Calculating Tension in Ropes for a Suspended Circus Performer

In summary, the problem involves a circus performer weighing 76.0 kg hanging from a trapeze while another performer pulls on the ropes. The task is to calculate the tension in the two ropes while the person is momentarily motionless. The solution involves creating a free body diagram and using the equations ∑Fx = T2cos10-T1sin(15)=0 and ∑Fy=T1cos(15)+T2sin(10)-m*g=0 to solve for the tension in the ropes. An alternative method is also mentioned, where the angle of T1 is calculated as 75 degrees and the equations are written as Σx = -T1cos(75) + T2cos(10) =
  • #1
qwertz

Homework Statement


After a mishap, a 76.0-kg circus performer clings to a
trapeze, which is being pulled to the side by another circus
artist, as shown here. Calculate the tension in the two ropes
if the person is momentarily motionless. Include a free body diagram in your solution
MhHZ9mj.png


Homework Equations


∑Fx = T2cos10-T1sin(15)=0
∑Fy=T1cos(15)+T2sin(10)-m*g=0

The Attempt at a Solution


Here is my free body diagram:

nyHF38Q.png


I am not sure are my equations valid.
 
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  • #2
Welcome to the PF. :smile:

Looks good so far, so keep on going...
 
  • #3
Is it also valid if I calculate angle of T1 as 90 - 15 = 75 and write equations as:

Σx = -T1cos(75) + T2cos(10) = 0
Σy =T1sin(75) + T2sin(10) - m*g = 0
 

1. How are Newton's laws applied in everyday life?

Newton's laws are applied in everyday life in various ways, such as when we push a door to open it (first law), when we feel a force pushing us back in a moving vehicle (second law), and when we observe objects falling to the ground (third law).

2. What is the significance of Newton's second law?

Newton's second law, also known as the law of force and acceleration, is significant because it explains the relationship between force, mass, and acceleration. It states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

3. How is Newton's third law applied in sports?

Newton's third law, also known as the law of action and reaction, is applied in sports such as swimming, where the swimmer pushes the water backwards with their arms and legs, and the water exerts an equal and opposite force on the swimmer, propelling them forward.

4. Can Newton's laws be applied in space?

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5. How do Newton's laws relate to the concept of inertia?

Newton's first law, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force. This concept of inertia is closely related to Newton's first law and is used to explain the resistance of objects to changes in their state of motion.

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