Can someone help me with physics?

Question

I missed ap physics this morning and i'm not sure how to do this problem, any help would be awesome.

A mass m1= 30kg slides without friction on the horizontal surface being pulled by m2=80kg with a string over a frictionless pulley. The pulley is a thin cylindrical shell of mass M=10kg and radius R. The string turns the pulley without slipping. Find a) acceleration of each mass, b) the angular acceleration of the pulley, C) the tension in each part of the string.

Answer 1

I assume the pulley is at the edge of the horizontal surface and the 80kg mass is being pulled downward by gravity. All the accelerating force is coming from the 80kg mass, and that force is 80*g. It must accelerate two items, the horizontal mass of 30kg, and the pulley. The inertia of the 30kg mass is 30*a, while the inertia of the pulley is T = I*aw, where T is the torque and aw is the angular acceleration. Since torque = tangential force times r, the equation for system motion is then

80*g = 30*a + T/r

The only hard part here is figuring the angular terms. For a thin cylinder of radius r, I = m*r^2 The angular acceleration is linear acceleration divided by r, or a/r. Therefore the torque on the pulley is m*r^2*a/r = m*a*r. The force on the pulley is then m*a, where m = mass of the pulley.

80*g = 30*a + 10*a

Solve for a.

The tension in the vertical part of the string is just the force from the 80kg mass, or 80*g. The tension in the horizontal portion is the force required to accelerate the 30kg mass, or 30*a

Answer 2

i aint that smart lol