Unit 3:  Constant Acceleration

CAPM.1

On a position versus time graph, velocity is not shown explicitly but, the velocity of an object in a graph with a constant acceleration can be determined by doing two things.

Slope of the tangent

Velocity is usually the slope of a x vs t graph, but when there is an acceleration the slope is not calculable. So, to find the instantaneous velocity can be find by calculating the slope of the tangent of the point.

Mathematic Expression

The second method is from a velocity vs time graph, when you find the acceleration of the object (Δv/time) you can use a mathematic formula to find the velocity at any given time. This formula is v=at+vi

CAPM.2.

Displacement can be found from two ways in a velocity vs time graph.

Area Under the Line

To find the displacement in a constant acceleration, velocity vs time graph you can calculate the area of the shapes under the line

Mathematical Expression

The other way is using the matemathical expression of the line to find the displacement. x=1/2at^2+vi

CAPM.3

There are four ways to calculate acceleration

Slope of a v vs t graph.

Acceleration can be found as the slope in a v vs t graph as Δv/time

Rearrange formulas

Solving for acceleration in equations is another way to find it. Acceleration can be found by rearranging: x=1/2at^2+vi and v=at+vi.

Connection to Real World.

This unit, helps us understand acceleration of objects in the real world, objects like a skateboard going down the hill or a baseball being thrown.

Ramp Challeng

Ramp Challenge

In this challenge we were asked to predict the acceleration of a ball rolling down a table that was inclined, we were also asked to predict the velocity of this ball at 4 seconds. After many trials we found the average of the position of the ball, at 0.5, 1, 1.5, 2, 2.5, and 3 seconds to find as many points as posible without revealing the answer to the challenge.

 our data was the following:

Time              Position

 0.5s                  6cm

   1s                  20.5cm

1.5s                   35cm

2s                     56cm

2.5s                   81cm

3s                     105cm.

After doing this we found that the acceleration of the ball was constant, this created a top-opening parabola in excel.

To find the slope of this line we needed to square the value of T and since most velocity units are meters over seconds we divided our position by 100 to find the values in meters, giving us this chart.

As you can see in the chart, the slope of this graph, is 0.1157, and as we learnt in the classroom, the slope of an x vs t graph, is 1/2a, meaning that the acceleration of an object is double of the slope of it x vs t graph, giving us a constant acceleration of 0.2314m/s^2.

Because we have the graph that shows us position vs time, we were able to find the acceleration, giving us a velocity vs time formula that is v=a(t) giving us a velocity at 4 seconds of v=0.2314(4) v=0.9256m/s

Unknown mass

Unknown Mass Challenge

In the picture above we can see an object with an unknown mass hanging from 2 ropes with different tensions and at different angles.

In this Free body diagram we see the forces and the components that affect this object, in this challenge we were asked to find the weight of the object. To do this we need to find FT1y and FT2y since all the forces in the Y axis need to be equal to 0.

To find these two forces you need Cos, and the strength of the original force (FT1, and FT2).

FT1y= Cos(20)= Adj

                            2.2

 Adj= 2.2 Cos(20)

FT1y=2.067

FT2y= Cos(55) = Adj

                               1

Adj = Cos(55)

FT2y = 0.573N

FT2y + FT1y + Fg = 0N

Fg = 2.067 + 0.573

 Fg = 2.64 N 

       

Unit 2 blog post

Unit 2: Forces

Types of Forces

Gravity: Always goes down, vertical towards the center of the earth.

Push force: when an external force is pushing the object

Normal Force: always perpendicular to the surface.

Tension: Always along a rope.

Spring Force: when an object is pushed or pulled and in immediatly returns to its original state.

Force of Drag: also known as air resistance is the ammount of push an object going at high velocities  recieves from the air.

Friction: Parallel to the surface, oposing motion. NOT AFFECTED BY SURFACE AREA

Newton's first Law.

