How Do You Calculate the Masses in a Two-Block System with a Tension of 18 N?

[johnec22]

Homework Statement

Two masses are joined together by a massless, inextensible string. A vertical force of 30 N applied to the upper mass gives the system a constant upward acceleration of 3.2 m/s^2.

If the tension in the connecting string is 18 N, what is the smaller of two masses?

If the tension in the connecting string is 18 N, what is the bigger of two masses?

F= 30 T=18 m=1.4 a=3.2 g=9.8

Homework Equations

F(net) = m*a

The Attempt at a Solution

The lower block can be solved for by:
T/(g+a) = M which is 1.4kg

but I can't get the value of the upper block(which I know should be smaller then 1.4)

M=(F+T-ma-mg)/(a+g) F=30 T=18 m=1.4 a=3.2 g=9.8
when I do this M= 2.3 but it should be smaller then 1.4 because I know 1.4 is the larger block.

 

[kuruman]

Call the bottom mass m₂. You know its acceleration is 3.2 m/s². You also know that the tension acting on it is 18 N. Can you set up a Newton's Second Law equation for that mass alone in which m₂ is the only unknown?

 

[Doc Al]

M=(F+T-ma-mg)/(a+g) F=30 T=18 m=1.4 a=3.2 g=9.8
when I do this M= 2.3 but it should be smaller then 1.4 because I know 1.4 is the larger block.

You messed up the forces in that equation. (And what's "ma" doing in there?) Just use Newton's 2nd law directly, rather than plug into a derived equation that may or may not apply. It's much simpler and you'll know it's right.

What's the net force on the upper mass?

 

[johnec22]

Isn't the net force 48 because both the 30 N and the 18 N of tension are moving in an upward direction.

48 = M(3.2-9.8)?

*edit: never mind I found the solution.. Thanks so Much!"

 

[Doc Al]

Isn't the net force 48 because both the 30 N and the 18 N of tension are moving in an upward direction.

No:
(1) The 30 N and 18 N forces act in different directions.
(2) The weight of the mass contributes to the net force.