A 34.3 kg block (m1) is on a horizontal surface, connected to a 6.3 kg block (m2) by a massless string as shown in the Figure. The pulley is massless and frictionless. A force of 216.9 N acts on m1 at an angle of 31.5°. The coefficient of kinetic friction between m1 and the surface is 0.189. Determine the upward acceleration of m2.

Question

A 34.3  kg block (m1) is on a horizontal surface, connected to a 6.3  kg block (m2) by a massless string as shown in the Figure. The pulley is massless and frictionless. A force of 216.9  N acts on m1 at an angle of 31.5°. The coefficient of kinetic friction between m1 and the surface is 0.189. Determine the upward acceleration of m2.

anonymous · Answer

attachment

anonymous · Answer

acceleration of m2 is acceleration of system  
|dw:1328975564405:dw|
iget left along +, so
$$Fcos \theta-T-f=m _{1}a$$where $$f=\mu _{k}N $$$$N+Fsin \theta=m _{1}g$$
$$T-m _{2}g=m _{2}a$$ 
so we have two equation with 2 passive ,set T & N in 2nd law & solve this for a
this ask is aspecial case of Atwood system with friction .