Free body diagram for a bag of coins suspended by an elastic band

In summary, for the free body diagrams of the elastic band and bag of coins, the following forces were considered: tension (T) and weight (mg) acting in opposite directions on the elastic band, and the elastic force (F=kx) and weight (mg) acting in opposite directions on the bag of coins. It was also noted that in this experiment, the elastic band and bag of coins were in equilibrium, with the tension force being equal to the elastic force.
  • #1
wizzle
26
0

Homework Statement


Draw a free body diagram showing all the forces on the elastic band, and a free body diagram showing all the forces on the bag of coins


Homework Equations



F=-kx
F=mg

The Attempt at a Solution



I drew the forces on the elastic band as T = mg (m = mass of coins since the elastic band's mass isn't stated) upwards

and mg downwards

The forces I drew on the bag were F = kx upwards (the force of the elastic's stretch pulling proportionally upwards on the bag) and F = mg downwards (m = mass of coins)

If it were a rope attaching the bag to the ceiling I'd be ok but I'm a bit thrown off since it's an elastic band. Please let me know if this seems logical.

Thanks in advance for your help!
 
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  • #2
Welcome to PF.

That sounds good.
 
  • #3
Wow, what a fast response! Thanks for the reassurance :)
 
  • #4
Hi, I just had one thought. This was from an experiment where coins were added one by one to a bag (attached to the elastic) and then the elastic stretched with each coin added (and I have to draw a free body diagram of the forces acting on the elastic and those acting on the bag).

Since the elastic band did move when the coins were added, am I wrong to say that these forces are in equilibrium? Maybe I should have instead said that the upward tension force on the elastic is equal to the spring force (F = kx)? Thanks again!
 

What is a free body diagram?

A free body diagram is a visual representation of all the forces acting on an object. It helps to analyze the motion and equilibrium of the object.

Why is a free body diagram important for a bag of coins suspended by an elastic band?

A free body diagram is important for this scenario because it helps to identify all the forces acting on the bag of coins, including the tension force from the elastic band, the weight of the coins, and any other external forces. This allows for a better understanding of the overall behavior and stability of the bag of coins.

What are the steps to draw a free body diagram for a bag of coins suspended by an elastic band?

The steps to draw a free body diagram for this scenario are:

  1. Identify the object of interest (the bag of coins) and draw it as a point or a simplified shape.
  2. Label all the forces acting on the object, including the tension force from the elastic band, the weight of the coins, and any other external forces.
  3. Draw arrows to represent the direction and magnitude of each force.
  4. Make sure the forces are labeled and positioned accurately with respect to the object.

How does the elastic band affect the free body diagram for a bag of coins?

The elastic band adds a tension force to the free body diagram, which is directed towards the point where the band is attached to the bag of coins. This tension force increases as the band is stretched further, and it helps to keep the bag of coins suspended.

Can a free body diagram predict the motion of a bag of coins suspended by an elastic band?

No, a free body diagram alone cannot predict the motion of an object. It only provides information about the forces acting on the object. To predict the motion, we also need to consider other factors such as the mass of the object, the elastic properties of the band, and any external influences. These factors can be used in equations of motion to determine the acceleration and velocity of the bag of coins.

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