Question

A car moves at speed v across a bridge made in the shape of a circular arc of radius r. (a) Find an expression for the normal force n acting on the car when it is at the top of the arc. (Use any variable or symbol stated above along with the following as necessary: m and g.) n

Answer 1

Answer:

$n=m(g-\frac{v^{2}}{r})$

Step-by-step explanation:

If a car is moving across a circular bridge, made in the shape of a circular arc then the force that balances the car when it is on the top of arc will be

n + F = mg

Where n = normal force acting on the car

F = centripetal force

m = mass of the car

We know centripetal force  $F=\frac{mv^{2}}{r}$

where m = mass of the car

v = velocity of the car on the top of the arc

r = radius of the arc

Therefore, the expression for the normal force 'n' will be

$n+\frac{mv^{2}}{r}=mg$

$n=mg-\frac{mv^{2}}{r}$

$n=m(g-\frac{v^{2}}{r})$