Final 13 - Double Inclined Plane

Given:

• $\mbox{Two masses connected by a rope and pully}$
• $\mbox{mass 1 is on a plane inclined at an angle alpha}$
• $\mbox{mass 2 is on a plane inclined at an angle beta}$
• $a = g \frac{M_{unknown}\sin{\beta}  {(operator)}  M_{unknown}\sin{\alpha}}{M_1 ({operator}) M_2}$

Question:

• $What are subscripts and operators?$

Rationale:

• $M_1 \; \mbox{is associated with angle alpha}$
• $M_2 \; \mbox{is associated with angle beta}$
• $a = g \frac{M_2 \sin{\beta}  {(operator)}  M_1 \sin{\alpha}}{M_1 ({operator}) M_2}$
• $\mbox{The denominator operator cannot be multiply or divide}$
• $\mbox{Since if either mass is zero, then the equation  would be indeterminate}$
• $\mbox{So the operator must be + or - }$
• $\mbox{But it cannot be minus,  since it would indeterminate is the masses are equal}$
• $\mbox{Therefore the denominator operator is plus.}$
• $\mbox{If the masses are equal and the angles are equal, }$
• $\mbox{Then the numerator must be zero}$
• $\mbox{Thus the numerator operator must be minus.}$
• 
  

Calculate:

References: