Unit 3 - Problem 6 - More Inclined Plane

Given:

• When $mass_1$ is moving up, $a$ is positive
• Observation: This is an Atwood Machine variation using an inclined plane on one side
• Don't solve the details.
• Use your intuition.

Reasoning (aka Intuition)

• When $mass_2$ is moving down, $g$ is negative since up is positive and therefore down is negative.
• $mass_2\times\sin\alpha = mass_{2-effective}$ due to previous problem where we calculated the inclined slope effective force.
• Consider the case where the numerator is $(M_2\times\sin{\alpha}-M_1)$ and the denominator is $M_1+M_2$
  • Suppose $M_2 = 0$ then $a=g\left(\frac{-M_1}{M_1}]\right)=-g$ which we know is TRUE.
  • Suppose $M_1 = 0$ then $a=g\left(\frac{M_2\sin(\alpha)}{M_2}\right)=g\times\sin(\alpha)$ which we know is TRUE.
Clearly, if the subtraction and addition were reversed, the results would be FALSE since the other way is TRUE.
• Also, no other arithmatic operation would produce these simple results and therefore must be FALSE.