Newton’s Laws
The First Law: Rocks Just Sit There
Ever watched a rock on the ground for a while? Probably not but they don’t move they just kinda sit there letting the world go by. Rocks don’t move of their own accord because no forces are acting on them. This brings us to Newton’s first law when something is sitting still it will continue to do so unless a force causes it to move. The same is also true for an object in motion it will keep on going forever until a force stops it.
In fancy language now: A body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it. Essentially, if a force isn’t acting on an object it isn’t going to speed up or slow down. This doesn’t mean that it can’t be in motion it just means that it doesn’t have a net acceleration.
[Latexpage]
\[F_{net}=ma=0\]
Assuming this is an object with mass when the net force equals zero so does acceleration.
[Latexpage]
If
\[F_{net}=0\]
then
\[a=0\]
When answering physics based questions look for constant acceleration it lets you know that the net force is zero and makes solving many questions possible. We will explore this idea later when discussing translational equilibrium.
The Second Law: Push To Move
However when we go up and push on the rock assuming it is small enough to move it does. This occurs because we forced it to do so by applying a net force. Throughout this process, the rock speeds up from a velocity of zero to some other velocity depending on how hard we pushed. This means that we accelerated the rock which is the essence of Newton’s second law.
[Latexpage]
\[F_{net}=ma\]
Again in fancy language: An object of mass m will accelerate when the vector sum of the forces results in some non-zero resultant force vector.
Third Law: The Rock Pushes Back
Let’s say the rock is too big to be moved. You still applied a force because you accelerated yourself into the rock but the rock didn’t budge. This occurred because the rock exerted an equally sized force against your own canceling it out. So the net force is zero thus the rock doesn’t move anywhere.
This seems terribly confusing it doesn’t feel like the rock exerted a force though. Sure but try punching the rock and you will probably agree with me. Here the rock is changing your acceleration causing your hand or body to decelerate thus it is producing a force.
Rocks aside this is why we are able to walk about places. We exert a force on the ground and the ground pushes us forward. Yep, the ground is what causes us to move forward as a result of us pushing into it. Expressed mathematically:
[Latexpage]
\[ F_{You\; on \;Rock}=-F_{Rock\; on \;You}\]
Remember the signs in physics denote direction so one of the force above points in one direction and one points in the other. Lastly in technical terminology: To every action there is always an opposed but equal reaction.
Friction: Why Newton’s Laws Aren’t Always Intuitive
Newton’s first law says that stuff keeps moving unless a force acts on it. This doesn’t seem to match with reality. When I push on a rock it doesn’t keep moving forever. That is true, but in our day to day lives the ever-present force of friction accounts for this.
Frictional forces always oppose movement and occur between an object and the surface the object moves against. So if I push an object up a wall the frictional force will push downwards against it towards the ground. If I slide a box right against the ground a frictional force will point leftwards against my force.
Static and Kinetic Friction
Turns out there are actually two types of friction at play when moving objects around. The above examples involve kinetic friction (fk) since the object is moving. While static friction (fs) describes frictional forces of objects that are sitting still. We will end up calculating both with the same equation setup but there is an important distinction between the two.
Static Friction
Static friction isn’t a set value while kinetic friction is. This occurs because static friction depends on the force we use to try and push an object forward. Let’s take the example we used in Newton’s third law of the rock that didn’t move. I am going to arbitrarily define 100N of force as the amount of force needed to move the rock. So any force below that amount and the rock won’t move due to friction.
If I push with 50N the rock pushes back on me with 50N of static frictional force. If I push the rock with 75N of force then the rock will push back on me with 75N of static frictional force. Here we can see that in both cases the rock doesn’t move and its opposing force has to counteract the amount of force I put into it. Therefore the frictional force can range from 0N up to 100N at which point the rock will start to move.
[Latexpage]
\[0\leq f_s\leq\mu_sN\]
Here μs indicates the coefficient of static friction or how “sticky” a surface is. For example, ice is quite slick and has a very low μs and indicates the surface isn’t sticky while rubber is much stickier and as a result has a much higher μs.
N stands for the normal force or the force pushing against a surface. The normal force (N) keeps objects from falling through the surface they sit on and in our rock’s case, it is equal to mg since the gravitational force pulls the rock downwards and the normal force opposes this per Newton’s third law keeping the rock from falling into the center of the Earth.
Kinetic Friction
By comparison, kinetic friction is pretty straightforward. It is still the force that opposes the rock’s motion except it replaces the static friction once the rock starts moving.
[latexpage]
\[F_k=\mu_kN\]
One important thing to note about kinetic friction is that it is lower than the static frictional forces at play because μk is less than μs. Once you get something moving it doesn’t take as much force to keep it moving. You have probably experienced this when trying to slide a heavy object against the ground. The object won’t budge so you push harder. Finally, the object jolts forward and moves faster than you expected.
What happened? At first, you were trying to overcome the greater static friction and once you did kinetic friction took over. Since kinetic friction is less than static friction you are now pushing way harder than is necessary to keep the object moving.