You're driving a vehicle of mass 1240 kg and you need to make a turn on a flat road. The radius of curvature of the turn is 79 meters. the coefficient of static friction and the coefficient of kinetic friction are both 0.2.

To determine the forces acting on the vehicle as it turns on a flat road, we can focus on the relationship between centripetal force and friction. The frictional force provides the necessary centripetal force to keep the vehicle on the curved path. Since the car is turning on a flat road, the friction must be static to prevent the car from sliding.

We can calculate the maximum speed at which the car can make the turn without sliding. The formula for the maximum speed \( v_{\text{max}} \) that the car can achieve without sliding is:

\[
v_{\text{max}} = \sqrt{\mu_s \cdot g \cdot r}
\]

Where:
- \( \mu_s = 0.2 \) is the coefficient of static friction,
- \( g = 9.81 \, \text{m/s}^2 \) is the acceleration due to gravity,
- \( r = 79 \, \text{m} \) is the radius of the turn.

### Step-by-step calculation:

1. **Substitute the known values into the equation**:
\[
v_{\text{max}} = \sqrt{0.2 \cdot 9.81 \, \text{m/s}^2 \cdot 79 \, \text{m}}
\]

2. **Simplify the expression**:
\[
v_{\text{max}} = \sqrt{0.2 \cdot 775.59 \, \text{m}^2/\text{s}^2} = \sqrt{155.118 \, \text{m}^2/\text{s}^2}
\]

3. **Calculate \( v_{\text{max}} \)**:
\[
v_{\text{max}} \approx 12.45 \, \text{m/s}
\]

Thus, the maximum speed the vehicle can achieve without sliding is approximately **12.45 m/s**.

Let me know if you need more details or have further questions!

Here are 5 relative questions to consider:
1. How does the radius of curvature affect the turning speed of the car?
2. What would happen if the coefficient of friction were lower?
3. Can you calculate the required friction coefficient for a higher turning speed?
4. How does kinetic friction affect the scenario if the car begins to skid?
5. What other forces are acting on the car while it makes the turn?

**Tip**: Increasing the frictional force, for example by driving on a rougher surface, would allow the car to make sharper turns at higher speeds!

You're driving a vehicle of mass 1240 kg and you need to make a turn on a flat road. The radius of curvature of the turn is 79 meters. The coefficient of static friction and the coefficient of kinetic friction are both 0.2.

This problem calculates the maximum speed a 1240 kg vehicle can achieve while turning on a flat road with a 79-meter radius without sliding. It explores key concepts in centripetal force, static friction, and physics of motion. Learn how the coefficient of static friction (0.2) and gravity affect the calculation. Suitable for students in Grades 10-12.

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