 ### Introduction to Scientific Programming Computational Problem Solving Using: Maple and C Mathematica and C

Author:
Joseph L. Zachary
Online Resources:
Maple/C Version
Mathematica/C Version

# Sliding Block Tutorial

In this tutorial we will explore the sliding block problem that is discussed in Chapter 12. The tutorial will help you understand the motion of a block on an inclined plane with and without friction.

## Simulation

We will be using a graphical simulation of the sliding block problem throughout this tutorial. You can start it by clicking on the following button.

A Java applet should appear here

## The Physics of a Sliding Block

A block on an inclined plane will accelerate down the plane. The amount of acceleration is determined by acceleration due to gravity, the angle of the plane, and the coefficient of friction of the block with the plane. The coefficient of friction is a measure of the amount of friction that exists between two materials as one slides over the other. It is zero if there is no friction, and it is infinite if no motion is possible. The coefficient of friction of skis on snow is 0.01; of brass on glass, 0.1; and of two hands rubbing together, 0.5.

Measured from the starting point of the block, the position at time t of the block in the diagram above is given below. We assume that the ramp is of length L and that the block stops moving when it reaches the bottom. ## Simulating a Sliding Block

The simulation displays a block on an inclined plane. Both the angle at which the ramp is inclined and the simulated length of the ramp are displayed in the upper-right hand corner. You can change the angle or the simulated length by using the mouse to drag the bottom of the ramp. You can also use the Scale menu to modify the scale with which the ramp is measured.

If you pull down the Slide menu and select the Start option, the block will begin sliding down the ramp. As it slides, the simulated distance that the block has moved is displayed in the lower-right corner, and the amount of simulated time that has passed is displayed at the top. Notice how the block starts out slowly and gradually accelerates.

If you pull down the File menu and select the Reset option, the block will return to the top of the ramp. Do this, and then rearrange the ramp so that it is at 45 degrees.

The coefficient of friction is displayed in the lower-right corner. Initially, it is zero, which means that there is no friction. Use the controls to set the coefficient of friction to 1.0, and then start the simulation. Simulated time will begin ticking, but the block will not move. When the coefficient of friction is 1.0, no motion occurs on a 45 degree ramp.

If you reduce the friction slightly, the block should begin moving, more slowly than it did in the absence of friction. Some example coefficients of friction are 0.01 for skis on snow, 0.1 for brass on glass, and 0.5 for rubbing your hands together.

Now pull down the Slide menu and select the Two Ramps option. The simulation window will double in size, and a second ramp (complete with its own controls) will appear. Although the two ramps will initially be identical, you can configure them individually and arrange "races" between the blocks.

Experiment with the sliding block simulator to get a better understanding of the physics of friction.

Last modified 16Jan97.