Question

A high-speed railway car goes around a flat, horizontal circle of radius 480 m at a constant speed. The magnitudes of the horizontal and vertical components of the force of the car on a 65.0 kg passenger are 208 N and 637 N, respectively. (a) What is the magnitude of the net force (of all the forces) on the passenger? (b) What is the speed of the car?

Answer 1

Answer:

Net force ( F ) = 208 N.

Speed of car ( v ) = 68.58 m/s.

Explanation:-

The radius ( r ) = 480 m.

Mass of passenger ( m ) = 65 kg.

Horizontal force ( $f_{x}$ ) = 208 N.

Vertical force ( $f_{n}$ ) = 637 N.

Net vertical component of force ( $f_{x}$ ) = m*g - 637   = 65 * 9.8 - 637 =  0 N.

a ) magnitude of net force .

$F = \sqrt{f^{2} _{x} + f^{2} _{y} } = \sqrt{208^{2} + 0^{2} }$   = 208 N.

b) The speed of car.

$f_{n} = \frac{m*v^{2} }{r}$    where v is the velocity.

$637 = \frac{65 *v^{2} }{480}$

v² = 4704

v = 68.58 m/s.