• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

### Select your language

Suggested languages for you:

Americas

Europe

Q10.

Expert-verified
Found in: Page 130

### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

### Answers without the blur.

Just sign up for free and you're in.

# A car maintains a constant speed v as it traverses the hill and valley shown in Fig. 5–34. Both the hill and valley have a radius of curvature R. At which point, A, B, or C, is the normal force acting on the car (a) the largest, (b) the smallest? Explain. (c) Where would the driver feel heaviest and (d) lightest? Explain. (e) How fast can the car go without losing contact with the road at A?

The normal force will be largest and smallest at point C and A, the driver feel the heaviest and lightest at point C and A, and the fastest speed of the car is $v=\sqrt{gR}$.

See the step by step solution

## Step 1. Given Data

The constant speed of the car is $v$.

The radius of curvature is $R$.

## Step 2. Understanding the normal forces

In this problem, for determining the largest and smallest normal forces exerting on the car, the centripetal force should be directed upwards.

## Step 3. Evaluating the point at which normal force acting on the car is largest

The normal force will be largest at point C because the direction of centripetal force is upwards and to provide the net upward force the normal force should be more than the weight of the car.

## Step 4. Evaluating the point at which normal force acting on the car is smallest

The normal force exerting on the car is lowest at the topmost point of the hill, point A. The centripetal force in this case is directed towards the centre that is downwards, hence the weight of car will be more than the normal force.

## Step 5. Evaluating the point at which the driver feels the heaviest

At the point C, the driver of the car will feel the heaviest because as mentioned in the above part the normal force is highest at this point.

## Step 6. Evaluating the point at which the driver feels the lightest

At the point A, the driver of the car will feel the lightest because as mentioned in the above part the normal force is lowest at this point.

## Step 7. Evaluating the fastest speed of the car without losing the contact with the road at point A

The maximum speed of the car without losing contact with the road is achieved at the point where the car almost loses the contact with the road related to the normal force. In this condition, the normal force will be zero.

The relation of vertical forces acting on the car is given by,

$\begin{array}{c}F=ma\\ mg-N=m\left(\frac{{v}^{2}}{R}\right)\end{array}$

On plugging the values in the above relation.

$\begin{array}{c}mg-0=m\left(\frac{{v}^{2}}{R}\right)\\ v=\sqrt{gR}\end{array}$

Thus, $v=\sqrt{gR}$ is the fastest speed of the car.

### Want to see more solutions like these?

Sign up for free to discover our expert answers

## Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.