Problem 30 - Elementary Algebra

Question

Use numerical evaluation on the equations. Physics (force) \(F=32 m . \) Find \(F\) if \(m=14\)

Step-by-Step Solution

Answer

Answer: The force acting on the object is 448 N.

Step 1: Write down the given values and equation

We are given the mass of the object (m) as 14 kg and the equation for calculating force (F): F = 32m.

Step 2: Substitute the given value into the equation

Now, we will substitute the given mass value (m = 14) into our equation F = 32m. This gives us the equation F = 32 * 14.

Step 3: Calculate the force

To find the force (F), we simply need to multiply the value of 32 by the mass (14). So, F = 32 * 14 = 448 N. Thus, the force acting on the object is 448 N.

Key Concepts

Substitution in Equations

One of the fundamental techniques in algebra is the substitution method. This process involves replacing a variable with its actual value to simplify an equation and solve for another variable. Here's how it works:

Imagine you have an equation and a specific value for a variable within that equation. By substituting the known value into the equation in place of the variable, the equation becomes easier to evaluate. For example, if you have the equation \(F = 32m\) and you know that \(m = 14\), you substitute 14 for \(m\), resulting in \(F = 32 \times 14\). With substitution, you can clearly see how the equation simplifies down to a numerical multiplication, making it much easier to find the solution.

Calculating Force in Physics

In physics, calculating force is often essential. Force quantifies the push or pull on an object, which may cause it to accelerate. One of the most common formulas for calculating force is Newton's second law of motion, which states that \(F = ma\), where \(F\) is the force in newtons (N), \(m\) is the mass in kilograms (kg), and \(a\) is the acceleration in meters per second squared \(m/s^2\).

In the given exercise, the force is given by the equation \(F = 32m\), suggesting that the acceleration due to some force is a constant value of 32 \(m/s^2\). To find the force \(F\) for a mass of 14 kg, you directly apply the formula, resulting in \(F = 32 \times 14\). This calculation returns the force in newtons, giving a straightforward method to approach such physics problems.

Unit Conversion

Unit conversion is a critical skill in both mathematics and science, allowing you to convert from one system of measurement to another. Consider this: different countries and disciplines use different units, so being able to convert between them is essential for clear, universal understanding and for checking the coherency of an equation or computation.

For instance, in the United States, force might be commonly expressed in pounds of force, while internationallly, newtons are the standard unit of force. To convert from one to another, you’d use a conversion factor, such as 1 pound of force equals approximately 4.44822 newtons. Understanding and correctly applying unit conversion ensures that your computations are accurate and applicable in different contexts and prevents potential misunderstandings when communicating your results.