The setup in the figure shows a cart of mass m1 attached by a cord under tension

Question

The setup in the figure shows a cart of mass m1 attached by a cord under tension, T, over a pulley to a hanging mass of m2. Assume m1 and m2 move with the same acceleration, a, and that there is no friction between m1 and the table. Calculate the acceleration, a, in terms of m1, m2 and g. The setup in the figure below is similar to that above, except that now m1 resides on an incline. Assume the acceleration of the hanging mass is downwards, and calculate the acceleration, a, in terms of theta, m1, m2, and g. Ignore friction between m1 and the incline.

Explanation / Answer

T = m1 * a
m2*g - T = m2 * a
m2*g -m1 * a = m2*a
a =m2*g/(m1 + m2 )
part B
m2*g - T = m2 * a
T - m1*g*sin = m1 * a

a = (m2*g - m1*g*sin) / (m1 + m2 )

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