Feather and hammer drop on the moon – Watch what happens to the motion of a feather and a hammer in complete free-fall. Because the moon has no atmosphere, there is no air resistance to counteract the effect of gravity. (This is the long version of the clip included in the lecture video.)
(Podcast) Houston we have a podcast, episode 16, spacesuits – This is the full-length version of the podcast that includes the clip about how massive spacesuits still have inertia, even in space where things are weightless.
Hello there! Welcome to lecture 4: Newton’s second law!
Newton’s second law of motion describes the relationship between force, mass, and acceleration. This will expand upon our current understanding of motion, and open us up to discussions about momentum, energy, and more, in the next several lectures.
Each of the following concepts will be discussed in this video: force, Newton’s second law, and mass and weight.
Simply put, a force is some type of push or pull that causes an object to change its motion. The symbol for force is the capital letter F, and because it is a vector, it will either be expressed in bold font or with an arrow over the top. The units used for force are Newtons. Recall from previous lectures that a Newton is equal to a kilogram times a meter divided by a second-squared.
There are many types of forces. A few of them will be discussed in some detail in this lecture, and many will be expanded on in future lectures when we specifically cover those topics in more detail.
Types of forces include gravity, support force, friction, air resistance, applied forces, tension, elastic and spring forces, the electromagnetic force, the strong force, and the weak force.
Gravity is one of the most prevalent forces in our lives. We constantly experience a downward force pulling us toward the center of the Earth. This force comes about due to Earth’s large mass exerting a gravitational force on us.
If you’ve ever dropped something, or rolled something downhill or down a ramp, then you’ve seen gravity’s effect on the motion of an object. In addition, our weight comes from gravity. We’ll discuss the concept of weight in more detail later on in this lecture video. Gravity in particular will be discussed in more detail in lecture nine.
A support force occurs whenever something is in contact with a surface such as the ground, the floor, a wall, or something else. As I am standing here recording this video, the floor is supporting my weight and keeping gravity from accelerating me to the center of the Earth. The support force is sometimes called a normal force as the force always acts perpendicular to the supporting object.
When an object is in contact with a flat surface, the normal force will point up. But when that surface is tilted, then the normal force no longer points up. It points perpendicular to the surface.
We will discuss the supporting force again in lecture nine when we discuss gravity and weight.
Friction is another force we experience in our daily lives. There are two types of friction: static friction and kinetic friction.
Static friction is the force that’s required to get an object at rest to start moving. For example, if you’ve ever tried to move something heavy by pushing it, perhaps you’ve noticed that it takes more effort to get the object to start moving than it takes to get it to continue moving. That’s because of static friction. Static friction is also the force we experience between our feet and the ground when we walk or run; and the force between wheels and pavement when we drive a car or ride a bicycle.
Kinetic friction is the force that occurs between an object and a surface as the object slides along the surface. The amount of kinetic friction depends on the two materials that are in contact with each other. Something like steel and ice will experience relatively low kinetic friction, which you may have experienced if you’ve ever gone ice skating. On the other hand, wood and steel would experience much more kinetic friction.
Another factor that influences the amount of kinetic friction is the support force between the object and the surface that it slides along. The larger the support force, the higher the kinetic friction, all other things being equal.
Air resistance is a force that occurs when an object travels through a fluid, such as air. Air resistance acts in the opposite direction of motion. That is, when an object is moving down, air resistance will point up. Air resistance is proportional to the speed of an object. The faster it is, the higher the air resistance will be.
Air resistance also depends on the form factor of the object. I dropped two otherwise identical sheets of paper. One of them was crumpled up, and the other was not. The flat sheet of paper took longer to hit the ground because it has a larger form factor with more of the paper dragging through the air and experiencing the air resistance. The crumpled paper does not experience as much air resistance and therefore drops down faster.
An entire area of study, aerodynamics, has been created to determine what kinds of objects travel through the air without experiencing too much drag, or air resistance. You can get an idea about aerodynamic shapes by looking at airplane design, especially fast airplanes that would otherwise be subject to very high resistance at their speeds. In the case of airplanes and other aircraft, air resistance is something that needs to be minimized to keep the fuel costs of air travel as low as possible.
Air resistance is not always a bad thing. We can use air resistance to make falls from great heights something that is not only survivable, but also fun. Skydivers use parachutes to decrease their terminal speed and allow them to survive after jumping out of an airplane.
Air resistance will reduce the acceleration of an object traveling through the air. Consider a rock dropped from the top of a tall skyscraper. If that rock were to fall only under the influence of gravity, then we would expect its speed to go up linearly over time as gravity increases its speed by 9.8 meters per second every second.
However, air resistance will act on the rock to reduce the rate at which the speed increases. At first, when the rock is initially dropped, air resistance will be zero because the rock is not moving yet. As the rock speeds up, the air resistance will increase. This limits the increase in speed. At a certain point, air resistance and gravity will become equal to each other, causing the object to move at a constant speed. That speed is known as terminal speed. The rock will continue moving at its terminal speed until it hits the ground.
