Question

A truck initially traveling at \(60 \mathrm{~km} / \mathrm{h}\) is brought to a complete stop at a traffic light. Does this change violate the law of conservation of energy? Explain.

Short answer

Stopping the truck transforms kinetic energy to other forms, preserving energy.

Step-by-step solution

Understand the Problem

We need to determine if stopping the truck, which initially travels at 60 km/h, violates the law of conservation of energy. This law states that the total energy in an isolated system remains constant, though it can change forms.

Identify Initial Energy

Initially, the truck has kinetic energy due to its motion. The formula for kinetic energy is \( KE = \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity. At 60 km/h, the truck's kinetic energy is transformed as it stops.

Analyze the Transformation

As the truck comes to a stop, its kinetic energy is reduced to zero. According to the conservation of energy, this energy must be transferred or transformed, not lost. Possible transformations include heat due to friction, sound, or deformation upon stopping.

Conclusion on Energy Conservation

Stopping the truck does not violate the law of conservation of energy because the initial kinetic energy is converted into other forms such as heat and sound rather than disappearing. Thus, energy is conserved in the process.

Key concepts

Kinetic Energy

Kinetic energy is a type of energy that objects possess due to their motion. When something is moving, like a car or a truck, it has the ability to do work. This is because the moving object can apply a force to other objects and cause a change. The formula to calculate kinetic energy is given by \( KE = \frac{1}{2}mv^2 \), where \( m \) refers to the mass of the object, and \( v \) is its velocity.
This formula tells us a few important things:

• Firstly, the kinetic energy increases with the square of the velocity. This means that if you double the speed of the vehicle, its kinetic energy becomes four times greater.
• Secondly, a heavier object will carry more kinetic energy at the same speed as a lighter one.

When a truck travels at a particular speed, it holds kinetic energy due to its mass and velocity. As it stops, this energy doesn't just vanish; instead, it gets transformed into other energies.

Forms of Energy

Energy exists in many forms and can be transferred from one form to another. Some of the most common forms of energy include:

• Kinetic Energy: Energy due to motion, as seen in moving vehicles or running water.
• Potential Energy: This is stored energy based on position, like water held behind a dam.
• Thermal Energy (Heat): Generated by the movement of particles within an object, usually due to friction.
• Sound Energy: Produced by vibrating objects and transmitted through mediums like air or water.
• Electrical Energy: Associated with electric charges and currents.

When an object like a truck stops moving, its kinetic energy is often converted into thermal energy and sound energy, due to friction and vibration, respectively. Understanding these forms helps us see how energy flows and transforms in real-life situations.

Energy Transformation

Energy transformation is the process of changing energy from one form to another. This is a key aspect of the law of conservation of energy. In the example of a stopping truck, the situation provides a clear picture of how energy is transferred.
As the truck comes to a stop, its kinetic energy is converted into:

• Thermal Energy: The brakes of the truck generate heat as they apply friction to the wheels. This heat energy is the largest recipient of the truck’s initial kinetic energy.
• Sound Energy: The screeching noise you might hear when the brakes are applied is a product of energy being converted into sound.
• Deformation Energy: If there is any noticeable change in shape or structure during the stop, this energy goes into bending or deforming materials.

This process shows that even though the truck stops completely, the energy it had doesn’t disappear but instead is transferred into these forms. Such transformations are happening all around us, highlighting the amazing journey of energy from one state to another.