Answer :
To find the coefficient of friction between the road and the tires of the car when it skids, we'll use the work-energy principle. Here is a step-by-step explanation of how to solve this problem:
1. Understand the Concept:
- The car initially has a certain amount of kinetic energy due to its motion.
- When the brakes are applied and the car skids, work is done by the frictional force to stop the car.
- The work done by the frictional force equals the initial kinetic energy of the car.
2. Calculate the Initial Kinetic Energy:
- The initial kinetic energy (KE_initial) can be calculated using the formula:
[tex]\[
KE_{\text{initial}} = \frac{1}{2} m v^2
\][/tex]
- We need to convert the weight of the car, given in Newtons, into mass. The formula for weight is [tex]\( w = m \cdot g \)[/tex], where [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex] (acceleration due to gravity). So, [tex]\( m = \frac{w}{g} \)[/tex].
3. Calculate the Work Done by Friction:
- The work done by the friction (which stops the car) equals the frictional force multiplied by the distance:
[tex]\[
\text{Work} = \text{frictional force} \times \text{distance} = \text{coefficient of friction} \times \text{weight} \times \text{distance}
\][/tex]
- Therefore, the equation becomes:
[tex]\[
KE_{\text{initial}} = \text{coefficient of friction} \times \text{weight} \times \text{distance}
\][/tex]
4. Solve for the Coefficient of Friction:
- Rearrange the above equation to find the coefficient of friction:
[tex]\[
\text{coefficient of friction} = \frac{KE_{\text{initial}}}{\text{weight} \times \text{distance}}
\][/tex]
5. Substitute the Values:
- With the initial kinetic energy calculated as approximately 173292.56 Joules and given the weight of the car (8500 N) and the distance (200 m), you substitute these values into the equation:
[tex]\[
\text{coefficient of friction} \approx \frac{173292.56}{8500 \times 200} \approx 0.1019
\][/tex]
6. Conclusion:
- The coefficient of friction between the road and the tires is approximately 0.1019, which is closest to option (A) 0.1 in the provided choices.
1. Understand the Concept:
- The car initially has a certain amount of kinetic energy due to its motion.
- When the brakes are applied and the car skids, work is done by the frictional force to stop the car.
- The work done by the frictional force equals the initial kinetic energy of the car.
2. Calculate the Initial Kinetic Energy:
- The initial kinetic energy (KE_initial) can be calculated using the formula:
[tex]\[
KE_{\text{initial}} = \frac{1}{2} m v^2
\][/tex]
- We need to convert the weight of the car, given in Newtons, into mass. The formula for weight is [tex]\( w = m \cdot g \)[/tex], where [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex] (acceleration due to gravity). So, [tex]\( m = \frac{w}{g} \)[/tex].
3. Calculate the Work Done by Friction:
- The work done by the friction (which stops the car) equals the frictional force multiplied by the distance:
[tex]\[
\text{Work} = \text{frictional force} \times \text{distance} = \text{coefficient of friction} \times \text{weight} \times \text{distance}
\][/tex]
- Therefore, the equation becomes:
[tex]\[
KE_{\text{initial}} = \text{coefficient of friction} \times \text{weight} \times \text{distance}
\][/tex]
4. Solve for the Coefficient of Friction:
- Rearrange the above equation to find the coefficient of friction:
[tex]\[
\text{coefficient of friction} = \frac{KE_{\text{initial}}}{\text{weight} \times \text{distance}}
\][/tex]
5. Substitute the Values:
- With the initial kinetic energy calculated as approximately 173292.56 Joules and given the weight of the car (8500 N) and the distance (200 m), you substitute these values into the equation:
[tex]\[
\text{coefficient of friction} \approx \frac{173292.56}{8500 \times 200} \approx 0.1019
\][/tex]
6. Conclusion:
- The coefficient of friction between the road and the tires is approximately 0.1019, which is closest to option (A) 0.1 in the provided choices.
