CAPM Challenge - Rolling Ball Acceleration

Introduction:
For this challenge, our physics class was tasked with finding the acceleration of a ball rolling down a table. We were allowed to use a ball, chalk, and a ruler. We also had to fined the instantaneous velocity of the ball at 4 seconds.

Procedure:
We are going to have a ball on the table(inclined). We will mark the position of the ball at each half second with the chalk and will measure with the ruler. We predicted that there will be a constant acceleration of the ball.


Raw Data:
This data came from an average of three trials, and is converted from originally cm to m.

Time(s)     Position(m)
.5               .056
1                .148
1.5             .283
2                .466
2.5             .682
3                .905

Evaluation of Data:
Originally, we found the x vs. t graph, but we changed it to be x vs. t^2 because that linearized the graph and gave us the equation for the line. We used this data to find the acceleration of the ball. Our equation from the x vs. t^2 Graph was:
Position=.0973(time)+.0546
We were able to use this equation to find our predicted acceleration of the ball.
Acceleration = 0.1946 m/s^2

This graph shows the position vs. time^2 graph after we manipulated the data

This graph shows the position vs. time from our raw data.

Conclusions:

From this lab we have used our learning from class, and applied it to the real world. We took data using only a ball, a ruler and chalk, and were able to calculate the acceleration of the ball. Our error margin was within ten percent also, which shows our knowledge of this material.

Unit 2 Summary: Forces

Introduction and Newton's First Law:
We started this unit with an experiment where we rode on a hovercraft and pushed bowling balls with brooms. While these experiments were fun, they also taught us about the topic of our upcoming unit: Forces. Our class began by riding on the hovercraft. We quickly realized that once we were in motion, we kept moving at a constant velocity until someone stopped us. There were no forces acting on us when we were on the hovercraft. The same principles applied to the bowling ball experiment. We began by pushing the ball with a broom, and we found that the ball would keep rolling indefinitely unless we changed its direction or stopped it with the broom. These two experiments demonstrated Newton's First Law. 

Newton's First Law:
An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. It may be seen as a statement about inertia, that objects will remain in their state of motion unless a force acts to change the motion.

Free Body Diagrams:
One of our new models that we developed over the course of the unit was the free body diagram. This diagram shows the direction of all forces acting on an object. If the object is moving at constant velocity or is at rest, the two opposite forces will be equal. If the object is gaining speed, losing speed, or changing direction, the forces will be unbalanced. The forces will also appear on an x and y axis. 

The Free Body Diagram pictured above is balanced,
meaning it is at constant velocity or at rest. 

Types of Forces:

Gravity: The force pulling objects to the center of the earth

Normal Force: The force opposing the force of gravity, it pushes

away from the earth.

Push Force: The force of one object pushing another.

Friction: The force of an object dragging. It can only be as strong as the force that it is opposing.

Tension Force: The force along a rope.

Spring Force: The elasticity of a spring; how much a spring wants to return to its original form. 

Real World Application:

This example shows a climber on the side of a mountain, repelling down. The forces in this example are the force pull or tension on the rope and the force gravity in the vertical direction. Also, the climber has his foot against the mountain which is creating a friction force that opposes the force of gravity. There is a normal force on his foot from the mountain. 

Force Formulas:
The first formula that we learned was for converting between Mass and weight

W=MG

The W in the equation is for weight (expressed in Kg). The M is for Mass (expressed in Newtons). The G is for gravity (Newtons), and it is equal to 10N. 

The second formula we learned was for calculating the friction of an object.

Newton's Third Law:

The final law that we learned was Newton's Third Law. It states that for every action there is an equal and opposite reaction. This means that there is always a pair of forces acting oppositely on two interacting objects. For example if a someone pushes a table across the room, the table also pushes the person with equal force.