Recap of Unit Three, Yippee!

Unit 3 was based in Newton's Third Law and its surrounding concepts and applications to real life. We covered Newton's Third Law, action-reaction pairs, how tug-of-war really works, forces in perpendicular directions, how tides work, momentum, impulse and the Law of Conservation of Momentum.

Newton's Third Law

Newton's Third Law states that for every action, there is an equal and opposite reaction. This is exemplified all around us in action-reaction pairs.


In this image, there are two sets of action-reaction pairs.

 In the first, the book pushes down on the table and, with the same amount of force, the table pushes up on the book. Note that in this action-reaction pair, the subject switches from book to table, but the verb stays the same, push.

The second action-reaction pair is a little bit different. In this pair, gravity pulls the table down and the table pulls the earth up. When writing action-reaction pairs involving gravity, the subjects will always be gravity and the earth, but the verb will stay the same.

How does tug-of-war really work?

Now that Newton's Third Law has been covered, it's time to face a harsh truth about tug-of-war. The secret to winning does not lie in the strength of one team versus the other, but in physics.

Watch this video, and consider how Newton's Third Law might be applied.

There are three action-reaction pairs at work in a game of tug-of-war.

1. Team A pulls Team B to the left, Team B pulls Team A to the right.
2. Team A pushes the ground forward, the ground pushes Team A backward.
3. Team B pushes the ground forward, the ground pushed Team B backward.

Now, because we know that for every action there is an equal and opposite reaction, we can also know that the two teams are pulling with the same amount of force. Therefore, no matter the teams are stacked, one team pulling harder than the other is not how the match is won. In fact, it is the relationship between the team and the ground that determines the winner. In the video, the team on the left won because they were pushing on the ground with more force than the team on the right was.



This same concept can be applied to a horse and cart. It may seem that because of Newton's Third Law, a horse and a cart would pull each other with equal force and therefore would remain at rest. However, the tug-of-war explanation can also be used to prove that logic to be uninformed.

Like in tug-of-war, there are three action-reaction pairs: between the horse and the cart, between the horse and the ground and between the cart and the ground. The horse pulls the cart with and equal and opposite amount of force that the cart pulls the horse with. This is because of Newton's Third Law. However, the horse pushes on the ground and the ground pushes on the horse with a greater amount of force than the cart pushes on the ground and the ground pushes on the cart with. Therefore, the cart is pulled in the horse's direction.

Forces in Perpendicular Directions

Momentum

The definition of momentum is inertia in motion. In other words, momentum is the product of an object's mass and velocity. The unit for momentum is kgm/s^2 (kilogram meters per second, squared).

The equation for momentum (symbol p) is p=mv.

NOTE: At rest, there is no momentum, which can just be written as 0kgm/s^2.

Impulse
Impulse (symbol J) is defined as force multiplied by the amount of time it takes to be applied. In other words, the equation is J=f x change in time. Impulse is measured in Newton seconds (Ns).

Momentum/ Impulse Relationship

So, now that impulse and momentum have been defined, it is now the time to explore the relationship between the two. Momentum is equal to mass times velocity and change in momentum is equal to an object's final momentum minus its initial momentum.

NOTE: The change in momentum will always be the same whether or not the object comes to a stop slowly or quickly.

Impulse is equal to change in momentum.

Let's take this further by looking at how this relationship applies to a real life situation. Why is it that airbags keep us safe?


First, remember that the car will go from moving to not moving no matter how it is stopped. Therefore impulse/change in momentum is constant. A small force therefore must mean a large change in time and a large force means a small change in time. Airbags protect the dummy because they increase the amount of time it takes for the dummy to feel the impact of the collision, therefore the force acting on the dummy is decreased. Small force = less injury.

The Law of Conservation of Momentum

The Law of Conservation of Momentum states that the momentums before and after an action are equal, so it is conserved. For instance, say that there are two carts on a track, one is at rest and the other is in motion. The law states that if these two carts collide, connect and continue down the track as a unit, the momentum of the system would be the same before and after the collision.

As an equation, this looks like p total before= p total after.

Let's use a to name the moving cart and b to label the cart at rest.

We can use the equation: mass of a times velocity of a + mass of b time velocity of b  = mass of a + mass of b (velocity of unit ab).

Now let's imagine that cart a has a mass of 2kg and is moving left at 5m/s toward cart b which has a mass of 3kg and a velocity of 0m/s. When they collide, connect and continue, is the momentum conserved?

p total before=p total after

p of a + p of b before=p of a + p of b after

mava+mbvb=ma+b(vab)

2(5)+3(0)=2+3(vab)

10+0=5(vab)

2m/s=vab

Now that we know the velocity of the unit, we can use p=mv to solve for the momentum before and after.

Before:

2kg(5m/s)+3kg(0m/s)=p

10kgm/s^2=p

After:





5kg(2m/s)=p

10kgm/s^2=p

So we've found that the momentum is conserved. 

But...is momentum conserved when to pool balls hit and then move away from each other at an angle?

Yes!

Gravity and Tides

The Universal Gravitational Law states that F=(G)(m1)(m2)/d^2, because of this we know that force is proportional to 1/distance squared. In other words, a short distance has a strong force and a long distance has a weak force.

Let's think about this in relationship to the Earth. The side of the Earth closer to the Moon experiences the Moon's gravitational force more than the side that is farther away from the Moon. The net force acting on each side of the Earth is what causes the tides. Say that the on the side closer to the Moon, the Moon's gravitational force exerts 150N and on the other side, only 50N. (note: these numbers are grossly exaggerated just to detail the concept) Additionally, the gravitational force from the center of the Earth is 100N. To find the net force on each side, the Earth's gravitational force is subtracted from the moon's force on each side. Therefore, the net force on the close side is 50N and the net force on the far side is -50N. The positive force indicates that the close side is being pulled toward the Moon and the negative force indicates that the far side is being pulled away from the moon. It is this imbalance that causes the tides. If the forces weren't opposite, tides wouldn't exist. Also, if tides were determined by gravitational pull instead of the relationship between force and distance, tides would be caused by the Sun, not the Moon.

This video explains tides really well: