A cyclist turns around a curve at 15miles/hour. If he turns at double the speed, the tendency to overturn is
Correct answer: A. Quadrupled
- A. Quadrupled
- B. Halved
- C. Unchanged
- D. Doubled
Explanation
Option A is correct.If a cyclist turns around a curve at double the speed, the tendency to overturn is quadrupled. The tendency to overturn is determined by the centripetal force, which is the force that keeps the cyclist moving in a circular path. The centripetal force is given by the following equation: F_c = mv²/r where: F_c is the centripetal force (N) m is the mass of the cyclist (kg) v is the speed of the cyclist (m/s) r is the radius of the curve (m) The greater the centripetal force, the greater the tendency to overturn. When the cyclist turns at double the speed, the centripetal force is quadrupled. This is because the speed is squared in the equation for centripetal force. Here is a mathematical explanation: Let the position vector at any time t be r, the instantaneous velocity be v, and the linear momentum be mv. The net force on the cyclist is mv^2/r. This is necessary to keep the cyclist moving in a circular path. When the cyclist turns at double the speed, the net force is quadrupled. Therefore, the tendency to overturn is quadrupled.
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