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

In summary, when drawing a free body diagram for block A suspended vertically by a massless rope, the downward force would only be the tension in the rope and not the weight of block B. This applies regardless of whether the system is stationary or accelerating. The tension in the lower string is equal to the weight of block B when the system is stationary, but when it is accelerating, the tension is equal to the weight plus the acceleration of the system. Newton's laws only apply to free bodies, meaning only the forces acting directly on the body should be considered, not forces exerted by the body on something else or other external forces.
  • #1
henry3369
194
0
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.
 
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  • #2
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.
 
  • #3
henry3369 said:
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 Tlower = MB * g
If it's accelerating the tension is Tlower = MB * (a + g)
 

What is a free-body diagram?

A free-body diagram is a visual representation of all the forces acting on an object. It shows the direction and magnitude of each force, and helps to analyze the motion of the object.

How do you draw a free-body diagram?

To draw a free-body diagram, you first identify the object of interest and then draw a dot or box to represent it. Next, draw all the forces acting on the object, such as weight, tension, friction, etc. Make sure to label each force with its direction and magnitude.

What is tension in a free-body diagram?

Tension is a force that occurs between two objects that are connected by a string, rope, cable, or any other type of flexible connector. It is always directed along the length of the connector and away from the object it is attached to.

How is weight represented in a free-body diagram?

Weight is a force that is exerted by a mass due to gravity. In a free-body diagram, weight is represented by a downward arrow pointing towards the center of the earth, with a magnitude equal to the mass of the object multiplied by the acceleration due to gravity.

What is the relationship between the tension and weight of blocks A and B in a free-body diagram?

The tension in a free-body diagram is equal to the weight of the object it supports. In the case of blocks A and B, if they are connected by a string or cable, the tension in the string will be equal to the weight of the block that is hanging from it.

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