Physics
Physics in actions - Activities and tests
Table of Contents
- Basics
- Scalar or vector?
- Vectors and Components
- Vectors and Components - Trig
- Vectors and Components - Test
- Sum and difference of two vectors - The parallelogram method
- Propagation of error in sum and multiplication
- Kinematics
- Linear motion without acceleration
- Exploration of a linear motion without acceleration
- Dynamics
- Pendulum Snake
- Parking
- Brownian Motion - A Simple Dynamic Animation
Scalar or vector?
Scalar or vector?[br]Click the check box that matches the correct answer.
Linear motion without acceleration
Let's explore a linear motion without acceleration.[br]Select the type of graph you want to show by clicking the related checkbox.[br]Type the speed of the car in the [b][i]speed [/i][/b]box, then press the [i]Enter[/i] key to confirm.[br]Start and stop the animation by clicking the [color=#0a971e][i]Start/Stop[/i][/color] button.[br][br]To drive the car back to its start position click the [i][color=#c51414]Restart[/color][/i] button.[br]Compare the graphs you obtain setting different speeds, each time driving the car back to the start point without deleting the traces and modifying the speed value.[br]What do you observe? How do [i]Position vs Time[/i] and [i]Velocity vs Time[/i] graph change?[br][br]To delete the graph click the [i][color=#888]Delete traces[/color][/i] button.
Pendulum Snake
The motion of a pendulum is not easy to describe analytically, but some simplifications (small-angle approximation) allow us to obtain simple formulas to describe its motion, period and frequency.[br][br]If we release the bob with a starting angle [math]\theta_0\ll1[/math] radian and no angular velocity, we can describe the [b][i]motion [/i][/b]of the pendulum at any instant with the formula [math]\theta\left(t\right)=\theta_0\cos\left(\sqrt{\frac{g}{\ell}}t\right)[/math], where [math]\ell[/math] is the length of the (massless) cord and [math]g[/math] the gravitational acceleration constant.[br][br]The motion of a pendulum is then harmonic, and the angle [math]\theta_0[/math] is the amplitude of the oscillation, that is the maximum angle between the cord of the pendulum and the vertical equilibrium position of the bob.[br][br]For [math]\theta_0\ll1[/math] the [b][i]period [/i][/b]of a pendulum can be approximated by the Huygen's law [math]T=2\pi\sqrt{\frac{\ell}{g}} [/math].[br]Quite counter-intuitively, the period doesn’t depend either on the mass of the pendulum bob or on how far the pendulum swings, but it depends only on the length of the cord! (see Galileo's isochronism for details).[br][br]The [b][i]frequency [/i][/b]is defined as the inverse of the period, therefore we have [math]f=\frac{1}{T}=\frac{1}{2\pi\sqrt{\frac{\ell}{g}} }[/math]. [br]Solving this equation for [math]\ell[/math], we can find which length of the cord generates a certain number of oscillations around the equilibrium position: [math]\ell=\frac{g}{4\pi^2f^2}[/math][br]
Try It Yourself Part 1 (ideal coplanar pendulums)
You now have all the necessary "ingredients" to create cool patterns using the pendulums in the app below.[br][br]We have 6 of them, fixed to the same pivot, and you can use the sliders to adjust the starting angle [math]\theta_0[/math] and the length of the cords of each pendulum.[br][br]Can you figure out how many oscillations will make each bob in 30 seconds, using the formulas above and the data in the app? [br][br]Use the [i]Play [/i]button without modifying the default lengths and angle to animate the pendulums and explore the current pattern, then use the sliders (and formulas!) to create your own pendulums.
Try IT Yourself Part 2 (pendulums move in parallel planes)
Same as in the app above, but this time the pendulums move in parallel planes, that is, they are not fixed to the same pivot.[br][br]Right click and drag the 3D View (or use the predefined gestures if you are on a touch device) to explore the animation from different points of view.
Brownian Motion - A Simple Dynamic Animation
Even though it seems that all the particles of a fluid are motionless, it's possible to observe that each particle moves randomly, and its motion depends (also) on the fluid temperature.[br][br]Move the slider to change the fluid temperature and observe the changes in the motion of the particles.