Calculating the Applied Force on a Truck Using Newton's Laws

Introduction

In this article, we will discuss the principles of force calculation and kinematics using an example of a truck. We will apply Newton's laws to determine the force applied on the truck that accelerates it from rest over a given distance in a specified time.

Problem Statement

A truck of mass 5000 kg starts from rest and travels a distance of 0.5 km in 10 seconds. To find the force applied on the truck, we will use Newton's second law of motion, which states that F ma.

Step 1: Calculate the Acceleration

To find the force, we first need to determine the acceleration of the truck. We can use the following kinematic equation to find the acceleration:

(d frac{1}{2}a t^2)

Where:

(d) is the distance traveled (0.5 km or 500 m) (t) is the time taken (10 seconds) (a) is the acceleration (to be determined)

Rearranging the equation to solve for acceleration:

(a frac{2d}{t^2})

Substituting the known values:

(a frac{2 times 500}{10^2} 10 text{m/s}^2)

Step 2: Calculate the Force

Now that we have the acceleration, we can use Newton's second law of motion to find the force:

(F ma)

Where:

(m) is the mass of the truck (5000 kg) (a) is the acceleration (10 m/s2)

Substituting the values:

(F 5000 times 10 50000 text{N})

Thus, the force applied on the truck is 50000 Newtons (N).

Using Newton’s Equations of Motion

Newton's three equations of motion are essential tools for solving such problems. The equations are:

(S V_i t frac{1}{2}at^2)

(V_f V_i at)

(V_f^2 V_i^2 2aS)

These equations allow us to solve for unknown variables based on the given values. In this case, we were given the distance traveled, initial velocity, and time. We used the first equation to find the acceleration and then applied Newton's second law to find the force.

Conclusion

In this example, we calculated the force applied on a truck using the principles of kinematics and Newton's laws. The force required to accelerate a 5000 kg truck from rest over 0.5 km in 10 seconds is 50000 Newtons. Understanding these calculations is crucial for various applications, including vehicle dynamics, engineering, and physics.