Chapter 5, Problem 2Q

A car rounds a curve at a steady 50 km/h. If it rounds the same curve at a steady 70 km/h, will its acceleration be any different? Explain.

To determine

To Explain: A car rounds a curve at a steady $\text{50km/h}$ . Whether there will be any difference if it rounds the same curve at a steady $\text{70km/h}\text{.}$

Answer to Problem 2Q

Solution:

We know that acceleration (centripetal) is given by $\frac{v^2}{R}$ , centripetal acceleration of car moving with $50\text{km/h}$ is less than the acceleration of car moving with $\text{70km/h}\text{.}$

Explanation of Solution

Given:

A car moves on the same curve with different speed.

Formula Used:

If a body moves on a circular path with steady speed v, then centripetal acceleration is $\frac{v^2}{R}$ .

Where v : speed of the body

R radius of the circular path

Calculation:

Centripetal acceleration when the car is moving with speed $v_1\text{=}\text{50 km/h}$

  $=\frac{{\left(v_1\right)}^2}{R}$

Centripetal acceleration of car when is moving with speed ${\text{v}}_{\text{2}}\text{=70km/h}$

  $=\frac{v_2{}^2}{R}$

Hence in both the cases, centripetal acceleration is not same, but in the first $\left(\text{50km/h}\right)$ magnitude of centripetal acceleration is less than second $\left(\text{70km/h}\right)\text{.}$

Conclusion:

A car moving on circular track. Its centripetal acceleration will change if its speed will change.

Centripetal acceleration $=\frac{v^2}{R}$

v : speed of the body

R : radius of the circular path.