Calculating the Mass of the Train

Oct 13, 2025 by leolavanderia.com.br 131 views

Introduction

In physics, the relationship between force, mass, and acceleration is governed by Newton's second law of motion. This law states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. In this article, we will use this law to calculate the mass of a train that is decelerating at a rate of 0.5 m s⁻² due to a resultant braking force of 88 kN.

Newton's Second Law of Motion

Newton's second law of motion is a fundamental concept in physics that describes the relationship between force, mass, and acceleration. The law is often expressed mathematically as:

F = ma

Where:

F is the net force acting on an object
m is the mass of the object
a is the acceleration of the object

Calculating the Mass of the Train

To calculate the mass of the train, we can rearrange the equation F = ma to solve for mass:

m = F / a

We are given the resultant braking force (F) as 88 kN and the deceleration (a) as 0.5 m s⁻². We can now substitute these values into the equation to calculate the mass of the train:

m = 88,000 N / 0.5 m s⁻²

Converting Units

Before we can calculate the mass of the train, we need to convert the units of the braking force from kilonewtons (kN) to newtons (N). We can do this by multiplying the braking force by 1000:

88,000 kN x 1000 = 88,000,000 N

Now we can substitute this value into the equation:

m = 88,000,000 N / 0.5 m s⁻²

Performing the Calculation

Now we can perform the calculation to find the mass of the train:

m = 88,000,000 N / 0.5 m s⁻² m = 176,000,000 kg

Converting to Tonnes

To express the mass of the train in tonnes, we need to convert the mass from kilograms (kg) to tonnes (t). We can do this by dividing the mass by 1000:

m = 176,000,000 kg / 1000 m = 176,000 t

Rounding to Two Significant Figures

Finally, we need to round the mass of the train to two significant figures. This means that we will round the mass to the nearest hundred:

m = 180,000 t

Conclusion

In this article, we used Newton's second law of motion to calculate the mass of a train that is decelerating at a rate of 0.5 m s⁻² due to a resultant braking force of 88 kN. We found that the mass of the train is approximately 180,000 tonnes.

References

Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica.
Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.