question below please answer asap

Question

Two boxes on a frictionless horizontal plane are connected by a massless string. The lefthand box has mass 2m and the right-hand box has mass m. A force F = 1/2mg is applied to the right-hand mass at an angle θ with respect to the horizontal. What is the magnitude of the tension in the string connecting the two masses?

 

possible answers:

 

1. mg cosθ

 

2. 2mg cosθ

 

3.1/4mg cosθ

 

4.2/3mg cosθ

 

5. 3mg cosθ

 

6. 1/3mg cosθ

 

7. 3/4mg cosθ

 

8. 4/3mg cosθ

 

 

 

Answer 1

Apply Newton's 2nd law (F = ma) to both masses, in the horizontal direction.  Get 2 equations in the variables tension (T) and acceleration (a).  Use one equation to eliminate acceleration, and then solve for tension in the other equation.

 

Right hand mass:

 

(i)   (mg/2)cosθ - T = ma  [T points left if (mg/2)cosθ points right]

 

Left hand mass:

 

(ii)  T = (2m)a ⇒ a = T/(2m)  [same a as in (i) since they accelerate together; T points right by Newton's 3rd law]

 

Plug a = T/(2m) into equation (i) and get

 

(mg/2)cosθ - T = m[T/(2m)] ⇒

 

(mg/2)cosθ - T = T/2

 

(mg/2)cosθ = (3/2)T

 

T = mg cosθ / 3

 

Answer (6) is correct.