Mass of Meter Stick

In class we were asked to find the mass of a meter stick by only using a meter stick and a 100g lead weight.

In this picture, the meter stick is balanced, so that means the torques are equal. The counter-clockwise torque equals the clockwise torque, because torque = (force)(lever arm)

In this picture, there is a 100g weight on the far side of the meter stick. The center of gravity stays the same, and the axis of rotation stays the same. The only thing that has changed is...

This picture demonstrates how to solve for the mass of the meter stick. We know gravity (9.8), the mass of the weight (100g or 1kg), how long the stick is (100m), the center of gravity (50m), the axis of rotation (70m) and the lever arms (20m and 30m). 50 is just the remaining mass of the meter stick, but it is not necessary to use in the equations for solving.

To solve for the mass of the meter stick, we first need to have to correct measurements. We know that the weight is 100g or 1kg, but weight is measured in Newtons so we need to do a conversion. 

w=mg

w=(.1)(9.8)

w=.98N

So we now know that the weight weighs 9.8N, and we can use that information in our equation.

torque = (force)(lever arm)

counterclockwise torque = clockwise torque

(force)(lever arm) = (force)(lever arm)

(force) (20) = (.98) (30)

20force = 29.4

force = 29.4/20

force = 1.47N

The question asked for the MASS of the meter stick, so we need to convert 1.47N back to mass.

w=mg

1.47 = (m)(9.8)

m = 1.47/9/8

m = 1.5kg

m=150g

The mass of the meter stick is 150g

Rotational Inertia/Angular Momentum & Center of Mass/Gravity

This video is about Rotational Inertia and Angular Momentum. I like this video for multiple reason; it makes the definitions easy to understand, teenagers created it and it has examples that we have used in class, both of which make it relatable. Rotational inertia is the amount of resistance an object has to rotate. The video related rotation inertia to mass by saying, "rotational inertia depends on where the concentration of mass is. If it is close to the axis of rotation, it will have a small inertia and if it is far away, it will have a big inertia". I thought inertia was how big the object was, but that definition really cleared it up for me. The video also made clear that rotational inertia and rotational velocity are inversely proportional to each other, which makes the conservation of angular momentum law make sense (angular momentum before=angular momentum after). I found this video very useful.


This video explains the center of mass through acceleration and numbers, so if you wanted to know exactly how to solve for the center of mass you could use this video. Although, for our purposes the center of mass and center of gravity will almost always be the same.


This video gives one specific example of the center of gravity, and it completely changed how I saw it. After you watch the experiment, you will see how all three points of the wooden board meet at one point in the middle (the center of mass).

Unit 3 Summary

Newton's 3rd Law and Action/Reaction Pairs

Newton's 3rd Law --> every action has an equal and opposite reaction

AS and CS pull each other with the same force due to Newton's 3rd Law that states, "every action has ann equal and opposite reaction". As you can see, the largest vector is "AS pushes ground right, and ground pushes AS left" because winning is not because of the pull, but rather the force on the ground. AS pushes harder on the ground, causing both teams to move left, so AS wins.

The big truck has a larger mass than the little car, but they have the same force on each other during a crash, because "every action has an equal and opposite reaction". Their equal force is justified by "big truck pushes little car, little car pushes big truck". Although, since the little car has a smaller mass its acceleration will be larger after the crash.

In this case, an apple is on a table and there are two action reaction pairs. The earth pulls the apple down, and the apple pulls the earth up. The table pushes the apple up, and the apple pushes the table down.

The horse pulls the buggy with the same force that the buggy pulls the horse, due to Newton's 3rd Law that states, "every action has an equal and opposite reaction". The only way a horse could pull a buggy would be if the horse had another interaction, and in this case that would be the ground. The horse must push on the ground with a harder force than the buggy pushes on the ground, so therefore both the horse and buggy would move in the horses direction to the right.

Forces in Perpendicular Directions 

 

Adding Non-Parallel Vectors

Boat "a" is going the slowest, but it's taking the most direct route.

Boat "c" has the longest vector so it has the faster ride, but it's route will take longer than boat "a".

Force of Gravity

This is the formula for the universal gravitational force.

G = (6.67) (10^-11)

You weigh less on a mountain than you do on the ground, because you're farther from the center of the earth.

