An Atwood machine consists of a mass of 3.5 kg connected by a light string to a mass of 6.0 kg over a frictionless pulley with a moment of inertia of 0.0352 kg ∙ m² and a radius of 12.5 cm.If the system is released from rest,what is the speed of the masses after they have moved through 1.25 m if the string does not slip on the pulley? A)2.0 m/s B)2.3 m/s C)4.0 m/s D)5.0 m/s E)6.0 m/s

Question

Quizplus · Accepted Answer

First, we need to find the acceleration of the system. Let's call tension T. 
For the 6 kg mass: 
$T - m_2g = m_2a$ 
For the 3.5 kg mass: 
$m_1g - T = m_1a$ 
We can solve for T by adding the two equations: 
$T = \frac{(m_1 - m_2)g}{m_1 + m_2}$ 
$T = \frac{(3.5 - 6.0)(9.81)}{(3.5 + 6.0)} = -2.209 N$ 
Note that the negative sign indicates that the tension is acting upwards on the 6 kg mass. 
Now we can use the tension to find the acceleration by looking at only one of the masses: 
$T - m_2g = m_2a$ 
$-2.209 - (6.0)(9.81) = (6.0)a$ 
$a = -2.06 m/s^2$ 
Note that the negative sign indicates that the system is accelerating downwards. 
Finally, we can use kinematic equations to find the final velocity after traveling 1.25 m: 
$v^2 = v_0^2 + 2ad$ 
$v^2 = 2(2.06)(1.25)$ 
$v = 2.28 m/s \approx 2.3 m/s$

An Atwood Machine Consists of a Mass of 3