Two Hanging Masses (TENSION)

  • Thread starter tizzful
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In summary, the problem involves two blocks with masses M1 and M2 hanging on top of each other. The blocks are accelerating upwards with an acceleration of magnitude a due to the tension in the strings. To find the tension in the lower rope, T2, the weight of M2 is used. However, for the tension in the upper rope, T1, three forces need to be considered: the weight of M1, the weight of M2, and the tension in the rope. Using Newton's 2nd law, the equation T2 + M1(g) - T1 = ma can be used to solve for T1, which is equal to T2 + M1(g).
  • #1
tizzful
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Two Hanging Masses (TENSION) :)

Homework Statement


Two blocks with masses M1 and M2 hag one under the other. For this problem take the positive direction to be upward and use g for the magnitude of the acceleration due to gravity. The blocks are now accelerating upwads (due to the tension in the strings) with acceleration of magnitude a. find the tension in the lower and upper rope.
Tension.jpg


Homework Equations


F=ma
W=mg


The Attempt at a Solution



I found the tension in the lower and upper rope when it was stationary and therefore in equilibrium.
T2=M2g
T1=M1g
Then to find the tension when accelerating I just used
T2=Ma+Mg
T1=Ma+M1g+M2g

For some reason it says that the tension in rope 2 does not depend on the variable M1... So I'm just really lost now on which direction to take..
Thanks in advance
 
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  • #2
Welcome to PF>

While acceleration T2 is the normal force arising only due to the weight of M2.
Hence T2 does not depend on variable M1.
 
  • #3
Oh thank you! That clears up the first one but I'm still stuck on the T1 when accelerating. Would I just go T1=(M1+M2)a + (M1+M2)g?
 
  • #4
Yes becoz the total downward force acting on T1 while acceleration is the sum of the weights of M1 and M2.
 
  • #5
tizzful said:
I found the tension in the lower and upper rope when it was stationary and therefore in equilibrium.
T2=M2g
T1=M1g
That would be correct for M2 but not for T1 (three forces act on M1). In any case, the equilibrium situation is not relevant to this problem.
Then to find the tension when accelerating I just used
T2=Ma+Mg
T1=Ma+M1g+M2g
Carefully apply Newton's 2nd law to each mass. Start by identifying all the forces that act on each mass. (Hint: three forces act on M1.)

(The diagram is misleading because it does not show all the tension forces acting on the masses.)
 
  • #6


first, solve for the T2.
T2=M1(g)
then, for T1,
since T1 is carrying the M2,
ΣF=ma
substitute ΣF to T2 + M1(g) -T1
so,
T2 + M1(g) -T1= ma (at rest)
T2 + M1(g) -T1= 0
T1=T2 + M1(g)
 

What is tension in the context of two hanging masses?

Tension refers to the force that exists in a stretched or compressed object, such as a rope or string. In the context of two hanging masses, tension is the force that pulls the two masses towards each other.

How is tension calculated in a system with two hanging masses?

Tension can be calculated using the formula T = (m1 + m2) * g, where T is the tension force, m1 and m2 are the masses of the two hanging objects, and g is the acceleration due to gravity (usually 9.8 m/s²).

What factors affect the tension in a system with two hanging masses?

The tension in a system with two hanging masses can be affected by the masses of the objects, the distance between them, and the acceleration due to gravity. Additionally, the angle at which the masses are suspended and the presence of any external forces can also impact the tension.

How does changing the angle between the two hanging masses affect tension?

Changing the angle between the two hanging masses can affect the tension by altering the direction of the force. As the angle increases, the tension force also increases, and when the angle approaches 180 degrees, the tension becomes equal to the weight of the objects.

Can tension ever be greater than the weight of the hanging masses?

No, tension can never be greater than the weight of the hanging masses. In an ideal system, the tension would be equal to the weight of the objects. However, in real-world scenarios, friction and other external forces may slightly affect the tension and make it slightly greater than the weight of the objects.

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