Every object will have a different terminal speed depending on its size, shape, density, and other factors. If we drop any object from a large enough height, it will speed up to its terminal speed, and then travel in dynamic equilibrium at that terminal speed until it hits the ground.
Objects moving through the vacuum of space will not experience any air resistance. This is because there is no fluid such as air to act on the object to change its motion. This concept was demonstrated in 1971 on the Apollo 15 mission by astronaut Dave Scott. He dropped a hammer and a feather at the same time, and because there is no atmosphere on the moon, there was no air resistance that would cause the feather to move slower than the hammer. Both objects hit the surface of the moon at the same time.
An applied force is simply a push or pull that is applied to an object by an outside influence. Whenever we move an object by pushing or pulling, we are applying a force. The magnitude and direction of that force depends on what force we apply.
Tension is the pulling force present in a string, cable, or other object as it holds something up. The direction of the tension force is along the string or cable. Tension is present in pendulums, pulley systems, and even in truss bridges.
Elastic and Spring Forces
Elasticity quantifies the ability of objects to deform when a force is applied to them and then return to their original configuration once that force is removed. Springs are a great example of an object that can be deformed with a force. After the force is removed, as long as the force wasn’t too large, the spring will restore itself to its original size and shape. This property will be discussed in more detail in lecture twelve.
Electromagnetism describes the interactions of charged objects and magnetic materials. In our daily lives, we experience electromagnetism any time we use an electronic appliance or gadget, and even when we do something as mundane as use a magnet to hang something on a refrigerator. We will discuss electromagnetism a lot more later in this class, starting with lecture 22.
The Strong and Weak Forces
The strong and weak forces are forces present inside the nucleus of an atom. They’re not forces we think about in our daily lives, and yet they are important in that they literally keep atoms together. Electromagnetism tells us that objects with like charges repel. So what is it that keeps the nucleus of an atom, comprised of like charged protons, together? The answer is the strong force. The strong force acts under very small scales to keep the nucleus of an atom together. It also helps us to understand nuclear processes such as radioactive decay, fusion, and fission, which we’ll discuss in lectures 33 and 34.
The weak force is also responsible for radioactive decay, fusion and fission processes. It is the force responsible for changing one type of quark into another; say, by turning a proton into a neutron.
While there are many different forces that can act on an object, there are only four fundamental forces. That is to say, all of the forces just described can be put into one of four categories. Those categories are: gravity, electromagnetism, the strong force, and the weak force.
Pretty much all of the forces that we experience in our lives, other than gravity, actually fall into the category of electromagnetic forces. The support force, for example, occurs due to the repulsion of electrons in two atoms when they are placed near each other. Friction occurs due to electromagnetic forces interacting at the surfaces of two objects that are touching each other. And so on.
Of the four fundamental forces, the strongest is the strong force, followed by electromagnetism, the weak force, and gravity. This means that gravity is the weakest of the four fundamental forces.
Newton’s Second Law
As discussed in lecture three, acceleration defines the rate at which the velocity of an object changes. Acceleration can mean one of three things: that an object is speeding up, slowing down, or changing direction.
While acceleration was described in the last lecture in terms of distance, velocity, and time, Newton’s second law defines the relationship between force, mass, and acceleration.
Newton’s second law states that the net force on an object is equal to its mass times the acceleration. In other words, F net equals m times a. The net force is the sum of all of the forces that act on an object, and it is a vector quantity. Acceleration is also a vector, and it will point in the same direction as the net force.
In lecture two, we discussed the concept of mechanical equilibrium, which occurs when the net force on an object is equal to zero. If the net force is zero, we can see from Newton’s second law that the acceleration is also zero.
In this example, a cart is rolling down a ramp with a motion detector measuring its position, velocity, and acceleration. I measured the mass of the cart to be 0.35 kilograms. The average acceleration of the cart was 0.9 meters per second-squared. We can use Newton’s second law to calculate the net force on the object.
Net force equals mass times acceleration. The mass is 0.35 kilograms, and the acceleration is 0.9 meters per second squared. When we multiply those two values together, we see that the net force is equal to 0.315 newtons. The direction of the net force is in the same direction of the acceleration, pointing down the ramp and parallel to the motion of the cart. The net force is the sum of all forces acting on the cart; gravity, the support force, friction, and probably a small amount of air drag.
Let’s consider a different scenario. Let’s say you were to push on a very heavy box to try to get it to move. However, as you push on the box, the box does not move. Friction is the force acting against your push, but how could we calculate the magnitude of that force? Is friction greater than, less than, or equal to the push? Think about it.
Now let’s use Newton’s second law to find an answer. Let’s say you push against the box with a force of 25 Newtons, and the box does not move. Because the box is not moving, it is in static equilibrium. We know from Newton’s second law that the net force on the box must be zero. The net force is equal to the applied force plus the friction force, and that sum is zero. We can plug in 25 Newtons for the applied force, and then subtract 25 Newtons from both sides of the equation to determine the force of friction. Friction is equal to negative 25 Newtons. The negative sign indicates that it points in the opposite direction as the applied force. But the applied force and friction have EQUAL magnitudes: 25 newtons!
