Computer illustrations to the laws of motion

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Computer illustrations to the laws of motion – 1 (of 3)

The law of inertia, now commonly known as the first Newton's law, was first clearly formulated by Galileo, and afterwards included by Isaac Newton in his new mechanics as one of the fundamental laws. To illustrate this law, we consider here the motion of different bodies in the absense of forces. This situation is hardly possible in a real laboratory on the earth. Therefore we should connect the experimental verification of the first Newton's law with extrapolating the results of real experiments to idealized conditions. Real experiments of this kind, often used as lecture demonstrations, exploit gliders supported by the air track cushion. The first two simulations of this section can be treated as experiments with an idealized track, in which friction is completely eliminated. To observe the graphs of the simulated motion, mark the corresponding check-box "Show graphs" in the Control panel.

Examples:

1. A uniform motion in the absence of friction. This example shows two bodies of different masses and sizes that move along the frictionless track with different initial velocities. The velocity is reversed each time the body encounters a wall (we assume that collisions with the walls are perfectly elastic). However, the velocity remains constant during the motion in one direction.

If we introduce some friction (to do this, use the "Resistance" scroll-bar in the Control panel, or simply click the button "Resistance" below), the motion slows down, and the bodies eventually come to rest.

2. A uniformly accelerated motion under a constant force. In this example two bodies of different masses start to move being subjected to equal forces. The small body gains speed faster than the large one: The acclelerations are inversely proportional to the inertial masses of the bodies. (Click also here to see the applet.)

3. Free fall in the gravitational field. In a vacuum, all bodies fall down under the force of gravity with the same acceleration. This example shows three bodies of different masses and sizes that fall down in a gravitational field from the same height with zero initial velocities. Though the masses are different, all the bodies aquire the same acceleration because their gravitational masses (and hence the gravitational forces exerted on the bodies) are proportional to the inertial masses. The bodies reach the floor simultaneously. (Click also here to see the applet.)

4. Free fall with non-zero horizontal velocity. This example shows that the vertical and horizontal motions of a body are independent. The bodies (except the smallest one) start to move with non-zero horizontal initial velocities. However, this 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.)

Eugene Butikov personal page | Overview | Previous section | Next section

Computer illustrations to the laws of motion – 1 (of 3)