# Force of friction on a curved road

• stunner5000pt
In summary, the mass m car is traveling at v and its speed is uniformly reduced from A to C until it comes to rest. The problem asks for the magnitude and direction of the total friction force exerted by the road on the car at different points. The solution involves finding the distance AC, acceleration between AC, braking force, velocity at B, lateral acceleration at B, lateral friction force, and adding the lateral and longitudinal components at each point. The minimum coefficient of static friction required for the car to complete the turn at B is also mentioned.
stunner5000pt

## Homework Statement

The mass m car is traveling at v on the straight portion of the road and then its speed is uniformly reduced from A to C, which point it comes to rest. Compute the magnitude and direction of the total friction force F exerted by the road on the car (a) just before it passes point B, (b)
just after it passes point B and (c) just before it stops at point C. (d) What is the minimum
coefficient of static friction required between the tires and the road for the car to be able to complete the turn at B?

2. The attempt at a solution

Part a - the force of friction as it approaches B
I thought about doing this in two steps:
If we assume that the force of friction is $F_{f}$ then the linear acceleration in the straight part is $a = \frac{F_{f}}{m}$

so we can use a kinematic formula to determine the velocity at point B

$$v_{B}^2 = v^2 + 2a d$$
then
$$v_{B}^2 = v^2 - \frac{2 F_{f}}{m}$$

now for the curved section, assuming the road has radius R, the force stays constant, then we can say that the linear acceleration is the same as above. then the angular acceleration is $\alpha = \frac{-F_{f}}{mr}$

then we can use the rotational version of the above kinematic formula. the velocity at c is zero

$$0 = \omega_{B}^2 + 2 \left( \frac{-F_{f}}{mr} \right) \left( \frac{\pi}{6} \right)$$

we can solve for Vb from the above equation
$$v_{B} = \frac{\pi F_{f}}{3mr^3}$$

and then we can substitute the equation just derived into the other expression for vb found above. But is this correct?
What about the curved section? IN the curved section, does the sum of the components of friction (caused by the tangential and normal components) the same as the friction we just calculated? In that case, isn't the answer for b and c the same?

Thanks for your help and input!

#### Attachments

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1. Find the distance AC (as if it was a straight path);
2. With your first equation of motion, find the acceleration between AC;
3. You can then find the (constant) braking force, i.e. the longitudinal component of the friction force;
4. With your first equation of motion, find the velocity at B;
5. With the velocity at B, you can find the lateral acceleration at that point;
6. With F=ma, you can then find the lateral friction force;
7. Add the lateral and longitudinal components at each point (VC ≠ VB) to find the total force. HINT: Forces are vectors.

## What is friction on a curved road?

Friction on a curved road is the force that resists the motion of a vehicle as it travels along a curved path.

## What causes friction on a curved road?

The friction on a curved road is caused by the interaction between the tires of the vehicle and the surface of the road. As the vehicle turns, the tires must change direction, creating a force that opposes the motion and causes friction.

## How does friction affect a vehicle on a curved road?

Friction on a curved road can affect a vehicle in several ways. It can cause the tires to slip, resulting in a loss of control. It can also slow down the vehicle's speed and increase the wear and tear on the tires.

## How can the force of friction on a curved road be reduced?

The force of friction on a curved road can be reduced by using tires with good traction, maintaining a proper speed, and ensuring that the tires are properly inflated. Additionally, smoother road surfaces and proper road maintenance can also help reduce friction.

## How is the force of friction on a curved road calculated?

The force of friction on a curved road is calculated by multiplying the coefficient of friction between the tires and the road surface by the normal force exerted on the tires. The normal force is the force that the road surface exerts on the tires in a perpendicular direction.

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