Another Double Check FBD String Tension

[Inferior Mind]

Calculate the tension in the cable connecting the two masses. Assume all surfaces are frictionless.

FBD

m₁ = 5 kg
θ₁ = 60°
m₂ = 6 kg
θ₂ = 70°

Equation 1 ~

F_T - F_g = ma

F_T - mgSinθ = ma

F_T = 5a + 5(9.8)Sin60

F_T = 5a + 42.44

Equation 2 ~

F_g - F_T = ma

mgSinθ - F_T = ma

6(9.8)Sin70 - 6a = F_T

F_T = 55.25 - 6a

~Set Equations Equal to Each Other ~

5a + 42.44 = 55.25 - 6a

11a = 12.81

a = 1.16 m/s²

~Sub into Eq to find Force Tension on da String Son !~

5(1.16) + 5(9.8)Sin60 = F_T

F_T = 48.2 N

 

[SammyS]

Calculate the tension in the cable connecting the two masses. Assume all surfaces are frictionless.

FBD
View attachment 55356

m₁ = 5 kg
θ₁ = 60°
m₂ = 6 kg
θ₂ = 70°

Equation 1 ~

F_T - F_g = ma

F_T - mgSinθ = ma

F_T = 5a + 5(9.8)Sin60

F_T = 5a + 42.44

Equation 2 ~

F_g - F_T = ma

mgSinθ - F_T = ma

6(9.8)Sin70 - 6a = F_T

F_T = 55.25 - 6a

~Set Equations Equal to Each Other ~

5a + 42.44 = 55.25 - 6a

11a = 12.81

a = 1.16 m/s²

~Sub into Eq to find Force Tension on da String Son !~

5(1.16) + 5(9.8)Sin60 = F_T

F_T = 48.2 N

The results looks correct.

Comment: If I were grading this, I would be concerned that you are using the same variable names for mass 1 quantities and mass 2 quantities, particularly F_g and m .

 

[Inferior Mind]

The results looks correct.

Comment: If I were grading this, I would be concerned that you are using the same variable names for mass 1 quantities and mass 2 quantities, particularly F_g and m .

Thanks for the input, I will make amends in future questions.

 

[SammyS]

Thanks for the input, I will make amends in future questions.

To be more specific: F_T and a are the same in magnitude for both masses, so it's fine to use the same variable name for them.