A car of mass $m = 100 k g$ , traveling over a convex bridge at certain speed, loses all its weight at the middle of the bridge. What will be its weight in the middle of a concave bridge of same radius raveling at the same speed?

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Solution

On convex surface,
$F_{N} = m g - \frac{m v^{2}}{r}$
As per question, $F_{N} = 0$
$\Rightarrow m g = \frac{m v^{2}}{r}$
On concave surface,
$F_{N} = \frac{m v^{2}}{r} + m g$
$A = 2 m g = 2 \times 100 \times 9.8 = 980 \times 2 = 1960 N$

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A car of mass m=100kg, traveling over a convex bridge at certain speed, loses all its weight at the middle of the bridge. What will be its weight in the middle of a concave bridge of same radius raveling at the same speed?

On convex surface,FN=mg−mv2rAs per question, FN=0⇒mg=mv2rOn concave surface,FN=mv2r+mgA=2mg=2×100×9.8=980×2=1960N

A car of mass $m = 100 k g$ , traveling over a convex bridge at certain speed, loses all its weight at the middle of the bridge. What will be its weight in the middle of a concave bridge of same radius raveling at the same speed?

On convex surface,
$F_{N} = m g - \frac{m v^{2}}{r}$
As per question, $F_{N} = 0$
$\Rightarrow m g = \frac{m v^{2}}{r}$
On concave surface,
$F_{N} = \frac{m v^{2}}{r} + m g$
$A = 2 m g = 2 \times 100 \times 9.8 = 980 \times 2 = 1960 N$