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PURPOSE

You will study the relationship between the net force applied to a given mass and its resulting acceleration.

MATERIALS  air track, glider, 7 brass washers, mass holder, and smart pulley with DataLogger interface.

RELEVANT EQUATIONS

DISCUSSION

According to Newton's second law of motion, a net force, F, acting on an object will produce an acceleration, a, of the object that is proportional to the force. Furthermore, the proportionality constant between acceleration and the force is the mass, m, of the object. In equation form, this relationship is:

In this experiment, this relationship will be tested by measuring the accelerations produced by different net forces acting on an air track glider.

Consider the set-up shown in Figure 7-1, with an air track glider of mass M. We will assume that the glider is connected to a small mass, m, by a string that runs over a pulley (which we assume is massless and frictionless). Because of the string and pulley, any downward acceleration of m will be matched by an equal horizontal acceleration of the glider. In the absence of friction, the net force acting on the glider is the string tension T.

The net force acting on the suspended mass m, is W - T, where W is the weight of m and T is the tension in the string. Applying Newton's law to each body:

Adding these equations gives:

This result implies that in order to figure out the acceleration, the masses M and m together may be considered as a system of total mass (M + m) with a net force W acting on it.

To test the proportionality between force and acceleration, we need to vary W and measure a, while keeping (M + m) unchanged. Under those conditions, a plot of W vs. a will be a straight line through the origin with slope = (M + m), if the proportionality holds and the assumptions are valid.

In the real world, the assumption of massless, frictionless pulleys and frictionless tables can only be approximated. When friction is present, the net force is reduced from W by the force of kinetic friction. When the pulley has mass, that mass is also accelerated (rotationally) by the net force. If the frictional force is f_e and the effective mass of the pulley is m_e, then the relation must be altered to include these factors:

With these corrections, a plot of W vs. a will still be a straight line, but with slope = (M + m + m_e), and intercept equal to the friction force, f_e.

The acceleration a, can be determined by a special pulley, called a "smart" pulley, that is interfaced to the computer. In order to keep the total mass of the accelerated system constant, while varying the net force on it, seven washers of equal mass will be used. To begin, a net force equal to the weight of one washer will be used by suspending the washer on the end of the string as mass m. The other six washers will be placed on the glider, so that the total mass of the accelerated system is equal to the mass of the glider plus the mass of seven washers. The next value of the net force will be provided by suspending two washers on the string while the other five remain on the glider. This process is continued until all seven washers are suspended, and their weight provides the net force which is accelerating the system.
 

NOTE: Please do not tie knots in the string! The first washer can be attached by threading one end of the string through the loop at the other end, as illustrated in Figure 7-2. When more washers are to be added, remove the end loop from the glider and simply slide them down the string so that they rest on the first washer.