Atwood machine - testing Newton’s Laws of motion
The Rev. George Atwood (1746-1807) developed a simple construction known as the Atwood machine which gives students an exceptionally simple but excellent tool for testing and verifying Newton’s Laws of Motion. The idea of the Atwood Machine is explained on Fig.1
A pulley is mounted about 2.0m from the ground on a stand with a scale on it to measure the positions of attached objects. Two weights are attached to both ends of a long string which passes over the pulley. In the free body diagram of the Atwood's machine, T is the tension in the string, m is the smaller mass, M is the larger mass, and g is gravity’s acceleration. Assuming that the pulley and the string are massless and the string doesn't stretch, and that there is no friction, the resultant force on M is the difference between the tension and mg . The net force on M is the difference between the tension and Mg. The resultant force exerted on both masses is
F = Mg - mg = (M - m)g (1)
and this force is accelerating both masses at
a = F/(M+m) (2)
Substituting (1) into (2) we get
(3)
If the difference M-m is relatively small, acceleration a is easy to measure with a simple stopwatch. If we assume the knowledge of gravitational acceleration g, the Atwood Machine allows us to check Newton’s Second Law of Motion.
When M = m we can verify Newton’s First Law of Motion. If we assumed Newton’s Second Law of Motion as true, we can then determine, from Equation (3), the value of gravitational acceleration g. The applications of the Atwood Machine are quite universal, especially for educational purposes.
Endless generations of students, including myself have learned Newton’s Laws of Motion with the Atwood Machine. Some of the { Problems link do problems } included in this Chapter are classical examples of the application of the Atwood Machine idea.
At the Atwood Machine web page you can see photos of many practical realizations of the equipment described above. You can also read there some historical information if you are interested in such matters.