Force is inversely proportionate to distance.

Force is also inverse square to distance.

Tides

Tides are caused by the difference in force felt by opposite sides of the earth. That force is determined by the distance from the moon.

As you can see, side A has a smaller distance from the moon, thus giving it a larger gravitational force. Side B has a farther distance from the moon, thus giving it a smaller gravitational force.

Side A and B feel different forces to the moon. Side A's net force will be towards the moon because of its strong gravitational force. In result, side B's net force will be away from the moon. This causes the tidal bulges. *It is
                                                                                    important to remember that if it was just the pull,
                                                                                    the sun would cause the tides, not the moon.

Spring tides occur when the sun, moon and earth are all in line. This occurs during a full or new moon. Spring tides cause higher than normal high tides and lower than normal low tides.

Neap tides occur when the moon is perpendicular to the sun and earth. This occurs during a half moon. Neap tides cause not as high tides and not as low tides.



There are two high tides and two low tides each day.
Each high tide and low tide are approximately 6 hrs apart.
Each high tide is approximately 12 hrs apart.
Each low tide is approximately 12 hrs apart.

Conservation of Momentum 

This is the equation for a collision where one object is moving with another object at rest, and one is moving with the other at rest in the second half of the equation as well. 

This is another equation for a collision with one object in motion and another at rest, but during the second half of the equation the objects become one moving force.

During a collision, you start out with some net force. During an explosion, you start out with no net force.

Since Newton's 3rd Law states that, "every action has an equal and opposite reaction" the force of object "a" will be equal to the negative force of object "b"

Similarly, the impulse of object "a" will be equal to the negative impulse of object "b"

 Similarly, the change in momentum of object "a" will equal the negative change in object "b"

So... the change in momentum of object "a" plus the change in momentum of object "b" will equal 0.

Why are cars built to crumble upon impact?

Cars used to be built with steel, but they are now built to crumble upon impact because it's safer.  With steel, the cars would come to an immediate stop during a crash. The car will go from moving to not moving no matter what surface it comes into contact with, so the ∆P will remain the same regardless of the surface because ∆P = mv and ∆P = P final - P initial. J = ∆P so if ∆P remains the same, then J will also remain the same. If J remains the same, then the time will increase and decrease the force on the car. Less force =  less injury.

Why do bullet-proof vests catch the bullets rather than reflecting them?

Bouncing requires two changes in momentum --> come to a stop and another to start again.

This means two impulses are needed because J = F∆ t  so two impulses means two forces. Bouncing will double the force than sticking.

Special Tides

Tides are caused by the difference in force felt by opposite sides of the earth. That force is determined by the distance from the moon.

As you can see, side A has a smaller distance from the moon, thus giving it a larger gravitational force. Side B has a farther distance from the moon, thus giving it a smaller gravitational force.

Side A and B feel different forces to the moon. Side A's net force will be towards the moon because of its strong gravitational force. In result, side B's net force will be away from the moon. This causes the tidal bulges. *It is
                                                                                    important to remember that if it was just the pull,
                                                                                    the sun would cause the tides, not the moon.

Spring tides occur when the sun, moon and earth are all in line. This occurs during a full or new moon. Spring tides cause higher than normal high tides and lower than normal low tides.

Neap tides occur when the moon is perpendicular to the sun and earth. This occurs during a half moon. Neap tides cause not as high tides and not as low tides.



There are two high tides and two low tides each day.
Each high tide and low tide are approximately 6 hrs apart.
Each high tide is approximately 12 hrs apart.
Each low tide is approximately 12 hrs apart.

This is the tide chart for Seabrook Island, SC.
http://www.tides4fishing.com/us/south-carolina/seabrook

Currently at 7:43pm it is low tide. The beach is experiencing neap tides, because the moons are half moons, but there will be a spring tide on Sunday the 23rd because there will be a new moon.

