Apply Newton's second law in component form to the ball, choosing the upward direction as positive: (1) Fx = 0
(2) Fy = T - m1g = m1ay = m1a
For the ball to accelerate upward, it is necessary that T > m1g. In Equation (2), we replaced ay with a because the acceleration has only a y component.
For the block it is convenient to choose the positive x' axis along the incline as in figure (c). For consistency with our choice for the ball, we choose the positive direction to be down the incline.
Apply Newton's second law in component form to the block:
(3) Fx' = m2g sin (?) - T = m2ax' = m2a
(4) Fy' = n - m2g cos(?) = 0
In Equation (3), we replaced ax' with a because the two objects have accelerations of equal magnitude a.
Solve Equation (2) for T:
(5) T = m1(g +a)
Substitute this expression for T into Equation (3):
m2gsin - m1(g + a) = m2a
Solve for a in terms of m1, m2, g, and :
(6) a =Substitute this expression for a into Equation (5) to find T in terms of m1, m2, g, and :
(7) T =