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Acceleration

Acceleration is a change in speed, or velocity

acceleration examples

Smartphone Physics Lab

 We need a lab to study displacement, velocity and accelerations.

We’ll attach a smartphone to a toy car, and take accurate measurements using the phone’s internal sensors.

d-v-a-smartphone-car

Physics Toolbox Sensor Suite (Google Android)

Physics Toolbox Sensor Suite (Apple iOS)

physics-toolbox-sensor-suite

Useful for STEM education, academia, and industry, this app uses device sensor inputs to collect, record, and export data in comma separated value (csv) format through a shareable .csv file. Data can be plotted against elapsed time on a graph or displayed digitally. Users can export the data for further analysis in a spreadsheet or plotting tool. See http://www.vieyrasoftware.net for a variety of usage ideas

SENSORS
(1) G-Force Meter – ratio of Fn/Fg (x, y, z and/or total)
(2) Linear Accelerometer – acceleration (x, y, and/or z)
(3) Gyroscope – radial velocity (x, y, and/or z)
(4) Barometer – atmospheric pressure
(5) Roller Coaster – G-Force Meter, Linear Accelerometer, Gyroscope, and Barometer
(6) Hygrometer – relative humidity
(7) Thermometer – temperature
(8) Proximeter – periodic motion and timer (timer and pendulum modes)
(9) Ruler – distance between two points
(10) Magnetometer – magnetic field intensity (x, y, z and/or total)
(11) Compass – magnetic field direction and bubble level
(12) GPS – latitude, longitude, altitude, speed, direction, number of satellites
(13) Inclinometer – azimuth, roll, pitch
(14) Light Meter – light intensity
(15) Sound Meter – sound intensity
(16) Tone Detector – frequency and musical tone
(17) Oscilloscope – wave shape and relative amplitude

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Acceleration in uniform circular motion

An object in uniform circular motion is always accelerated inwards.

Magnitude of acceleration is constant
Direction of acceleration always changes – always facing radially inward.

Hewitt

Hewitt

The car goes around the circular track at a constant speed,
yet it’s velocity is changing. How?
Velocity = speed + direction.

The direction is always changing, so it’s velocity vector is always changing.

Velocity vector is always tangent to the car’s path
That’s the direction the car would fly off in, if it lost friction.

Since it’s velocity is always changing, by definition it must be accelerating

Acceleration vector is always pointing radially inward.
That’s the direction of the force keeping the car in a circular motion.
Without this force, the car will move in a straight line (inertia)

How to calculate the average acceleration

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The units are m/s on top, and s on the the bottom

So the units of acceleration are m/s / s  ,  or m/s 2

Direction of the acceleration vector?

The direction of the acceleration vector depends on two things:

whether the object is speeding up or slowing down
whether the object is moving in the + or – direction

Here’s the rule:

If an object is slowing down, then its acceleration is in the opposite direction of its motion.

Let’s work through the examples here: Acceleration on PhysicsClassroom.Com

Limitations

For the most part, we only study examples with constant acceleration. In real life, though, acceleration isn’t always constant: acceleration can change!

Consider:  When you first get in a stationary car, your velocity and acceleration are zero to start. Hit the accelerator: the engine accelerates the car, and the car changes velocity. Just one-tenth of a second later, the acceleration is larger – and another tenth of a second later, the acceleration is larger still!

Your car’s acceleration will eventually reach a maximum, perhaps 3 or 4 seconds after you hit the accelerator. At that point the car has constant acceleration – and thus it’s change in speed thus increases smoothly after that.

Changing acceleration are analyzed in detail in AP Physics.In this class we note that, yes, acceleration changes, but to make our math simpler, we’ll deal only with cases of constant acceleration.

Learning standards

2016 Massachusetts Science and Technology/Engineering Standards
HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations.

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
PS2.A Forces and motion. How can one predict an object’s continued motion, changes in motion, or stability?

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)
Introductory Physics. Motion and Forces. Central Concept: Newton’s laws of motion and gravitation describe and predict the motion of most objects.

1.1 Compare and contrast vector quantities (e.g., displacement, velocity, acceleration force, linear momentum) and scalar quantities (e.g., distance, speed, energy, mass, work)

1.2 Distinguish between displacement, distance, velocity, speed, and acceleration. Solve problems involving displacement, distance, velocity, speed, and constant acceleration.

1.3 Create and interpret graphs of 1-dimensional motion, such as position vs. time, distance vs. time, speed vs. time, velocity vs. time, and acceleration vs. time where acceleration is constant.

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