Atwood machine.

1. , Atwood machine. We are able to derive an equation for the acceleration by using force analysis. If we consider a massless, inelastic string and an ideal massless pulley the only forces we have to consider are: tension force (N), and the weight of the two masses (mg). To find an acceleration we need to consider the forces affecting each individual mass. Using Newton's laws (if m1 > m2) we can derive a system of equations for the acceleration (a). Forces affecting m1: forces affecting m2: and adding the two previous equations we obtain, and at last

2. . • Conversely, the acceleration due to gravity, g, can be found by timing the movement of the weights, and calculating a value for the uniform acceleration a: • The Atwood machine is sometimes used to illustrate the Lagrangian method of deriving equations of motion. • It can be useful to know an equation for the tension in the string. To evaluate tension we substitute the equation for acceleration in either of the 2 force equations. • For example substituting into m1a = N − m1g, we get • The tension cannot accurately be found in using this method due to torque of the pulley.

3. Atwood Example: • Using an Atwood machine m1 = 4kg • m2 = 3.5kg • Find the acceleration of the setup and the tension in the wire.

4. Answer: • a = 9.81 m/s2(4kg – 3.5 kg) (4kg + 3.5 kg) • a = .654 m/s2 • N = 9.81 m/s22(4kg)(3.5 kg) (4kg + 3.5 kg) • N = 36.624 N