Free-Body Diagrams: Tension & Weight of Blocks A & B

[henry3369]

Let's say that block A is suspended vertically by a massless rope which you are holding and block B is suspended under block A by another massless rope.

If I am drawing a free body diagram for block A, would the downward force be the weight of block B and Tension as well as an upward Tension? Additionally, if start lifting the system, would there be a force of tension as well as a lifting force on block A upward? I'm confused about whether or not I should write a tension force whenever I see a rope.

 

[Stephen Tashi]

Considering A as the free body, the forces acting upon it are the tension of the rope you are holding, the tension of the rope holding the other block, and gravity equal to the weight of block A. If you start accelerating the system upward, the tensions in the two ropes change.

Newtons laws apply to an object only if you analyze it as a "free body". To do that, you consider only forces acting upon the free body, not forces exerted by the body on something else and not forces exerted by other things on other bodies. The force of gravity on block B is not a force acting upon block A. You can say the force of gravity on block B is is a "contibuting cause" to the forces on block A, but it is not a force acting directly on block A. The only gravitational force acting on block A is its own weight.

For example, if a mass M is at rest on a table the forces on M should analyzed as gravity and the upward force of the table on M. If you also include the downward force exerted by M on the table in the analysis you would end up with unbalanced forces and this would imply the object should be accelerating.

"Tension" is a property of a string that causes Forces at each end of the string. The magnitude of the force at each end of an idealized string is the same, but the forces exerted by the string at each end have opposite signs.

 

[CWatters]

If I am drawing a free body diagram for block A, would the downward force be the weight of block B and Tension..

No. Just the tension. Try drawing the free body diagram of block B first.

If everything is stationary the tension in the lower string _is_ the weight of block B eg T_lower = M_B * g
If it's accelerating the tension is T_lower = M_B * (a + g)