help , cant figure out how to find acceleration and tension of this pulley problem.?

Question

Aceleration and Tension of pulley and cart?
Pulley and cart question?

A cart m1=400g rolls along a track with very low friction. It is attached by a string over a pulley to an object M2=40g that is hanging vertically. Both are at rest when m2 is released.

a) what are all the forces acting on the cart. What are all the forces acting on the hanging mass?

b) Write a Newton's second law equation for the horizontal forces on the cart (no numbers)

c) Write a Newton's second law equation for the vertical forces on the hanging mass. (no numbers)

d) Use the equation you found in parts b and c to dermine the acceleration of each cart and the tension force in the string.

Answer 1

a. Gravitational force from m2 which is m2*g is pulling the mass m1 which resists (by the Newton third law) the acceleration a with the counterforce m1*a and mass m2 which resists with counterforce m2*a. Therefore the cart is pulled by m2*(g - a) and resists with counterforce m2*a. Hanging mass is pulled by m2*g which resists by counterforce (m1+m2)*a.

b. m1*a = m2*(g - a)

c. (m1 + m2)*a = m2*g, the same as c.

d. a = g*m2/(m1+m2) = g/11, where g = 9.81 m/s^2 is gravitational constant. The tension force in the string is m1*a = g*m1*m2/(m1+m2) = g*400/11.