Students frequently have a hard time with this concept. If you struggle with the idea that friction and the applied force are equal when the box is not moving, then consider an extreme example. Consider what would happen if the force of friction could somehow be greater than our applied force. In this case, as we push against an unmoving box, if friction somehow became larger than our applied force, it would cause a net force in the direction opposite our push, causing the box to accelerate against the direction of our push! That’s definitely not what happens when we push on an object.
This situation would be the same once we got the box moving at a constant speed. Let’s say we get the box moving and are pushing it at a constant velocity. Because the velocity is constant, the net force is zero, and as long as there are no other forces acting on the box, the force of friction must be equal and opposite to our push.
It’s possible to do an analysis of forces and equilibrium in two dimensions as well. In this demo, I use a force table to get a system of 2D forces into equilibrium. With a force table, I can place different masses at different angles away from a central location.
I placed 55 grams at the zero degree mark and 90 grams at the 110 degree mark. If we use 10 meters per second-squared for little g, we can calculate the forces as 0.55 Newtons at zero degrees and 0.9 Newtons at 110 degrees. I converted these to horizontal and vertical components. We can analyze the horizontal and vertical forces separately.
The horizontal net force is 0.55 Newtons plus negative 0.31 Newtons which is 0.24 Newtons. The vertical net force is 0.85 Newtons. This is a vector pointing up and to the right. The force table is not in equilibrium. When I pull out the center pin, the system accelerates up and to the right, in the direction of the net force.
To put the system into equilibrium I need a force that causes the net force to be equal to zero. That would be a force with (-0.24 N, -0.85 N) components. That corresponds to a force of 88 grams placed at 254 degrees. Indeed, when I place a third mass at that location, the system is in equilibrium. When I remove the center pin, everything stays put.
A 2D analysis of forces like this can be difficult without trigonometry. However, it is possible. When you do your lab on vectors, you will be asked to keep a force table like this in equilibrium. Even without trigonometry, you can graphically determine the sum of the vectors by adding them together tail to tip, tail to tip. That’s how you can determine what angle a third or fourth mass should be placed at to cancel out the masses on the force table. The magnitude can be determined by estimating horizontal and vertical components using graph paper or an online vector simulation tool. Then use the Pythagorean theorem to calculate the magnitude of the force that would be required to place the system into equilibrium.
Mass and Weight
Once again, I’d like to discuss the concepts of mass and weight and how they differ from each other. This was something discussed briefly in lecture two.
Mass comes from the “stuff” in an object, the atoms and molecules that it made out of. Mass gives an object inertia, a resistance to changes in its motion. Because mass comes from the molecular configuration of something, it does not change based on position or location. While the situation for humans is admittedly complicated due to the fact that we eat, excrete, and exercise, if we could somehow hold our masses constant, that mass would not change if we were to be here on Earth, on the moon, on Saturn, or just floating in the vacuum of space.
Weight, on the other hand, is a force that comes about due to the force of gravity. While weight is a somewhat complicated topic that we’ll discuss in more rigor in lecture nine, for now it is sufficient to say that weight is equal to our mass times the acceleration we experience due to gravity, little g. In other words, W = m times g. Little g is equal to negative 9.8 meters per second squared. We’ll learn where the 9.8 meters per second squared value comes from in lecture nine.
If we were to change our location, our mass will stay the same, but our weight may change. The gravitational force on the moon is one sixth that of Earth. Therefore, our weight on the moon will be one sixth the value of our weight on Earth. Astronauts visiting the moon experienced this decreased weight as they conducted moonwalks.
Jupiter, however, has a much higher gravitational force than the Earth. If we were to go to Jupiter we would find ourselves weighing 2.5 times more than we weigh on Earth. Meanwhile, if we could somehow safely transport ourselves to the sun, the gigantic gravitational field of the sun would make us weigh nearly 30 times our weight on Earth!
When astronauts visit the space station, or otherwise orbit the Earth, the lack of supporting force causes them to be weightless. They are still under the influence of Earth’s gravity, which is what causes the space station to orbit the planet, but the astronauts and other objects traveling in orbit appear to be weightless. However, that does not mean that inertia has stopped impacting the motion of an object. Mass, and inertia, exist everywhere.
This NASA podcast is a fascinating look at the impact of inertia in space. Even when astronauts and their bulky equipment are weightless, the inertia of the objects still affects their ability to move around, put on their spacesuits, and get things done in space. Listen to NASA’s spacesuit hardware manager Les Padilla describe the effect of inertia in microgravity.
What can be our friend at times is momentum or inertia. That can be an enemy at times as well when you’re in that microenvironment. Crew members are trained specifically to go slow along a space station. If you get 300 pounds moving, it can be difficult to stop. Now, they can stop it, but it’s just wasted energy. So they go very slowly so they don’t get that large mass moving too quickly.
Thanks for taking the time to learn about Newton’s second law. Until next time, stay well.