What values of F make the tension zero?

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SUMMARY

The discussion focuses on determining the values of the horizontal force \( F_x \) that result in zero tension in a system involving two masses, \( m_1 \) (7.00 kg) and \( m_2 \) (4.00 kg). It is established that for the tension to be zero, \( F_x \) must be less than or equal to 0 N, as this condition allows both masses to accelerate downward under gravity without any opposing force. The weight of \( m_2 \) (approximately 39.24 N) plays a crucial role in this analysis, as it directly influences the tension in the cord connecting the two masses.

PREREQUISITES
  • Understanding of Newton's Second Law (\(\sum F = ma\))
  • Basic concepts of forces acting on objects in a frictionless environment
  • Knowledge of gravitational force calculations (weight = mass × gravity)
  • Familiarity with tension in strings and its relationship with forces
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  • Learn about free-body diagrams to visualize forces acting on objects
  • Explore the concept of equilibrium and its relation to tension
  • Investigate the dynamics of multiple mass systems under different force applications
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This discussion is beneficial for physics students, educators, and anyone interested in mechanics, particularly those studying forces, tension, and motion in systems involving multiple objects.

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Homework Statement


In the system shown in the figure below, a horizontal force x acts on the 7.00 kg object (m1). The horizontal surface is frictionless.
p5-37alt.gif

I solved the first part.
(a) For what values of Fx does the 4.00 kg object (m2) accelerate upward?
Fx> 39.24 N
I am totally confused on the second part.
(b) For what values of Fx is the tension in the cord zero?
Fx\leq ?

Homework Equations


\sumF=ma
(I don't think any other equations play a role.)

The Attempt at a Solution


I would think that for the tension to the zero, the Fx should be opposite value of the weight of m2. So -39.24 N. However, that's not right. I am confused about what forces are acting on the objects.
 
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The tension holds m2 back, preventing it from accelerating at g.
So when the tension is zero, m2 and m1 WILL accelerate at g.
Looks like Fx will have to be negative so it makes m1 keep up with m2.
 
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Okay, so if m1 is accelerating towards the end of the table at the same rate as g, then the tension will be zero? That makes sense...

So, m1*g=7*-9.81=-68.67.

EDIT:
Which is right, thanks for clearing that up for me.
 
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Which is the same as saying that if Fx= 0, there is no force supporting the weights and they fall freely- so no tension on the string.
 
Hm? If Fx=0, then the tension in the string is the same as the weight of m2, is it not?
 
Super - wasn't so tough after all!
 

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