Newton's 3rd Law and Vectors Resource

I found this video helpful, because it first reviewed Newton's 2nd Law before explaining Newton's 3rd Law, so the viewer is able to make connections between the two laws. It first stated Newton's 2nd Law, "things in motion will stay in motion unless acted upon by an outside force" and then later on stated Newton's 3rd Law, "for every action there is an equal and opposite reaction". The video also contains many examples and diagrams, which personally draws me to the video because I'm a visual learner. For example, there is a diagram with a box of a specific weight and two vectors pushing in opposite directions of an equal force of 10N so the box remains at rest. The vectors are just guidelines to know the actual direction and Fnet (total force on the object) of the object. When the video was reviewing Newton's 2nd Law, it had an example of a person that had been pushed on frictionless ice, and that person kept moving unless something or someone stopped that person. I know this video is reliable, because I compared the content of the video to my class notes and they match up.

--> To skip to Newton's 3rd Law, skip to 9:40
Newton's 3rd Law states, "for every action there is an equal and opposite reaction", but the video alters that definition to "for every action force there is an equal magnitude and opposite direction reaction". This definition is actually a little clearer to me, because it is a little bit more specific. For example, the video has a diagram where someone is pushing on a wall with 10N so the wall is pushing back on the person with 10N, because for that force there is an equal magnitude of the same force in the opposite direction. The video then proceeded to explain that the only exception would be if the person was so strong that it could push on the wall to the point where the wall couldn't push back with sufficient force, causing the wall to briery accelerate and topple over.

Newton's 2nd Law and Newton's 3rd Law relate, because the Fnet (total force on the object) will cause the equal and opposite reaction force. For example, if a box is being pushed with an Fnet in the right direction, then the box is pushing on the ground to the right and the ground is pushing on the box to the left. The only way the box could move forward would be if someone were pushing harder on the box in the right direction than the ground was pushing on the box in the left direction. I liked this video, because it helped me to see that connection between the two laws.

Newton's 2rd Law Resource

I found this resource helpful, because it is not only long and thorough but it explains the equations in a similar way to how we looked at them in class. Although equations will be the same anywhere, this particular video explained them in a way that reminded me of how Mrs. Lawrence explained them, which is what drew me to this video. For example, F = ma is formed by (a~F) and (a~1/m). I know this video is reliable, because I compared the video content with my class notes, and they match up. The video also contains example experiments, which makes use of the equations and makes them clear to the viewer. One of the experiments in this video exemplified how to solve for force (F = ma) as well as for acceleration (a = F/m). The experiment showed how the velocity was increasing, because the distance in between the time intervals were getting longer each time. I am a visual learner, so I personally learn faster from experiments and diagrams, which is another reason why I enjoyed this video. I watched many other videos before choosing this one, but the other videos didn’t quite cover the material like this video did. An approach the video took that I had not seen before was defining force as the "rate of change of momentum". That definition actually made a lot of sense to me, so during this video I reviewed Newton's 2nd Law as well learning something new about it. One thing I would change about this video was that it didn't explicitly state Newton's 2nd Law in word form. The video stated the law with equations and made the equations very clear, but failed to state how the equations relate to the law as a whole. For example, in class we wrote (F =ma) as
force = (mass) (acceleration). For someone who was just learning about Newton's 2nd Law, that would have been a nice explanation to add to the video. 

Unit 2 summary

Free Fall

Free Fall - when objects fall due to the acceleration of gravity only

-no air resistance

-weight doesn't get factored in
-when falling, the object increases by 10m/s every second

To find how fast the object is moving, use the formula --> v = gt
To find how far the object has gone, use the formula --> d = 1/2gt^2

Example problem:
A ball is dropped from a cliff, and it took the ball 3 seconds to hit the ground.
How high up is the cliff? How fast is the ball moving?

d=1/2gt^2                          v=gt
  =1/2(10)(3^2)                    =(10)(3)
  =(5)(9)                               =30m/s
  =45m

Projectile Motion

 


constant a                             constant v
(vertical distance height)     (horizontal distance)
d=1/2gt^2                              v=d/t
v=gt                                       d=vt
*vertical distance can
only be calculated if
the object starts at rest
(0m/s) so only if the object
is in free fall

A plane at a height of 125m is going 90m/s drops a package. How long is the package going to be in the air?
*the only thing controlling an object's time in the air is the vertical distance (hang time)
d=1/2gt^2
125=1/2(10)(t^2)
125=(5)(t^2)
t^2=25
t=5

How far back will the plane need to drop the package in order for it to hit the target?
*We're looking for the horizontal distance
d=vt
  =(90)(5)
  =450m

Velocity in the horizontal distance is treated differently than how we previously treated the vertical distance. The horizontal velocity stays constant, unlike the vertical velocity that is increasing by 10m/s
every second.

