{"id":51182,"date":"2025-08-25T04:39:04","date_gmt":"2025-08-24T19:39:04","guid":{"rendered":"https:\/\/phys-edu.net\/wp\/?p=51182"},"modified":"2025-08-25T04:40:16","modified_gmt":"2025-08-24T19:40:16","slug":"from-tablecloth-tricks-to-rockets-the-fascinating-world-of-the-equation-of-motion","status":"publish","type":"post","link":"https:\/\/phys-edu.net\/wp\/?p=51182&lang=en","title":{"rendered":"From Tablecloth Tricks to Rockets! The Fascinating World of the “Equation of Motion”"},"content":{"rendered":"

I’m Ken Kuwako, a science trainer. Every day is an experiment. <\/p>\n

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Equation of Motion: F=ma<\/p><\/div>\n

This article is also available as a podcast!<\/a><\/p>\n

Have you ever seen the formula “F = ma”? It’s the equation of motion, one of the most famous formulas in high school physics.<\/p>\n

We use the word “force” every day, but what exactly is it? For example, could you explain “force” in simple terms to a small child? This is the first question I ask my students in class. It’s surprisingly difficult to describe an intangible concept like “force” with just words. However, the equation of motion was created precisely to define what force is.<\/p>\n

Imagine this. You’re on an ice-skating rink, and you, being a bit of a prankster, give a child a push from behind. The child glides forward smoothly, right? This shows that the “force” you applied changed (accelerated) the child’s velocity. The “F” on the right side of the equation of motion represents the force applied, and the “a” on the left side represents acceleration. In other words, the equation of motion defines that “force is the ability to accelerate an object.”<\/p>\n

Besides “F,” this equation also includes the symbol “m,” which stands for mass. Why is mass relevant? Let’s go back to the same ice rink and this time, push a heavier adult instead of the child. You’ll find it’s harder to get the adult moving, meaning they accelerate less. This is because acceleration “a” and mass “m” are inversely proportional.<\/p>\n

If you solve the equation of motion (F = ma) for acceleration (a), you get the following:<\/p>\n

a<\/span>=\u00a0 <\/span><\/span>F \/ m<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n

Looking at this equation, it’s obvious that since mass (m) is in the denominator, the larger the mass, the harder it is to accelerate.<\/p>\n

The Unit of Force: The Newton<\/h3>\n

In our daily lives, we have an intuitive sense of how strong a force is. But since this feeling is subjective, we can’t compare forces accurately. That’s why in the world of physics, the equation of motion is used to define the magnitude of force.<\/p>\n

A Newton (N) is defined as the force required to accelerate a 1 kg object at a rate of 1 m\/s\u00b2.<\/p>\n

It’s important to have a feel for what a “Newton” is. Let’s look at some common examples:<\/p>\n

    \n
  • 10 N (Newtons)<\/b>: The weight you feel when holding a carton of milk (1 kg) is approximately 10 N.<\/li>\n
  • 1 N (Newton)<\/b>: The force you feel when holding a single AA battery (about 100 g) is approximately 1 N.<\/li>\n<\/ul>\n

    How to Use the Equation of Motion to Solve the Mysteries of the Universe<\/h3>\n

    \u25a0 The Balance of Forces<\/h4>\n

    An apple resting on a desk is acted upon by two forces: gravity (W) and the normal force (N). The normal force might be an unfamiliar term. If you stand on the floor for a long time, your feet start to hurt, right? This is because the floor is pushing up on your feet to support your weight. This upward force is the normal force. An apple “standing” on a desk, just like us, is also subject to the normal force.<\/span><\/p>\n

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    Let’s use the equation of motion to understand the magnitude of these two forces. The apple on the desk is at rest. This means its acceleration (a) is 0. Substituting a = 0 into the equation of motion gives us:<\/p>\n

    m<\/span>\u00d7<\/span><\/span>0 <\/span>= <\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/div>\n
    \u2192 <\/span><\/span>F<\/span>=<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/div>\n

    However, this doesn’t mean that no force is acting on the apple. The “F” in the equation of motion actually represents the “net force,” which is the sum of all forces acting on an object. F = 0 means that all the forces acting on the apple at that moment are canceling each other out, leaving no net force.<\/p>\n

    From this, we can see that the magnitude of gravity and the normal force are equal.<\/p>\n

    N <\/span>= <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span><\/div>\n
    Upward Force <\/span>= <\/span><\/span>Downward Force<\/span><\/span><\/span><\/span><\/span><\/div>\n

    Forces of equal magnitude are canceling each other out, resulting in a net force of zero. This is called the “balance of forces.” An object at rest has zero acceleration, so its forces must always be in balance.<\/p>\n

    Similarly, let’s imagine we put this apple in water, and it floats motionless. Since it’s at rest, the forces must be balanced. However, it’s not on a desk, so there’s no normal force. Gravity still acts on it, pulling it downward. So, what is the upward force that balances gravity in this case?<\/p>\n

    \"\"<\/p>\n

    The answer is buoyancy. In water, an object receives an upward force called buoyancy, which is created by water pressure. From the balance of forces, if the apple’s weight is 1 N, the buoyant force must also be 1 N.<\/p>\n

    When you look around with the mindset that “an object at rest must always be supported by some force,” you’ll start to notice various forces, and it becomes quite interesting.<\/p>\n

    There are also cases where forces can be balanced even if the object is not at rest. Try to imagine a situation where acceleration is zero but the object is still in motion.<\/p>\n

    Zero acceleration means the velocity isn’t changing. This means that when an object is moving at a constant velocity, the sum of all forces is zero. For example, a curling stone glides across the ice at a constant speed. At this point, there are almost no forces on the stone besides gravity and the normal force, so the sum of the forces is zero.<\/p>\n

    Here’s a video of a homemade hovercraft.<\/p>\n