Question

A 1500 kg car drives around a flat 200 m diameter circular track at 25 m/s. what are the magnitude and direction of the net force on the car? What causes this force?

Answer 1

Concepts and reason

The concept of centripetal force is required to solve the problem.

Initially, find out the radius of the circular track. Finally, use that radius to find out the centripetal force using its formula.

Fundamentals

A centripetal force is a force that makes a body follows a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the center of curvature of the path.

The expression of the centripetal force is given as follows:

$F = \frac{{m{v^2}}}{r}$

Here, m is the mass of an object, v is the speed and r is the radius of circular track.

The radius of the circular track is given as follows:

$r = \frac{d}{2}$

Here, d is the diameter of the circular track.

Substitute 200 m for d in equation $r = \frac{d}{2}$ .

$\begin{array}{c}\\r = \frac{{200{\rm{ m}}}}{2}\\\\ = 100{\rm{ m}}\\\end{array}$

Substitute 1500 kg for m, 100 m for r and 25 m/s for v in the expression $F = \frac{{m{v^2}}}{r}$ .

$\begin{array}{c}\\F = \frac{{\left( {1500{\rm{ kg}}} \right){{\left( {25{\rm{ m/s}}} \right)}^2}}}{{100{\rm{ m}}}}\\\\ = 9375{\rm{ m}}\\\end{array}$

The centripetal force acts towards the center. To balance the outside friction force from the ground, centripetal force acts towards the center.

Ans:

The magnitude of the net force is 9375 N and direction is towards center.