**Motion in One Dimension:** Acceleration and Free Fall

**Motion in One Dimension:**

__Reading__

BJU book: Ch. 3 "Motion in one dimension" (continued)

__Topics__

The concept of acceleration

Free-fall problems

The Skydiving Cat and Elephant Formation gifs illustrate "free fall". All satellites, including the Moon, are actually in "free fall" towards the earth. The reason they don't crash into the Earth is because they "side step" at just the right amount so as to stay in orbit. The Moon orbits the Earth at about 2,000 miles per hour. The Earth orbits the Sun at about 80,000 miles per hour. A man-made satellite orbiting near the Earth's surface needs to travel at about 18,000 miles per hour to stay in orbit, and completes its journey around the Earth in about 90 minutes. We will cover gravity and orbits later in the year.

__Lecture outline:__

Velocity (Review from last session)

- Velocity indicates how your location changes with time. It is distance divided by time, as in “miles per hour” or “meters per second”
- We write the formula as follows:

vavg = (x2 – x1) / (t2 – t1)

Acceleration (this is what we're covering now)

- Acceleration indicates how your
__velocity__changes with time. - Positive acceleration means "speeding up". Negative acceleration (i.e. deceleration) means "slowing down".
- We use units of "meters per second per second" or "meters per second squared".
- We write the formula as follows

aavg = (v2 – v1) / (t2 – t1)

Be able to use the 5 equations of motion from Unit 1. They are reprinted here for your convenience. Take a minute right now to write these on the inside cover of your book!

- Be able to solve straight-line acceleration problems using one or more of the 5 equations.
- The definition of 'acceleration' was given in Unit 1.
- When solving a "free-fall" problem, use the acceleration of gravity as the "a" term in your equation. On Earth, at sea level, use 9.81 m/s^2 as the acceleration.
- When solving a "free-fall" problem on a different planet or moon, the problem will need to specify what the acceleration of gravity is.

__Galileo's Inclined Plane lab, part 2__

In this exercise we reproduce Galileo's famous inclined-plane experiment using a modern Vernier cart and track set at 3 different angles.

After collecting the raw data from the 3 different scenarios, we plot distance vs. time and use a best-fit curve to calculate the

__velocity__of the moving cart at different points on the track, for each scenario.

Then, using this information, we calculate the average

__acceleration__of the cart down the track for each track angle.

Finally, using the angle of the track we estimate 'g', the acceleration of gravity, and compare with the known value of 9.8 m/sec^2.

This is exactly what Galileo did using a bronze ball and wooden track with a groove down the middle. Galileo, however, didn't have a movie camera with an electronic timer; his "clock" consisted of allowing water to drip into a container and then weighing the container!

__Galileo's lab report, part 2 (see class emails for due date):__

Use the teacher's example, below, as a guide. (sheets 1 & 2)

We will go over this in class.

Requirements: Complete and turn-in the following 4 items while referring to the teacher's example below:

- Compute the final velocity for each track as shown on sheet 1. Hint: Draw a tangent line and calculate the rise-over-run as depicted on sheet 1 of teacher's example.
- Using sheet 2 of teacher's example as a guide, compute the average acceleration of the cart down each track.
- Using the principle of "similar triangles", as shown on sheet 2, calculate the acceleration of gravity 'g' for each of the 3 runs.
- Analysis: compare your 3 values of 'g' with the known value of 9.8 m/s^2. Comment. Try to explain any differences.

TEACHERS EXAMPLE_galileo_inclined_plane_pt.2_lab_writeup.pdf |

__Homework (see class emails for due dates)__

2._acceleration_homework_problems.docx |