Momentum is a force associated with moving objects.
When objects move, they do so with a certain amount of energy - this is essentially what momentum is.
Momentum is the product of the mass and velocity of an object (P = mv).
So, for two objects that are the same mass, the object moving at a higher speed has more velocity, and, therefore, more “energy of motion.”
For two objects traveling the same speed, the object with the higher mass has the higher momentum.
Think about it like this - which object is harder to stop, a baseball flying through the air at 20 m/h, or a baseball traveling at 100 mi/h?
Sometimes, objects in motion collide.
When they do, some interesting things happen to those objects, and their momentum.
In one type of collision, called an inelastic collision, objects that collide stick together. When they do, their masses combine. Their velocity does not, however increase…the object moves more slowly in the direction of the greater force.
In another type of collision, called an elastic collision, objects bounce off one another. In this case, the objects affect one another’s direction, but no momentum is lost. Some momentum may, in fact, be transferred to another object (from the object with greater momentum to lower).
The simulation below shows elastic collisions. Adjust the overall mass of one of the spheres and observe the interaction between the two.
Good old Isaac Newton developed a law or two that we use to describe motion in physics.
Newton’s First Law of Motion:
Objects in motion tend to stay in motion, objects in rest tend to stay at rest.
Basically, Newton claims that objects are stubborn - they like to keep doing what they’re doing. If they’re moving, they want to stay moving; if resting, they want to stay at rest.
The resistance to a change in motion is called inertia.
The greater the mass of an object, the greater the inertia; the lower the mass, the lower the inertia.
So the motion of lower mass objects will be easier to change.
Examples of inertia and Newton’s 1st Law are everywhere – consider what happens when you slam on the brakes of a car…inertia causes you to slam forward as the car stops.
Notice the motion of the crash test dummy in the video above. When the cart crashes, it stops because it reaches a barrier. Inertia causes the dummy in the cart to continue moving. Real world connection: as you can see, inertia is the main reason we use safety belts in automobiles. In an accident without them, your inertia could cause you serious injury (e.g.: flying out of the front window!).
Newton’s Second Law of Motion:
Formally: the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Otherwise: For an object with a specific mass, the more force is applied to it, the greater it will accelerate.
Also, when a set force is applied to two objects of different masses, the object with the lowest mass will accelerate the greatest.
This law is expressed mathematically as F = m/a, which can be conveniently (and algebraically!) rearranged to find the acceleration of a object given force and mass (a = F/m), and the mass of an object involved in a motion (m = F/a).
Newton’s Third Law of Motion:
Every action has an equal and opposite reaction.
This statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.
The direction of the force on the first object is opposite to the direction of the force on the second object.
In other words: all forces act in pairs.
The pennies in the video below hit the desk with a downward force. The desk also pushes back up on the pennies with equal force. Thus, the bounce.
How this works for you: every time you push on a door to open it, the door pushes back on you with equal force. The reason why this doesn’t appear to be so is because your mass is combined with the mass of the building during the push. In space, however, it’s another story (see the video).
Often, we have difficulty working with physics concepts because of the “reality” factor. On earth, many of the concepts we cover are “sticky” because forces like friction and combined masses of objects muddy concepts. In space, however, pure physics concepts are reality, as in the video above.
Speed, velocity and acceleration all deal with motion. Motion is defined as: a change in position of an object, relative to a reference point.
All motion is relative - without using stationary or other comparative objects to guage motion, we would not be able to determine if and when objects are moving.
For Instance:
When standing on a subway platform, the platform is your reference point, so the train appears to be moving. BUT! when standing inside the train, it is your reference point, so everything outside the train appears to be in motion.
When watching a dog run across a field, the surface of the earth, trees, and anything in motion slower (or faster) than the dog is a reference point.
With all motion comes speed. Speed is defined as: the distance traveled by an object, divided by the time it took to travel that distance, or: s=d/t. Speed is, therefore, evalauted in units of distance over time, using meters/seconds.
For Instance:
If a hot air balloon floats 50 meters through the air in 10 seconds, its speed is 5m/s (50m / 10s = 5 m/s)
Speed is a scalar measurement: it has magnitude only.
We will discuss 2 types of speed: Instantaneous Speed (speed at any exact moment) and Average Speed.
Most of the time, objects do not travel at a constant speed.
So, we will most often talk about speed as average speed: average speed equals the total distance traveled by an object divided traveled by the total time to do so. (Total Distance / Total Time)
Often, people confuse speed and velocity…typically, we think of them as one and the same. Velocity is defined as: the measurement of speed and direction of travel of an object. It is a vector quanitity - it has magnitude and direction. This is a very important distinction: 50 m/s North is a velocity, while 50 m/s is not…it is simply speed.
Because velocity measures speed & direction, it changes a lot.
Any time speed, direction or both change, velocity changes.
For Instance:
If a bus is travelling at 15m/s and speeds up, its velocity has changed. If a bus is traveling at 15m/s and turns left, while remaining at 15 km/h, it velocity has still changed.
The only time velocity remains constant is when speed and direction are constant (which almost never occurs with objects in motion).
Because velocity is relative, and relies on direction, multiple velocities can be combined. This is called resultant velocity: the addition of two velocities.
For Example:
If you are moving on a Septa bus that is going 30 m/s, and get up to walk to the front of the bus at 5 m/s, your resultant velocity is 35 m/s (Because you are on the bus, you are already moving 30 m/s. By moving forward in the bus, you’ve increased your velocity an additional 5m/s.)
If you are moving on a Septa bus that is going 30 m/s, and walk backwards, from the front of the bus to the rear at 5 m/s, your resultant velocity is 25 m/s.
Another insteresting effect of velocity’s reliance on direction is the difference between average speed of motion and the average velocity of motion.
Unlike when calculating average speed, where we divide the total distance traveled by the time of motion, to calculate average velocity of motion, we divide the total displacement of an object by the time of motion (Total Displacement/Time).
The animation below provides a good refresher on the difference between distance and displacement.
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Acceleration is another measurement of motion, and is a whole different ball of wax. We usually consider acceleration to be “speeding up.”
This is not true! Acceleration is actually equal to how quickly velocity changes, and can be positive (speeding up), or negative (slowing down)!
Anytime velocity changes, acceleration is affected.
A neat result of this is:
in our car, the gas pedal is often called the accelerator, however, it only speeds us up. Any other instrument that changes velocity in our car is also an accelerator. This means that the brake, and also the steering wheel fit in this category as well.
Just as we discuss average speed and average velocity, we will often discuss average acceleration.
Average acceleration is calculated using the following formula:
Average Acceleration = (final velocity – starting velocity)/time to change velocity.
It is expressed in m/s/s, or m/s2.
Centripetal Motion
Objects in circular motion are constantly changing direction.
As such, they are constantly changing velocity, and, therefore, constantly accelerating.
Practice recognizing speed, velocity and acceleration on a graph: Play the game linked below. Take notice of how velocity graphs change over time with changes in velocity.
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