Chapter 5, Problem 3Q

Will the acceleration of a car be the same when a car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

To determine

To explain:

Whether the acceleration of a car will be the same when a car travels around a sharp curve at a constant $60\text{km/h}$ as when it travels around a gentle curve at the same speed.

Answer to Problem 3Q

Solution:

No, acceleration of a car is not same because the radii of curvatures of circular paths are different because one curve is a sharp curve and another is gentle.

Explanation of Solution

Given:

One curve is sharp, and another is a gentle curve.

Formula used:

The magnitude of centripetal acceleration for a body moving on a circular path $=\frac{v^2}{r}$

v : speed of body on a circular path

r : radius of curvature of the circular path

The sharp curve has a smaller radius of curvature than a gentle curve.

The speed of car in both cases are same so

  $\left(\frac{v^2}{r}\right)\text{sharp}$ >$\left(\frac{v^2}{v}\right)\text{gentle}$

Hence centripetal acceleration for the sharp curve is greater than a gentle curve.

Conclusion:

Acceleration of body moving on a circular path not only depends upon speed but also upon the radius of curvature of the circular path.

  $\text{centripetal}\text{acceleration}\propto \frac{1}{r}$