Calculating the Work Required to Stop the Car

Oct 13, 2025 by miodeya.com 76 views

Introduction

When a car is traveling at a high speed, it possesses a significant amount of kinetic energy. In order to bring the car to a complete stop, a certain amount of work must be done to overcome the kinetic energy. In this article, we will explore the concept of work and kinetic energy, and calculate the amount of work required to stop a $925 \, \text{kg}$ car traveling at $95 \, \text{km/h}$ .

Kinetic Energy

Kinetic energy is the energy of motion, and it is a measure of the energy an object possesses due to its motion. The kinetic energy of an object is given by the equation:

KE = \frac{1}{2}mv^2

where $m$ is the mass of the object and $v$ is its velocity.

Work

Work is the transfer of energy from one object to another through a force applied over a distance. The work done on an object is given by the equation:

W = F \cdot d

where $F$ is the force applied and $d$ is the distance over which the force is applied.

Calculating the Work Required to Stop the Car

To calculate the work required to stop the car, we need to first calculate the kinetic energy of the car. We can do this by plugging in the values for the mass and velocity of the car into the equation for kinetic energy:

KE = \frac{1}{2} \cdot 925 \, \text{kg} \cdot (95 \, \text{km/h})^2

First, we need to convert the velocity from kilometers per hour to meters per second:

95 \, \text{km/h} = 95 \, \text{km/h} \cdot \frac{1000 \, \text{m}}{1 \, \text{km}} \cdot \frac{1 \, \text{h}}{3600 \, \text{s}} = 26.39 \, \text{m/s}

Now we can plug in the values:

KE = \frac{1}{2} \cdot 925 \, \text{kg} \cdot (26.39 \, \text{m/s})^2

KE = \frac{1}{2} \cdot 925 \, \text{kg} \cdot 697.51 \, \text{m}^2/\text{s}^2

KE = 323,511.25 \, \text{J}

Calculating the Force Required to Stop the Car

To calculate the force required to stop the car, we need to use the equation for work:

W = F \cdot d

We know that the work required to stop the car is equal to the kinetic energy of the car, so we can set up the equation:

323,511.25 \, \text{J} = F \cdot d

We also know that the car will come to a complete stop when the force is applied over a distance equal to the stopping distance. The stopping distance is given by the equation:

d = \frac{v^2}{2 \mu g}

where $\mu$ is the coefficient of friction and $g$ is the acceleration due to gravity.

Assuming a coefficient of friction of 0.7 and an acceleration due to gravity of 9.8 m/s^2, we can plug in the values:

d = \frac{(26.39 \, \text{m/s})^2}{2 \cdot 0.7 \cdot 9.8 \, \text{m/s}^2}

d = 20.51 \, \text{m}

Now we can plug in the values for the work and distance into the equation for force:

323,511.25 \, \text{J} = F \cdot 20.51 \, \text{m}

F = \frac{323,511.25 \, \text{J}}{20.51 \, \text{m}}

F = 15,753.19 \, \text{N}

Conclusion

In this article, we calculated the amount of work required to stop a $925 \, \text{kg}$ car traveling at $95 \, \text{km/h}$ . We found that the kinetic energy of the car is $323,511.25 \, \text{J}$ , and the force required to stop the car is $15,753.19 \, \text{N}$ . This demonstrates the importance of considering the kinetic energy of an object when calculating the work required to stop it.

References

Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). John Wiley & Sons.
Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.

Introduction

In our previous article, we explored the concept of work and kinetic energy, and calculated the amount of work required to stop a $925 \, \text{kg}$ car traveling at $95 \, \text{km/h}$ . In this article, we will answer some frequently asked questions related to stopping a car in motion.

Q: What is the main factor that determines the amount of work required to stop a car?

A: The main factor that determines the amount of work required to stop a car is its kinetic energy. The kinetic energy of an object is given by the equation:

KE = \frac{1}{2}mv^2

where $m$ is the mass of the object and $v$ is its velocity.

Q: How does the coefficient of friction affect the amount of work required to stop a car?

A: The coefficient of friction affects the amount of work required to stop a car by determining the stopping distance. The stopping distance is given by the equation:

d = \frac{v^2}{2 \mu g}

where $\mu$ is the coefficient of friction and $g$ is the acceleration due to gravity.

Q: What is the relationship between the force required to stop a car and the kinetic energy of the car?

A: The force required to stop a car is directly proportional to the kinetic energy of the car. The equation for work is:

W = F \cdot d

where $F$ is the force applied and $d$ is the distance over which the force is applied.

Q: Can the amount of work required to stop a car be reduced by using a different type of braking system?

A: Yes, the amount of work required to stop a car can be reduced by using a different type of braking system. For example, using a regenerative braking system can reduce the amount of work required to stop a car by converting some of the kinetic energy into electrical energy.

Q: How does the mass of the car affect the amount of work required to stop it?

A: The mass of the car affects the amount of work required to stop it by determining the kinetic energy of the car. The kinetic energy of an object is given by the equation:

KE = \frac{1}{2}mv^2

where $m$ is the mass of the object and $v$ is its velocity.

Q: Can the amount of work required to stop a car be reduced by using a different type of road surface?

A: Yes, the amount of work required to stop a car can be reduced by using a different type of road surface. For example, using a road surface with a lower coefficient of friction can reduce the amount of work required to stop a car by reducing the stopping distance.

Q: How does the velocity of the car affect the amount of work required to stop it?

A: The velocity of the car affects the amount of work required to stop it by determining the kinetic energy of the car. The kinetic energy of an object is given by the equation:

KE = \frac{1}{2}mv^2

where $m$ is the mass of the object and $v$ is its velocity.

Conclusion

In this article, we answered some frequently asked questions related to stopping a car in motion. We hope that this article has provided you with a better understanding of the concepts involved in stopping a car, and has helped you to answer some of the questions that you may have had.

References

Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.). John Wiley & Sons.
Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (10th ed.). Cengage Learning.