CAPM Challenge 1

CAPM Challenge 1

 Graphs and Data Charts

This graph represents the data that was initially taken for the ball's position over time.  As we observed, the ball is accelerating constantly, as the graph's shape goes into an upward slant.

In order to better interpret the data, we had to square the time to get a straight line.  This gave us a more accurate and readable sense of how much the ball was accelerating.  From our data, the graph's equation is x = 0.0951t^2 + 0.0349.  

Reminders about formulas

y = mx + b (for a straight line)

to straighten a line, you must use y = mx^2 + b

velocity = change in position / change in time

acceleration = change in velocity / change in time

Mathematical Expression

The acceleration of an object is shown by the change in velocity over the change in time.  We used the formula a = v final - v initial / t final - t initial to solve for the acceleration.

Predicted acceleration 

0.1902 m/s^2

How did we get the velocity of the ball at 4 seconds?

By using our formula , we were able to find the velocity of the ball at four seconds.  We first found the position of the ball when t=5, which was found by substituting 5 for t in the equation above.  We then found the position of the ball when t=3, which was also found by using the equation.  The position of the ball at 5 seconds was 2.41 meters, and the position of the ball at 3 seconds was 1.55 meters.  We subtracted those, and divided them by 2 (5-3) to find the average velocity at four seconds, which was 0.427 m/s.   

Were we within 10%?

We were within 10%!  We found the percentage error by doing the (approximate-predicted) / approximate.  We were only 1% off!  The real acceleration was 0.187 m/s^2, and we got 0.1902 m/s^2.

Conclusion

This was an overall interesting challenge, because we were forced to use all of the knowledge that we had accumulated from the last class to solve the problems.  With help from my two partners, Will R. and Isabella, we were able to find some shortcuts and use the new formulas to find the acceleration of objects, and the velocity of objects.  I thought it was really cool to see us solve this physically by using our knowledge, and then compare it to the actual information by using the cart roller.  It's pretty cool to be so accurate without using all of the technology!

BFPM Practicum

BFPM Practicum

The Set Up:

Free Body Diagram:

Workings and Challenge Solving:

Cos θ =  adjacent / hypotenuse                                                               Cos θ  = adjacent / hypotenuse

Cos 53 = Ftby / 0.9N                                                                              Cos 13 = Ftay / 2.2N

0.9 cos 53 = Ftby                                                                                    2.2 cos 13 = Ftay

0.5N = Ftby                                                                                            2N = Ftay

PREDICTED TOTAL : 2.5N

Unit 2 - Balanced Force Particle Model

Bowling Balls and Hovercrafts

To speed up an object...

- Apply more force on it from behind

- The boy continuously pushed the ball with a greater force 

To stop an object...

- Apply force in the opposite direction of travel

- The boy stopped the ball by putting his hand on it

To keep an object moving at constant velocity...

- Apply no force once it is moving

- Nothing needs to keep this object moving as long as nothing stops it

Constant Velocity Misconception

Situation: A cart is moving at a constant velocity of 10mph, and a ball will pop out of it.  Will the ball land in front of the cart, behind the cart, or in the cart?

Explanation: Many people don't understand that the ball is moving with the same velocity as the car.  Once the car starts moving, the car and the ball move forward at the same speed because the ball is in the car.  When the ball is thrown upwards, with the cart continuously moving, the ball moves forward with the cart and lands back inside.  There was no outside sideways force to prevent the ball from continuing on its path of 10mph with the cart.  

Introducing Full Body Diagrams

When systems are balanced, they have an equal amount of force on each side.  There is also no change in the up and down motion.

When systems are unbalanced, they have an unequal amount of force on each side.

Newton's 1st Law 

 When all forces are balanced, an object in motion/at rest stays in motion/at rest unless an outside force acts upon it.

Types of Forces

Normal Force - The force perpendicular to the two surfaces that touch each other

Frictional - The force parallel to the surface at which an object travels

Tension - The force evident when there's a rope/chain exerting tension on an object

Gravitational - The force exerted through a force field by two objects (when the situation is on earth)

FBD Examples

 The ball is not moving, therefore it is resting at a constant velocity.  There is no force going horizontally that is making it stay that way, therefore the only forces on this object are the gravitational force and the normal force, which are going vertically.  (Make sure you use vectors to indicate balance)

The man is pushing the table with a force of 20 N.  By removing friction from this situation, the speed at which he's pushing the table is speeding up.  The forces acting on the table are the push, gravitational, and normal.  

The ball has been thrown into the air.  While it is in the air, the only force acting on it the entire time is the gravitational force.  Whether it be travelling upwards, at it's peak, or travelling downwards, the only force evident is the gravitational pull from the earth.  

The parachutist is moving at a constant velocity after pulling his parachute out.  If the skydiver didn't have the parachute, there would be a greater gravitational force and a smaller air force until it would reach terminal velocity.

Imaging you're in a car that's moving 50mph.  When braking, there is an unbalanced net force pushing the car backwards, slowing the car down.  The seatbelt prevents you from moving forward by providing an unbalanced backwards force.  

Introducing Newton's 3rd Law

For every action, there is an equal and opposite reaction.

Example 1 - A Mercedes Benz going 50mph and a Mac cement truck going 50mph collide on I-40.  Which one was hit with more force?  Why?
Answer - Neither was hit with more force!  According to Newton's 3rd Law, each action has an equal and opposite reaction.  So, if the Mercedes Benz hit the Mac truck with 1000N of force, the Mac cement truck hit the Mercedes with the same amount of force.  
Example 2 - A man is applying a push force on a table in the science lab, but it's not moving!  What is going on?
Answer - Two things are happening in this situation.  Not only is friction working against his push force on the table, but the same amount of force exerted onto the table is being pushed back onto the man.

Tug of War (expanding on Newton's 3rd Law)

When playing a game of tug of war, you may think that the way to win is through having a strong team.  However, whichever team has the most friction tends to win.  

*Keep in mind that both surface area and velocity DO NOT affect friction.

Full Body Diagrams with Slope

The skier on the left is moving in a downward slope on a mountain at a constant velocity.

The free body diagram shows the tilted axis, that's friction force is now parallel to the surface.  We had to split the Fg to make it a balanced diagram.

Full Body Diagrams with Angle

The box is being pulled at a constant velocity.  If the box had a weight of 200N, you could use a formula like cosine = adjacent/hypotenuse to find the Fgy.  The Ft in this situation is the 200N.  

cos x = adj/hyp

cos30 = Fgy/200

200 cos30 = Fgy

31N = Fgy

Finding the Mass of an Object

w = mg

Remember: 

w = weightm = massg = gravity (a constant of 10N)

Example 1 - An object has a mass of 20 kg.  What's the weight of the object?

w = mg
w = (20kg)(10N)
w = 200N

*Reminder: When calculating the weight of an object, the mass has to be in kg, so convert it from grams to kg if necessary.

Finding the Kinetic Friction of an Object

Ff = µk * weight