Incline angle for accelerating cart and Tensions in strings for a suspended mass

[JAZZ541]

Homework Statement

Hi all, I have solved these problems just wanted to see if it's all ok

problem 1:
a trolley starts at the lowest point of a diagonal plane with a 20m/s speed. Its acceleration is 4m/s^2 going downhill, the trolley goes up then slows until it reaches 0 speed and then goes down the plane with the same acceleration
a. what is the slopes incline? Its is known that the trolley moves without friction?

problem 2:
A weight that has m = 12Kg is pendent in rest on a string attached to two other strings and creating an identical β = 60° with the ceiling, calculate the tension of all strings

Homework Equations

The Attempt at a Solution

solution 1:
[/B]

V0 = 20m/s

a = -4m/s2

g = 10m/s2

m1g • sinα = m1a

N = m1g • cosα

-m1g • sinα = m1a

Sinα = a/-g

Sinα = -4m/s2/-10m/s2

α = 23.58°solution 2:

T1 = mg

m = 12Kg

mg = T1 = 120N

T1 = T2cos30° + T3cos30°

T1 = cos30° • (T2 + T3)

120N = cos30° • (T2 + T3)

T2 + T3 = 120/cos30° = 138.56

T2sin30° = T3sin30°

T2 + T3 = 138.56

2T = 138.56

T2 = T3 = 69.3

TY!

 

[kuruman]

Both solutions look OK.

 

[JAZZ541]

Ty very much!