A virtual laboratory with idealized experimental conditions is used for the simulations. It looks like a rectangular box with transparent walls. The investigated motion occurs within this box. There are options which allow us to rotate this box about the vertical and horizontal axes, thus changing the aspect in order to choose a convenient point of view. To do this, you can open the panel 'Options' and change the relevant angles alpha and beta by dragging the slides on the corresponding scroll-bars. If you want to observe the vectors of the total forces and/or the velocities of the bodies during the simulation, mark the corresponding check-boxes in the Control panel. The program will show you (in a separate window) also the time-dependent graphs of the position and velocity for one of the bodies if you mark the check-box 'Show graphs'. With the mouse, you can resize this window and drag it to any convenient position on the screen.

Collisions of the bodies (moving balls) with the walls of the box can be handled as wholly elastic (the direction of the velocity vector changes, but its magnitude remains the same), wholly inelastic (the ball 'sticks' to the wall), or partially inelastic (or partially elastic, if you like). The choice depends on the restitution coefficient, whose value shows the ratio of the velocities after and before a collision. Actually, this coefficient depends on the properties of materials that are used for manufacturing the walls (and the moving bodies). Depending on the adopted model, we can assign for this coefficient any value from the interval between 0 and 1. The boundaries 0 and 1 correspond to purely inelastic and purely elastic collisions, respectively. The value can be changed with the mouse by dragging the slide of the corresponding scroll-bar in the Control panel, or, with the keyboard, by typing the desired value into the box over this scroll-bar and pressing 'Enter' afterwards.

The first section illustrates the principle of inertia (uniform rectilinear motion in the absence of forces), and the motion under a constant force (a uniformly accelerated motion). The latter case clarifies also the important concept of the inertial mass.

The second section presents several simulations of motion in a uniform gravitational field, which can help understanding the concept of gravitational mass, as well as the universal proportionality between the inertial and gravitational masses. When the bodies fall down under the gravitational force in a viscous medium, the opposing force of friction increases as the body gains the velocity, and eventually we can observe a uniform downward motion in the situation, in which all the forces are compensated.

The simulations of the third section show bubbles rising in a viscous medium. In this case the final uniform upward motion also occurs in conditions of full compensation of the buyoant and frictional forces exerted on the rising bubble.

Contents

1. The laws of motion. The uniform rectilinear motion in the absence of forces, and the motion under a constant force are simulated.

2. Falling objects. The motions of bodies falling down under the gravitational force in the idealized situation of a vacuum, in which bodies move without any resistance, and in a viscous medium are simulated.

3. Rising bubbles in a viscous liquid. The motion of a bubble occurring under the buoyant force and the opposing force of viscous friction is simulated.

Back to top

Eugene Butikov personal page | Contents | Next section