The greatest physicist of the 20th century, Albert Einstein, discovered that gravity is actually a manifestation of geometry.
He showed that as objects get closer to one another, they experience a force that pulls them together. This force is due to something called spacetime curvature, which is an effect of the object’s distribution of mass and relative velocity to other objects.
As objects get farther away from each other, they experience a force that pushes them apart. This too is due to spacetime curvature.
What if we could measure this spacetime curvature? Then we would know the strength of gravitational force! We would have achieved one of the fundamental principles of physics: To measure force (which is related to physics) in terms of physics (that is, in terms of itself).
In this article, we will discuss how to do just that using an experiment you can do in your own home. First, let’s discuss what ball bearings are and where you can find them.
Calculate the mass of the ball
The mass of the ball can be calculated by finding the volume of the ball and multiplying that by the material density of the ball. A one-kilogram ball made of rubber with a volume of one liter has a mass of one kilogram.
To find the net force acting on the ball, you must first calculate its velocity. To do this, you need to know how long it takes for the ball to fall and how far it has fallen. You then calculate how much time it took for the ball to fall that far and use some math to find its velocity.
You can now add up the gravitational force and the opposition force to find the net force acting on the ball. The opposition force is anything other than gravity pulling on the ball, like air resistance.
Determine the center of mass of both objects
The first step in solving this problem is to determine the center of mass (also called the centroid) of both objects. The center of mass is the average position of all the masses in an object.
In this problem, you need to find the center of mass of the 1-kg ball and the 2-kg ball. To find the center of mass of a ball, you need to know its shape and its weight distribution.
You can find the weight distribution of a ball by putting it on a scale and looking at what fraction of its total weight is due to the ball itself. In other words, how much does the ball weigh relative to how much does the box weigh?
To solve this problem, we will first solve for one object, then add that solution onto the solution for the other object. This way, we can find both objects’ centers of mass.
Find the distance between the objects
Next, you need to find the distance between the objects. In this case, you are looking for the distance between the ball and the floor, which is just under one meter.
You already know that gravity is pulling the ball down at 9.8 m/s², so all you have to do is subtract that from the height of one meter. This gives you how far down the ball would be on the floor.
You can’t just add or subtract velocity values due to math complications, so instead you need to find out what fraction 9.8 m/s² is of 1 m and then multiply or divide those values accordingly.
You want to end up with a number less than one, since you are finding how far down the ball would be on the floor.
Calculate gravitational force between objects
The gravitational force between two objects is the product of the mass of each object and the other object’s proximity to each other.
To calculate the force between two objects, you must know both objects’ masses and their distance apart. However, since you are only given one of these variables in this problem, you must use a different method to determine the gravitational force.
You can calculate the gravitational force between two objects using geometry. You first need to understand what perpendicular means in this context. Perpendicular simply means straight up and down.
You can draw a line perpendicular to the floor that goes straight up and hits the ball (or any object) in question. By doing this, you have determined the ball’s own mass as being 1 kg.
Calculate air resistance force between objects
Air resistance, also called drag, is the force that is exerted on a moving object due to collisions with other particles in the surrounding medium.
In the case of falling objects, the surrounding medium is air. The air pushes on the falling object, slowing it down. This is why a bullet shot straight up falls slower than a ball dropped from the same height.
Air resistance depends on several factors, including density, flow velocity of the surrounding air, and surface roughness. Because of this, calculations of air resistance vary depending on what parameters are used.
For instance, if a falling object has very smooth surfaces and passes through very slow moving air then its drag force will be lower than for another object that has rougher surfaces or moves through faster moving air.
To get an accurate calculation of the net force acting on a 1-kg ball in free fall we need to calculate the total drag force due to air resistance and subtract this from the weight.
Find acceleration due to gravity
The next step is to determine the acceleration of the ball due to gravity, or what physicists call g. To do this, you have to find out what net force acts on the ball.
You know the weight of the ball, so you can determine the magnitude of the weight force acting on the ball. The weight acts in a downward direction, so that means it is a negative force.
You will have to find the net force acting on the ball by adding up all of the forces acting on it. One way to do this is to draw a free-body diagram of the ball. You can do this by drawing a rectangle around the ball with its top and bottom exposed, and drawing in arrows indicating which way each part of the ball is moving.
There are many ways to draw a free-body diagram, so try experimenting with different sizes and shapes for best results.
Compare with other situations where gravity is present
A second way to understand what is happening when a ball and the table are both in free fall is to compare this situation with situations where gravity is present but there is no motion.
For example, imagine a 1-kg ball sitting on a tabletop that does not move. Because the ball and tabletop are not moving, it takes effort to pull them apart. This requires work, which means it costs energy.
The harder you try to pull the ball off the table, the more work it takes. Because work is energy, this means that pulling the ball off the table takes energy.
There is a force acting on the ball and tabletop that keeps them stuck together: gravitational force. The bigger gravitational force is, like on a bigger planet or in a different dimension where there is more gravity, it will be harder to pull the ball off the table.
Make a diagram for visualizing net force
A simple way to understand what net force means is to create a diagram of a situation where force is involved.
Imagine a 1-kg ball sitting still on a smooth surface. According to physics, nothing can hold this ball in place, so it will slowly start to move either up, down, left, or right.
To illustrate this concept, draw a picture of the situation. Place the ball in the middle of the page and draw lines extending from the ball to all directions on the surface.
These lines represent what physics calls forces. Forces are what make something move, or change its speed or direction of movement.