Calculate the magnitude of force required to stop a car

Enter the mass of the car, the initial velocity or current velocity, and the stopping distance to determine the braking force.

Braking Force Formula

The following formula is used to calculate the braking force of a car given a speed, weight, and stopping distance.

• Where F is the required force to stop in distance d
• m is the mass of the car
• v is the velocity of the car before braking
• d is the stopping distance

To calculate the braking force, divide the mass by 2, multiply by the result of the velocity squared, then divide by the distance.

Braking Force Definition

Alternatively known as Brake Power, the braking force refers to the total amount of force exerted on a moving body that causes it to slow to a halt.

The body—or the vehicle—must be traveling at a known constant velocity for this force to be calculated correctly. The brake force is measured in newtons “N.”

In this article, we explain this force in-depth as well as other related terms.

How Does Motion Stop?

Brakes mostly employ friction to stop motion. Friction is caused by the abrasion of two surfaces (even air) together.

Brakes are very important. They’re what you use to control when to stop your vehicle and when to start moving again.

What Is the Stopping Force and the Stopping Distance?

Wondering what these two terms mean? Well, here’s a quick comparison.

Stopping Force

For a vehicle to stop, there has to be an opposing force applied to it. This force is called the stopping force.

It’s simply the force large enough that can make a moving object halt.

Stopping Distance

When one applies the stopping force, the moving body doesn’t stop all at once. It takes a certain distance to halt, and this distance is called the stopping distance. This term can also be referred to as the “braking distance.”

In some cases, though, both have separate definitions. In an emergency, when a driver is forced to stop the car, the stopping distance is equal to the thinking distance added to the braking distance.

What Two Factors Affect Stopping Distance?

The braking distance depends on two aspects: speed and drag.

The speed of the vehicle is what decides the length of braking distance and also the braking force.

Drag is the measure of resistance of an object on air or water. It’s a unitless quantity defined by the size and shape of the object and the speed of the object and the air.

How Do You Calculate the Braking Force?

For us to calculate the braking force, we must first know the moving body’s constant speed, weight, and stopping distance. After acquiring these factors, apply the equation:

Kinetic Energy = Force x Distance

First, we calculate the kinetic energy. For the brake to stop a car, the kinetic energy has to be a zero. And so, the car’s speed and weight (divided by the value of gravity) are used to calculate it: ½ x Mass x Velocity2

Once you calculate the kinetic energy, you get the force by dividing the kinetic energy value by the traveled distance.

The accuracy of these calculations is limited by several conditions, though. If the surface of the road is icy or wet, such parameters can change completely.

What Is the Maximum Braking Force?

The maximum braking force is the total amount of force used to stop a moving object, just before it can torque out of control. For example, on icy roads, maximum braking forces occur just at the point of sliding.

It can be calculated by multiplying the “coefficient of road adhesion” to the weight of the vehicle. The coefficient of road adhesion is the maximum value of friction present on that road.

Wrap Up

Braking force is one of the most important terms in the world of dynamic physics. Hopefully, now you know what it means and how you can calculate it.

How to calculate braking force?

Example Problem #1

The first step to calculating braking force is to determine the mass of the car. For this example, we will say the car is an even 15,000 kg.

Next, the current velocity of the car must be measured. For this problem, the car is found to be traveling at 25m/s.

Next, determine the stopping distance. Since a different force would be required to stop the car at different distances, this is a key variable to know. In this problem we want the car to stop in 25m.

Finally, calculate the braking force using the formula above.

F = (.5*15,000*25^2) / 25

= 187,500 N = 187.5 kN

Example #2

In this next example, we will explore how the braking distance changes the force required. So, we will take the mass and the velocity of the problem above, 15,000kg and 25m/s respectively, but the braking distance is now 100m.

Using the formula, we analyze the change in force.

F = (.5*15,000*25^2)/100

= 46,875 N

This may not be immediately apparent to your eye, but the stopping force is exactly 1/4 of that from example 1 because the stopping distance is 4 times that from example 1.

In other words, the stopping distance is inversely proportional to the braking force.

You've got an object being acted upon by 4000 lb force downwards, and a normal force up and to the right at a five degree angle from the vertical, and a value equal to the amount of gravitational force acting in the line perpendicular to the slope. For simplicity, we can then translate this by rotating it five degrees, so that the normal force acts vertically and the gravitational force is sloped five degrees to the right.

You can calculate this value by drawing a right triangle with the gravitational force on the hypotenuse and the x and y components of the force on the other two sides of the triangle. The vertical component is equal to the normal force, in the opposite direction, while the horizontal component is equal to the amount of force pulling the car down the slope. We can then use trigonometry to calculate this; sin = opposite over hypotenuse, and we want to work out the opposite side given the values of the hypotenuse and angle, so sin (5 degrees) = opposite/4000, and therefore the horizontal value of the force is 4000 sin (5 degrees).

We can therefore state that the force needed to stop it sliding down the cliff, in the original coordinate scheme, is 4000 sin (5 degrees) pounds-force up and to the left at a 5 degree angle.

If we need to work out the vector components for this vector in the original coordinate scheme, we can do the same thing again, with 4000 sin (5) degrees on the hypotenuse of a right triangle with an angle of 5 degrees, the horizontal component on the adjacent side and the vertical component on the opposite side. We can then work out that the horizontal component of the force is cos (5 degrees) = adjacent/4000 sin (5 degrees) and therefore equal to 4000 sin (5 degrees) * cos (5 degrees), while the vertical force is similarly 4000 sin (5 degrees) * sin (5 degrees).