Question

State the equation used to calculate an object's kinetic energy. Define the symbols used in the equation. Which variable has a larger effect on kinetic energy when it is doubled?

Short answer

Kinetic energy (KE) is calculated by the equation \( KE = \frac{1}{2}mv^2 \). Velocity (\

Step-by-step solution

Write the Kinetic Energy Equation

The equation for calculating an object's kinetic energy (KE) is given by: \[ KE = \frac{1}{2}mv^2 \] where 'm' stands for mass of the object, and 'v' represents the velocity of the object.

Define the Symbols

In the equation \( KE = \frac{1}{2}mv^2 \), 'm' is the mass of the object measured in kilograms (kg), 'v' is the velocity of the object measured in meters per second (m/s), and KE is the kinetic energy measured in joules (J).

Analyzing the Effect of Doubling Variables

Since kinetic energy is proportional to the mass (m) and the square of the velocity (v^2), when either of these variables is doubled, the effect on the kinetic energy differs. Doubling the mass (2m) would just double the kinetic energy, whereas doubling the velocity (2v) would increase the kinetic energy by a factor of four, since \((2v)^2 = 4v^2\).

Key concepts

Kinetic Energy

Kinetic energy (KE) is the energy an object possesses due to its motion. It’s a fundamental concept in physics illustrating how an object in motion can do work by applying force to another object. For instance, a rolling ball can push another ball into motion upon impact. The kinetic energy of an object increases with its speed and its mass.

To simply put, the faster an object moves, or the heavier it is, the more kinetic energy it has. This is why heavy trucks cause much more damage than small cars at the same speed during an accident – the truck has more kinetic energy because of its larger mass.

Mass and Velocity Relationship

The relationship between mass and velocity in the context of kinetic energy is pivotal. Mass (m) is a measure of how much matter an object contains, while velocity (v) is the speed of the object in a specific direction.

• Mass is linearly proportional to kinetic energy, meaning that if you doubled the mass of an object while keeping the velocity constant, the kinetic energy would also double.
• Velocity, however, has a squared relationship with kinetic energy. This means that any change in velocity has a significantly larger impact on kinetic energy. If you double the velocity, kinetic energy increases by a factor of four since kinetic energy is proportional to the square of velocity.

This distinction is crucial when considering how different factors affect the energy of moving objects and stays fundamental in practices such as engineering and safety calculations. Understanding this relationship helps in predicting the effects of changes in an object's speed or mass.

Calculating Kinetic Energy

The process of calculating kinetic energy is straightforward using the formula: \[ KE = \frac{1}{2}mv^2 \] In this equation, 'm' represents the object’s mass in kilograms (kg), 'v' is the object’s velocity in meters per second (m/s), and the result, KE, is the object’s kinetic energy in joules (J).

For example, if a car (mass = 1000 kg) is moving at a velocity of 20 m/s, its kinetic energy can be found as follows: \[ KE = \frac{1}{2} \times 1000 \text{ kg} \times (20 \text{ m/s})^2 \] \[ KE = 200000 \text{ J} \] This computation illustrates that both mass and velocity are equally important in determining kinetic energy; however, because velocity is squared in the equation, its effect on the kinetic energy is more significant when it changes.