Motion on a Ramp and More

Kinematics

Uniform Acceleration

Galileo's Ramps

Intro to data collection activity:

Learning to Learn:
- Using data to identify relationships and create generalized formula.
- It's not about the acceleration, but about the process.
What can you measure?
- Variable id pic (Pic of set up in center of page - ID variables surrounding the pic.)
- What will you change? measure? keep constant?
- What is your baseline (zero-point)?
- What is the 'noise' in your data?
How will you show your results?
- Pictoralily (motion maps)
- Graphically

Galileo's Experimentation and Graphing:

How does angle of ramp affect acceleration?
How does mass affect the acceleration of a cart on a ramp?
How does the mass of the cart affect the bounce of the cart? (Use spring steel)

Create an inclined plane with the track provided.
Begin with a small angle and be prepared to describe how you would find the angle of the ramp, using a meterstick.
Observe the cart rolling down the ramp.
Draw motion maps (a minimum of 5) to represent the motion of the cart as it travels down the ramp.
Mark two points on your ramp using a small piece of tape.
Using the LabQuest, determine the acceleration of your cart.
1. Record this value in your data table.
2. Repeat this process until you have determined a consistent acceleration.
Increase the angle of the ramp, repeat the process for a minimum of 4 angles.
Setup B -Up and Down the Ramp:
1. Using the same process to collect data, give the cart a gentle push so that is rolls up and down the ramp.
2. Compare the acceleration of the cart as it moves up the ramp to the acceleration as it moves down the ramp.

Three Kinematic Graphs:

Sketches of Graphs:

Significant Points:
- Indicate significant points
  - Max, min, intercepts, inflection points
Meaning of Slope:
- On your graphs indicate places where the slope is:
  - increasing, decreasing, or constant.
  - positive or negative
  - state what the slope represents.
Meaning of Area under the curve:
- The importance / meaning of the area under the curve.

Uniformly Accelerated Motion Equation

Complex Motion on a Ramp

For each of the following scenarios:

Description:
- Describe the motion of the object while moving unaided using the appropriate vocabulary.
Sketch of Setup
- Sketch the scenario, including position of the appropriate variables.
Motion Maps:
- Draw velocity and acceleration motion maps of the object in motion.
Sketches of Graphs:
- From your data:
  - Sketch each of the three graphs
  - Be sure to align them according to their time.
- Significant Points:
  - Indicate significant points
    - Max, min, intercepts, inflection points
- Meaning of Slope:
  - On your graphs indicate places where the slope is:
    - increasing, decreasing, or constant.
    - positive or negative
    - state what the slope represents.
- Meaning of Area under the curve:
  - The importance / meaning of the area under the curve.
Change a Variable:
- Choose a variable that you can change
- Show on your graphs how this would change your graph.

B - Up and Down a Ramp

C - Bouncing Along

Gently, push the cart up the ramp.
Observe a cart rolling up and down an inclined ramp.
Describe the motion of the cart while it is coasting.
Set your zero point as the lowest point.

Using a cart with a spring steel, release the cart a the top of the ramp.
Observe the cart as it is moving along the track.
Describe the motion of the cart while it is coasting.
Set your zero point as the lowest point

Practice with the various graphs.

Position, Velocity and Acceleration v. Time Graphs

Uniform Acceleration in one Direction

Sample Questions:

A. The graph shows the variation of speed v of an object with time t.

Sketch the corresponding position-time graph.
Sketch the corresponding acceleration-time graph.

B. An object is at rest at time t=0. The variation with t of the acceleration a of the object is shown from t = 0 to t=8 s.

Determine the object's speed at 4s?
Determine the object's speed at 8s?
Determine the object's speed at 6s?

C. The graph below describes the motion of a mass oscillating on a spring. Upwards is considered positive.

The position marked 'C' indicates
1. A maximum displacement and a maximum velocity
2. A maximum displacement and a minimum velocity
3. A minimum displacement and a maximum velocity
4. A minimum displacement and a minimum velocity.
The position marked 'D' on the graph indicates the location where the mass experiences:
1. Maximum positive acceleration
2. Zero acceleration.
3. Maximum negative acceleration.
4. The acceleration is constant throughout the cycle.

Tangent Lines (Slopes/Gradients at a point)

List of Variables

Galileo's Ramps

Given a water clock and various spherical masses, determine the relationship between the distance traveled and time elapsed, and this relationships independence of mass.

A - Cart on an Air Track

B - Sliding v. Rolling

Create comparison graphs of the 5 objects.

E - Down the Ramp, across the board, onto the carpet

F - Fan Cart with 2 Settings

This will be done without data collection. Combine the motions from above to describe the motion of the cart until it comes to a stop (off screen).

G - Mass on a Spring (Oscillating)

H - Swinging Pendulum

Mass on a Spring:

Describe two complete cycles of motion.
Begin your description at a position of maximum displacement.

Pendulum:

While often described as changes in Radians v. time. The motion is also very consistent when described a position v. time.
As an additional descriptor challenge, plot velocity v. position. Indicate similar positions on both a velocity-time and velocity-position graphs.

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