atwood machine. we are able to derive an equation for the acceleration by using force analysis. if...
TRANSCRIPT
![Page 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](https://reader036.vdocuments.site/reader036/viewer/2022083004/56649ecf5503460f94bdd393/html5/thumbnails/1.jpg)
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
,
![Page 2: 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](https://reader036.vdocuments.site/reader036/viewer/2022083004/56649ecf5503460f94bdd393/html5/thumbnails/2.jpg)
• 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.
.
![Page 3: 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](https://reader036.vdocuments.site/reader036/viewer/2022083004/56649ecf5503460f94bdd393/html5/thumbnails/3.jpg)
Atwood Example:
• Using an Atwood machine m1 = 4kg
• m2 = 3.5kg• Find the acceleration of the
setup and the tension in the wire.
![Page 4: 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](https://reader036.vdocuments.site/reader036/viewer/2022083004/56649ecf5503460f94bdd393/html5/thumbnails/4.jpg)
Answer:
• a = 9.81 m/s2 (4kg – 3.5 kg) (4kg + 3.5 kg)
• a = .654 m/s2
• N = 9.81 m/s2 2(4kg)(3.5 kg) (4kg + 3.5 kg)
• N = 36.624 N