Problem $13$: $(7\%$ of Assignment Value$)$

Displayed to the right are two carts connected by an ideal cord that passes over an ideal pulley that is massless and frictionless. Each cart rolls with negligible friction. The mass of the cart on the left is $m_1,$ and the incline on which it rolls makes an angle ${}_1$ with the horizontal. The mass of the cart on the right is $m_2,$ and the incline on which it rolls is makes an angle ${}_2$ with the horizontal.

Part $($a$)$

Enter an expression for the acceleration of the carts in terms of the variables defined in the problem statement, and use $g$ for the acceleration due to gravi acceleration as positive if the cart on the right rolls down its incline.

$a=m_2$gsin$({}_2)-m_1$gsin$\frac{{}_1}{m_1+m_2}$

Attempts Remain

Part $($b$)$

Enter an expression for the tension in the rope in terms of the variables defined in the problem statement, and use $g$ for the acceleration due to gravity.