Throwing Things At An Angle

Someone hits a baseball, and this is the shape the ball took in the air. The ball is in the air for 4 seconds and goes a total distance of 120m. At the top of the ball's path, it is only moving with horizontal velocity. What is its horizontal velocity?
                                                                                    v=d/t
If we didn't already know, and wanted to find              =120/4
how far downhill the ball would land...                        =30m/s
d=vt
  =(30)(4)
  =120m

                                                                             

 To find how fast the ball is actually moving, we would need to find the hypotenuse.
 a^2+b^2 = c^2
(20^2) + (30^2) = c^2
400+900 = c^2
c^2=1300
c=36m/s

A ball thrown up with a horizontal velocity is in the air the same amount of time as a ball that is thrown up without a horizontal velocity, as long as their vertical distances are the same.

Newton's 2nd Law

Force causes acceleration.

-force is proportional to acceleration (if force decreases, then acceleration decreases, and if force   increases, then acceleration increases)

mass increase --> acceleration decreases

mass decrease --> acceleration increases

acceleration is directly proportional to force --> a~F

acceleration is inversely proportional to mass --> a~1/m

Newton's 2nd Law --> a = F/m 

(this is true because a~F and a~1/m)
The law in words --> Acceleration is directly proportional to force, and acceleration is inversely proportional to mass.

You are pushing a 10kg box to the right with a force of 50N and your friend is pushing the box in the opposite direction with 10N. What is the acceleration of the box? What direction is the box accelerating?
a = F/m
   = (50-10) / 10
   = 40 / 10
                                                                                       = 4m/s^2 in the right direction

What is the weight of a 10kg box with the upward force of 50N and the force of gravity in the opposite direction?
*weight (net force) = (mass) (gravity)
w = mg
    =(10)(10)
    =100N

Newton's 2nd Law Lab

The hanging weight will apply the force that causes acceleration. 

If the mass of the cart increases, but the force (hanging weight) remains the same, then the acceleration will decrease because mass and acceleration are inversely proportionate. 

If we keep the hanging weight the same, then the net force on the system will remain constant. 

If we take mass from the cart and move it to the hanger, the acceleration will increase because the acceleration is directly proportional to force, and the weight of the hanger is the force that accelerates the system. *Doing this is still keeping the mass of the system constant*

BUT we can't just simply add mass to the hanger from an outside force, because that would be changing the mass of the system AND the force. 

If the net force on a body is zero, the acceleration of that body is also zero because force and acceleration are directly proportionate.

--> If the net force on a body is constant, the acceleration is also constant. 

a = F/m looks like y = mx+b

so... whatever is kept constant in the experiment is the slope in the equation of line. 

If the mass was kept constant --> a = (1/m)(F)

If the force was kept constant --> a = (F)(1/m)

To determine if your date confirms Newton's 2nd Law, your generated slope needs to be within 10% of the given slope. 

For example, if the given line is y = 0.5531x and your generated slope is .49 then your date confirms Newton's 2nd Law because .49 is within 10% of .5531

Skydiving 

A person with a weight of 100N is skydiving. The Fair is 20N.

*remember that if speed increases, air resistance also increases

Fnet = Fweight - Fair

Fnet = 100N - 20N

Fnet = 80N

*If Fnet decreases, then the acceleration also has to decrease because force and acceleration are directly proportional. (the weight is the force) 

As the person is falling, their speed is increasing, thus increasing their air resistance.

t = 0

Fweight = 100N

Fair = 20N

t = 1

Fweight = 100N

Fair = 30N

t = 2

                                                                                    Fweight = 100N

                                                                                    Fair = 40N 

*Acceleration is decreasing, but speed still is still increasing. 

This person has reached a point in skydiving called terminal velocity, which is how fast an object can possibly go.

Fnet = Fweight - Fair

Fnet = 100-100

Fnet = 0N

Terminal velocity is achieved if...

-Fnet = 0N

-a = 0m/s^2

-the object is at equilibrium

-the object is moving at constant velocity

Thrown Straight Up