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.

 

[Nickie]

Based on the given information and equations, the tension in the cable connecting the two masses is 48.2 Newtons. This calculation assumes that all surfaces are frictionless and that the only forces acting on the masses are gravity and the tension in the cable. It is important to double check calculations like this to ensure accuracy and to account for any possible errors. Further experimentation or analysis may be necessary to confirm the calculated tension value.