Laws of Motion

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Computer illustrations to the laws of motion 2

Falling objects

To illustrate the fundamental laws of classical Newtonian dynamics, we consider here the motion of bodies falling down under the gravitational force. First we simulate the idealized situation of a vacuum medium, in which all bodies move without any resistance. Then the motion in a viscous medium is simulated, in which the frictional force is proportional to the velocity and to the linear dimension (diameter) of the moving body. To observe the graphs of the simulated motion, mark the corresponding check-box "Show graphs" in the Control panel.

Executing experiments on your own in this virtual laboratory, you can vary the magnitude of the gravitational acceleration, the viscosity of the medium, the restitution coefficient for collisions of the balls with the walls of the box. If you open the panel "Parameters" by marking the corresponding check-box, you will be able to vary the masses of two bodies and driving forces exerted on them, and the initial conditions. When the desirable values of all the parameters are entered, click on the "Ready" button.

Examples:

1. Free fall in a vacuum. In a vacuum, all bodies fall down with the same acceleration. This example shows two bodies of different masses and sizes that fall down in a gravitational field from the same height with zero initial velocities. The bodies reach the floor simultaneously.

2. Independence of the vertical and horizontal motions. In this example the bodies have non-zero horizontal initial velocities. However, the horizontal motion doesn't influence the motion in the vertical direction. Hence in this case all the bodies also reach the floor simultaneously. (Click also here to see the applet.)

3. Different balls in a viscous medium. For different balls of the same density (of the same material), the gravitational force is proportional to the third power of their linear dimensions (diameters), while the force of viscous friction is proportional to the first power. Hence the final velocity is proportional to the square of the diameter. (Click also here to see the applet.)

4. Identical balls falling down in a viscous medium. At first instance the velocity is zero. Hence the frictional force is negligible, and the acceleraton is due only to gravity. As the velocity increases, the resistance becomes greater, and finally compensates for the gravitational force. The net force is zero, and the bodies move down uniformly. Identical balls reach the floor simultaneously. (Click also here to see the applet.)

5. Identical balls in a viscous medium with different horizontal initial velocities. When the medium is characterized by a frictional force which is proportional to the velocity, the horizontal and vertical components of motion are independent. Thus at non-zero horizontal initial velocities all the balls also reach the floor simultaneously. (Click also here to see the applet.)

6. Free motion of bodies in a vacuum in the absence of gravity. This example illustrates the law of inertia. It shows the uniform free motion of two bodies that have arbitrary initial velocities. Between collisions with the walls the bodies move with constant velocities. Direction of the velocity is changed each time the body bounces from a wall of the box. (Click also here to see the applet.)

7. The projectile motion in the absence of air resistance. This example illustrates the free motion of bodies in a uniform gravitational field without the air resistance. The bodies move along parabolic trajectories. All the bodies have initial velocities of equal magnitudes, which make different angles with the horizon. (Click also here to see the applet.)

8. The projectile motion complicated by the air resistance. All the bodies have initial velocities of equal magnitudes, which make different angles with the horizon. (Click also here to see the applet.)

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Computer illustrations to the laws of motion 2 (of 3)