Physics
Physics in action - Activities and practice
Inhaltsverzeichnis
- Basics
- Scalar or vector?
- Vectors and Components
- Cartesian Notation of a Vector
- Vectors and Components - Trig
- Vectors and Components - Test
- Vectors: Addition and Subtraction - The Parallelogram Law
- Vectors: Scalar Multiplication
- Kinematics
- Uniform rectilinear motion
- Exploration of a uniform rectilinear motion
- Dynamics
- Pendulum Snake
- Thermodynamics
- Brownian Motion - A Simple Dynamic Animation
Scalar or vector?
Scalar or vector?[br]Click the check box that matches the correct answer.
Uniform rectilinear motion
A ladybug is at the origin of a Cartesian reference system at time [math]t=0[/math] and is moving with uniform rectilinear motion.[br][br]Select a graph type to explore, enter the speed and start the animation.[br]The time interval displayed refers to the first 15 seconds of the ladybug's motion.[br][br]To examine the motion in detail, pause the animation and drag the point on the [i]time[/i] axis.
Uniform Rectilinear Motion
Practice Zone
Compare the graphs obtained by setting different speeds.[br]What do you notice? [br]How do the [i]position - time[/i] and [i]velocity - time[/i] graphs change as they describe the ladybug's motion?
A car travels at a constant speed of 108 km/h.[br]Convert the speed into meters per second (m/s), and calculate the time needed to travel 36 km.
The following table shows the distance traveled by a car in the first 10 seconds of its motion.[br][br][img]data:image/png;base64,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[/img][br][br]What type of motion is it? Explain your answer.[br]Write the equation of motion and calculate the distance traveled by the car after 11 seconds.
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.