Force Basics and Gravity
So far we have explored a variety of different ways to describe and quantify the motion of objects. Let us now turn towards why these things were moving in the first place, forces.
Force
Force, measured in Newtons (N), describes the pushing or pulling of an object. It is what accelerated an object and gave it velocity.
Fundamental Forces
In all of physics, there are four fundamental forces that explain the world around us: electromagnetic forces, gravity, strong force, and weak force. While we will briefly discuss all of the forces the MCAT is primarily concerned with the first two electromagnetic forces and the force of gravity.
Since electromagnetism is a whole topic in and of itself we will explore it in greater detail later on in the course. For now, we will explore the perplexing force, gravity (Fg).
Gravity
If you have lived on Earth for any amount of time then you have almost certainly experienced gravity. From skinned knees to broken jars it is an ever-present force in our life. Specifically, gravity is an attractive force between objects with mass. This means that while you are attracted to the Earth it is also attracted to you.
That doesn’t make sense though after all the Earth doesn’t come flying after you when you jump off of its surface. True but it is still attracted to you its acceleration is just so small that it doesn’t actually budge at least not perceptibly. We can quantify the exact force between any two objects using the following formula.
[latexpage]
\[
F_g=\frac{Gm_1m_2}{r^2}
\]
Here G represents the gravitational constant (6.7 x 10-11 Nm2/kg2), m1 and m2 the mass of the two objects, and r the distance between the two objects. Overall having this equation memorized isn’t of high importance. What is important is understanding the proportionality.
In this equation r, representing distance is squared this means that the distance between two objects plays a much larger role in determining the force between objects than does the mass.
Proportionality Questions
To illustrate this point and understand how to solve proportionality based question let’s look at two scenarios.
Distance is King
Scenario 1: Two objects with mass are placed 20 m away from one another and exert 1.2 x 10-30 N attractive force due to the gravity between them. What will the attractive force between the two objects be if the distance between them is reduced so the objects are now 10m apart?
We won’t be able to solve for the new force in this scenario unless we first want to determine the mass of the two objects from the force between them. That is a ton of extra work and more importantly time. There is a much easier way of solving this equation using the idea of proportionality.
Here the only quantity that differs between the initial setup of the two objects and the final setup is the distance between them. Therefore we only need to determine what effect the change in distance has on the gravitational force. The easiest way to do this is to determine the factor by which our distance changed.
[latexpage]
\[
Factor\;Change = \frac{final\;value}{initial\; value}
\]
\[
Factor\;Change = \frac{10m}{20m}
\]
Now we plug in our factor change into the proportionality expression for gravity. To find this expression simply set every other variable except distance in the equation to one. This yields the following equation:
[latexpage]
\[
F_g \propto \frac{1}{r^2}
\]
\[F_g \propto \frac{1}{\frac{1}{2}^2} \to \frac{1}{\frac{1}{4}} \to 4
\]
The final calculated value represents the factor difference between the final and initial setups. Therefore the force is 4 times larger when the objects are moved closer together. So the force between the two objects when they are 10m away is 4.8×10-30 N. Here we can see that distance is inversely proportional to Fg meaning that as the distance decreases the force increases and vice versa.
Mass Still Matters
Scenario 2: Two objects with mass are placed 20 m away from one another and exert 1.2 x 10-30 N attractive force due to the gravity between them. What will the attractive force between the two objects be if the mass of one of the objects is doubled?
Now that you have seen the setup for solving proportionality questions try and solve this one on your own. Don’t worry if you get stuck just hit the hint button for a guided walkthrough.
Proportionality PBL
We will continue to see proportionality questions come up as we progress through more of the physics material and will explore advanced proportionality questions later. For now keep an eye out for these questions as you practice. They are pretty easy to spot just look for questions that have an initial and final situation where a variable or two are changed while the rest remain the same.