Inclined Plane Problem: How to Calculate Acceleration and Tension?

[haengbon]

Homework Statement

A 3kg load on an inclined plane of angel 30 degrees is connected by a cord over a frictionless pulley to a second load which has a mass of 2 kg. Find the:

a) Acceleration of each load
b) tension of each chord

Homework Equations

none?

The Attempt at a Solution

block A / box on inclined plane

$$\sum$$F_y= 0
-W_ycos30$$\circ$$ + N_F= 0
-30cos30 + N_F = 0
-25.98 + N_F = 0
-25.98 = N_F
N_F = 25.98

f=$$\mu$$ N_F
f= 0.3 (25.98)
f= 7.794

$$\sum$$F_x= ma
W_xsin30$$\circ$$ - T - f = ma
15 - T - 7.794 = ma
15 - 7.794 - T = (3)(a)
-T = 3a - 7.206
T = 7.206 - 3a

block b

$$\sum$$F_x= ma
T-W = ma
T - (2)(10) = (2)a
T - 20 = 2a
T= 2a+20

T=T
2a+20 = 7.206 - 3a
2a+3a = 7.206 - 20
5a = -12.794
a = - 2.56 m/s²

T₁=7.206 - 3a
T= 7.206- 3(-2.56)
T= 14.886 N

T₂= 2a+20
T= 2(-2.56) + 20
T= -3.1176 N

T₂+T₁ = Total_T
14.886 + (-3.1176) = Total_T
Total_T= 11.7684 N

I'm not sure if I got the right answer :( someone help?

 

[rl.bhat]

Loads are connected by a single cord. So T1 = T2 = T.

 

[haengbon]

Loads are connected by a single cord. So T1 = T2 = T.

so the tensions I got are incorrect then?
may I ask if the acceleration is correct?

 

[rl.bhat]

Your acceleration is correct.

 

[haengbon]

Your acceleration is correct.

thank you ! :) so I only need to use one equation for my tension, and that's the answer? thank you very much again :) I really appreciate it ^^