2, meaning the lateral force increases by four times.
Quadratic scaling causes outward force to expand rapidly as speed increases.
3
Determine the resulting traction demand on the tires and evaluate the statement.
The tires must supply four times the lateral grip to counteract the quadrupled centrifugal force, verifying the statement as True.
If available tire-road traction is less than the required quadrupled force, the vehicle will skid or roll over.

Key Concept

Quadratic relationship between vehicle speed, centrifugal force, and lateral traction demands in curves.
Estimated Time:1m 0s
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Topics

Speed on Curves and Downgrades

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