Hanging Masses and Tensions: Finding Equilibrium Angle

  • Thread starter c-murda
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In summary, the conversation discusses a physics problem involving two hanging masses and tensions. The masses and angles are given, and the system is in equilibrium. Three free body diagrams are drawn, and equations are set up for each. The final solution finds the angle labeled theta to be 79.1 degrees.
  • #1
c-murda
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[SOLVED] Hanging masses and tensions...

Homework Statement


attached is drawing of diagram...

two masses m1 and m2 are attached as shown in the figure. If the system is in equilibrium, find the angle labled theta.
m1 = 35.0 kg
m2 = 65.0 kg




Homework Equations





The Attempt at a Solution


well...to start i drew three FBD one for the mass, one for the intersection, and one for the second mass...
for the first FBD:
Tm = m * g

for the second FBD:
Fx = T2 cos 53 - T1 cos 37 = 0
Fy = T2 sin 53 + T1 sin 37 - m1*g = 0

for the third FBD:
Fx = T3 cos (theta) - T2 cos 53 = 0
Fy = T3 sin (theta) - T2 sin 53 - m2*g = 0

so...

First:
Tm = m*g; which equals (35.0kg) ( 9.80 m/s^2) = 343N

Second:
.602 T2 - .799 T1 = 0 ; so... T1 = (.602/.799)(T2) so...

.602 T1 +.799 T2 = 343
.602[((.602)/(.799))T2 + .799 T2 = 343
.453T2 + .799T2 = 343
1.25T2 = 343
T2 = 274.4N

Third:
T3=T2(cos 53/cos (theta))

[T2(cos 53/cos (theta))] sin(theta) - T2 sin 53 = m2*g
T2 tan(theta) cos 53 = m2*g + T2 sin 53
tan(theta) = m2*g + T2 sin 53/T2 cos 53
theta = tan^-1(m2*g + T2 sin 53/T2 cos 53)
theta = 79.1?


uhmm any help? that's what i got correct me if i am wrong
 

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  • #2
anyone?
 
  • #3
Looks good to me. Well done!
 
  • #4
thank you much...i have more to come so sit tight!
 

Related to Hanging Masses and Tensions: Finding Equilibrium Angle

What is the concept of hanging masses and tensions?

The concept of hanging masses and tensions involves the study of the forces acting on an object that is suspended by one or more strings or cables. These forces include the weight of the object and the tension in the string or cable.

What is the difference between tension and weight?

Tension is the pulling force exerted by a string or cable, while weight is the downward force exerted by gravity on an object. In the case of hanging masses, the tension in the string or cable is equal to the weight of the object.

How is tension affected by the mass of the hanging object?

The tension in the string or cable increases as the mass of the hanging object increases. This is because the weight of the object increases, and the string or cable must exert a greater pulling force to support it.

What happens to the tension if the hanging object is in motion?

If the hanging object is in motion, such as swinging back and forth, the tension in the string or cable will vary. As the object swings downwards, the tension will increase, and as it swings upwards, the tension will decrease.

How can the tension in a hanging mass system be calculated?

The tension in a hanging mass system can be calculated using the equation T = mg, where T is the tension, m is the mass of the object, and g is the acceleration due to gravity (9.8 m/s²). This equation assumes that the string or cable is massless and that there is no air resistance.

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