Calculating the Stopping Force for a Moving Truck

When dealing with the mechanics of a moving truck, one of the key calculations is determining the force necessary to decelerate and stop the vehicle. This involves understanding Newton's second law of motion and the principles of constant acceleration.

Understanding the Problem

The problem presented here deals with a truck of mass 1540 kg traveling at a speed of 95 km/h. The question revolves around the force required to bring the truck to a complete stop in 10 seconds. It's important to first convert the speed into meters per second (m/s) to ensure all units are consistent.

Converting Units and Initial Calculations

Let's begin by converting the speed from km/h to m/s:

95 km/h 95 × 1000/3600 26.39 m/s

Given the constant acceleration, we can use the following formula:

a (final velocity - initial velocity) / time

Here, final velocity 0 m/s, initial velocity 26.39 m/s, and time 10 seconds:

a (0 - 26.39) / 10 -2.64 m/s2

Applying Newton's Second Law of Motion

Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula can be expressed as:

F ma

Where F is the force, m is the mass, and a is the acceleration.

Applying the values:

F 1540 kg × (-2.639 m/s2) -4062.52 N

Note that the negative sign indicates the force is acting in the opposite direction of the truck's movement.

Considering Different Mass and Speed

To explore a different scenario, let's consider a truck with a mass of 3000 kg and an initial velocity of 90 km/h, which needs to stop in 10 seconds.

Converting Units

Similar to the previous example, we need to convert 90 km/h to m/s:

90 km/h 90 × 1000/3600 25 m/s

Calculating the Acceleration

Using the same formula for acceleration:

a (final velocity - initial velocity) / time

Final velocity 0 m/s, initial velocity 25 m/s, and time 10 seconds:

a (0 - 25) / 10 -2.5 m/s2