Newton had three laws of motion. His first law was demonstrated in the first class period that we went over this unit,  we used the gym floor as the our physics lab, we used a hovercraft to show how after an object was pushed if no other forces were applied it would not stop, at first this was a really big misunderstanding because the hovercraft was moving so most people thought that there had to be a force pushing to it. After a lot of discussion, we learnt Newton's first law, which says: "All objects at rest will stay at rest and all objects in motion will stay in motion unless an external force is applied". The hovercraft case is a perfect example for this law because the hovercraft will stay at rest unless someone pushes on it, and this motion will continue unless the hovercraft is stopped.

Free Body Diagrams

After we talked about forces we introduced a concept of a picture that shows what forces are being applied to an object.

Above you see 4 drawings all you might see is arrows and shapes, but this describes the type of motion an object is in, or if its accelerating, decreasing speed or changing direction. When forces are balanced (Arrows on opposite directions are congruent) means that an object is at rest or at constant velocity. when forces are unbalanced (Arrows not congruent) it can mean one of three things, that the object is speeding up, slowing down or changing directions. at some point the axis of the diagrams will be slanted, this means that the surface were the object is placed is slanted.

Weight Vs. Mass

 mass is what we usually see when we when we usually think about weight but it is the ammount of mass an object or a human has. Weight is this mass affected by the force of gravity.

Newton's 3rd law

Newton's 3rd law says that all actions have an equal and opposite reaction, these are called action reaction pairs, for example:

In this picture the kid is pushing on the ball but the ball is also pushing the kid back.

Connection to real life

when a baseball is thrown up, after it is released, there is only one force acting on it, gravity, contrary to popular beliefs there are no forces pushing this ball forward, only pushing it down, and it is causing the ball to change direction, it is not going in a perfectly straight line but going down.

Texting While Driving

During this challenge, we were asked to determine how far we would travel while texting LOL to a friend.

Trials

We took about 5 different times and averaged it out, and we got 1.125 seconds

Math

So, we determined that we were driving at 60 Mph, but we need to convert that to meters over seconds so that it is compatible with our trial.

60 miles          X   1609.344 Meters          X       1 Hour

      hours                    1 Mile                               3600 secs

60 miles          X   1609.344 Meters          X       1 Hour

      hours                    1 Mile                               3600 secs

After the units cancel out and we do the math we get 26.8 m/s, now we have the time and the velocity this is setting us up for the constant velocity formula.

x= vt+x initial

x=26.8(1.125)+0

x=30.15m

Answer

using this equation determines the displacement, and it tells us that we move 30.15 meters while texting LOL to a friend.

Unit One Summary

Unit One Summary

Constant Velocity Model

Velocity

Velocity describes at what rate the object is moving, it is usually found by dividing displacement of an object over the time it took it to displace. Velocity is found as the slope in a position Vs. Time graph, objects can have positive or negative slopes, this only indicates direction, a negative slope means that the object is moving backwards, a positive means its moving forward.

Above is shown a positon Vs. time graph, there, velocity is shown as the slope of the graph, another way to show velocity is a velocity over time graph, in this graph, velocity is displayed on the Y-Axis.

In this case the object's velocity is constant and an object at rest is shown as a straight line on the X axis (Y=0)

Displacement

Displacement is the change in position of an object in relation to its starting point, in a velocity Vs. Time graph, displacement can be found by multiplying the velocity of the object by the time it traveled at that velocity. On a Position Vs. Time graph, displacement is found by finding the difference on the Y-Axis, (final position-Initial position). Displacement is usually confused with distance covered, and that is not true, although some time distance is equal to displacement they are not the same, distance is the total distance covered and displacement is the change of position in relation to the origin.

Motion Map

Above is shown a motion map, motion maps are used to describe the motion of an object, as you can see there are small dots with arrows, each dot represents a second that has passed, and the arrow shows the direction in which the object is moving, and the lenght of the arrow shows a bigger or smaller velocity in relation to other arrows.

Speed

Speed is commonly confused with velocity, speed is how fast an object is going at a certain period of time, while velocity describes a change in position in relation to the origin.

Motion

Motion can be shown in many different ways, motion can be discribed as a change in position, increase velocity or even decrease velocity.

Connection to the real world.

This unit can be related to the real world, since we constantly see objects in motion or even we are in motion. Cars a prime example of this, they are usually at a constant velocity, they sometimes accelerate or decelerate but usually when they travel they mantain a constant velocity