Understanding and Solving a Momentum Problem: A 1200 kg Car and a 4600 kg Truck Collision

Introduction to Momentum

Momentum is a fundamental concept in physics, representing the quantity of motion an object possesses. It is defined as the product of an object's mass and its velocity. This article will delve into a problem that involves the conservation of momentum in a collision scenario. We will explore the physics behind the interaction of a 1200 kg car moving east at 13 m/s and a 4600 kg truck traveling west at 16 m/s. Post-collision, the car bounces off the truck with a velocity of -9 m/s. The goal is to determine the velocity of the truck after the collision.

Conservation of Momentum Principle

The principle of conservation of momentum states that in a closed system, the total momentum before a collision remains the same as the total momentum after the collision, assuming no external forces act on the system. This principle is essential for solving such problems and understanding the dynamics of collisions. In mathematical terms, the conservation of momentum can be expressed as:

Momentum Before Collision Momentum After Collision

Or:

mvinitial mvfinal

Setting Up the Equation

Let's begin by defining the variables:

Mcar 1200 kg (mass of the car) Mtruck 4600 kg (mass of the truck) vcar, initial 13 m/s (initial velocity of the car – east is positive direction) vtruck, initial -16 m/s (initial velocity of the truck – west is negative direction) vcar, final -9 m/s (final velocity of the car) vtruck, final ? (final velocity of the truck – to be calculated)

Applying the Conservation of Momentum

Using the conservation of momentum principle, we write the equation as:

Mcar * vcar, initial Mtruck * vtruck, initial Mcar * vcar, final Mtruck * vtruck, final

Substituting the values:

1200 * 13 4600 * (-16) 1200 * (-9) 4600 * vtruck, final

Let's solve for vtruck, final.

Solving the Problem

First, calculate the initial momentum of the system:

Initial momentum (1200 kg * 13 m/s) (4600 kg * -16 m/s)

Initial momentum 15600 kg*m/s (-73600 kg*m/s)

Initial momentum -58000 kg*m/s

Now, apply the conservation of momentum:

-58000 kg*m/s 1200 kg * (-9 m/s) 4600 kg * vtruck, final

-58000 kg*m/s -10800 kg*m/s 4600 kg * vtruck, final

-58000 kg*m/s 10800 kg*m/s 4600 kg * vtruck, final

-47200 kg*m/s 4600 kg * vtruck, final

vtruck, final -47200 kg*m/s ÷ 4600 kg

vtruck, final -10.26 m/s

Interpretation of the Result

The final velocity of the truck is -10.26 m/s, which indicates that the truck bounces off in a northeastern direction after the collision (considering the east direction as positive).

Conclusion

In this article, we explored how to apply the principle of conservation of momentum to solve a physics problem involving a collision between a car and a truck. We used the conservation of momentum equation to calculate the final velocity of the truck. This is a practical application of physics in everyday scenarios, showcasing how basic principles can be used to understand complex interactions.

Related Keywords

Momentum, conservation of momentum, collision physics