How much force do you have to exert on a \(3-\mathrm{kg}\) brick to give it an acceleration of \(2 \mathrm{~m} / \mathrm{s}^{2}\) ? If you double this force, what is the brick's acceleration? Explain.

Understanding how to calculate force is fundamental in physics, especially when dealing with objects in motion. According to Newton's second law of motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration, which is expressed in the equation:
\[\begin{equation}F = m \times a\tag{1}ewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewline.ewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewline.ewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewlineewline.ewlineewlineewlineewlineewlineewline.ewlineewlineewline.ewlineewlineewline.ewlineewline.ewlineewline.ewlineewline.ewlineewline.ewline.ewline.ewline.ewline.ewline..\end{equation}\] In the textbook problem presented, we know the mass of the brick is 3 kg, and the desired acceleration is 2 m/s². Simply by plugging these values into equation (1), we can calculate the force required to achieve this acceleration.
Through understanding and applying this force calculation, students can tackle a wide range of physics problems involving motion. It’s important to remember that force is measured in Newtons (N), which are derive from the formula where 1 N = 1 kg \times m/s².

Mass and acceleration are two other key concepts in Newton's second law. Mass refers to the amount of matter contained in an object, and is measured in kilograms (kg) in the International System of Units (SI). Acceleration, on the other hand, signifies the rate at which an object’s velocity changes over time, quantified in meters per second squared (m/s²).

Relation Between Mass and Acceleration

The relationship between mass and acceleration in the context of force is an inverse one. This means that when force is constant, an increase in mass results in a decrease in acceleration, and vice versa. It's crucial to understand that acceleration is directly proportional to force, while inversely proportional to the mass, as seen in the equation provided earlier (1). In the example problem, the initial acceleration was given, and the mass was known, allowing us to calculate the force. If the force is altered, as it is when doubled in the second part of the problem, the acceleration accordingly changes, showcasing the direct proportionality in action.
When students grasp this concept, they can analyze how different weights (masses) affect the motion of objects under the same amount of force, leading to a deeper understanding of motion dynamics in the physical world.

Problem-solving is an essential skill in physics as it allows students to apply theoretical concepts to practical situations. A robust strategy is to break down problems into smaller, more manageable steps and systematically apply physics principles. For instance, let’s revisit our original problem with these steps:

Step-by-Step Approach

Firstly, identify the known quantities and the physical principles involved. In our example, the mass of the brick and the desired acceleration were known, and the applicable principle was Newton's second law of motion. Secondly, recognize what needs to be solved; in this case, force and then, by altering it, the resultant acceleration. Thirdly, apply the appropriate equation, which for force is expressed as equation (1), and for finding acceleration when force is given and mass is known, rearrange the equation to find acceleration. Lastly, substitute the known values into the equation and solve for the unknown.Through this structured method, students are guided on how to effectively deconstruct and solve a range of physics problems. Regular practice with different scenarios reinforces their understanding and ability to apply these concepts flexibly. Physics problems can often seem daunting, but by breaking them down, applying laws and formulas correctly, and carrying out calculations carefully, any student can master the art of physics problem-solving.