Chapter 5, Problem 26P

For each of the cases described below, sketch and label the total acceleration vector, the radial acceleration vector, and the tangential acceleration vector. (a) A car is accelerating from 55 km/h to 70 km/h as it rounds a curve of constant radius. (b) A car is going a constant 65 km/h as it rounds a curve of constant radius. (c) A car slows down while rounding a curve of constant radius.

To determine

For each of the cases, sketch and label the total acceleration vector, the radial acceleration vector,and the tangential acceleration vector

Explanation of Solution

Given:

a. A car is accelerating from 55 km/h to 70 km/h as it rounds a curve of constant radius.

b. A car is going a constant 65km/h as it rounds a curve of constant radius

c. A car slows down while rounding a curve of constant radius.

Calculations:

1. A car is accelerating from 55km/h to 70 km/h on a circular track will have radial as well tangential accelerations. When a car rounds a curve of constant radius, then the radial acceleration $a_r$ and the tangential acceleration $a_t$ are perpendicular to each other.

Use Pythagorastheorem for total acceleration $a_{total}$ as

  $a_{total}=\sqrt{a_r{}^2+a_t{}^2}$

Now below figure shows, the total acceleration vector, the radial acceleration vector, tangential acceleration vector of a car which is taking anticlockwise turn.

  

2. A car is going at the constant speed of 65km/h on a curve will have only radial acceleration, directed towards the center of the curve in such case it has only radial acceleration.
Now below figure shows the radial acceleration vector of a car.

  

3. As a car slows down while rounding a curve of constant radius, then the tangential acceleration $a_t$will act in opposite direction to the direction of motion of the car.

However, the radial acceleration $a_r$ and the tangential acceleration $a_t$ will be perpendicular to each other.

Use Pythagorastheorem for total acceleration $a_{total}$ as

  $a_{total}=\sqrt{a_r{}^2+a_t{}^2}$

Now below figure shows, the total acceleration vector, the radial acceleration vector, tangential acceleration vector of a car which is taking anticlockwise turn.