Torque and equilibrium

In summary, the conversation is discussing a problem where the tension in a tie rope needs to be calculated. The given picture shows a block hanging from a slanted rod attached to a wall, with a rope holding the block to the rod at a 30 degree angle. The answer key provided uses cos 60 instead of sin 30 because the angle created by the rope and the slanted rod is equivalent to 30 degrees, and sin 30 is equal to cos 60.
  • #1
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Homework Statement


Here's the picture and I am asked to calculate the tension in the tie rope between the rod and wall

http://img399.imageshack.us/img399/2625/masslg8.jpg [Broken]
http://g.imageshack.us/img399/masslg8.jpg/1/ [Broken]


Homework Equations





The Attempt at a Solution



The answer key is:

http://img399.imageshack.us/img399/4733/answermo0.jpg [Broken]
http://g.imageshack.us/img399/answermo0.jpg/1/ [Broken]

I just want to know why is it using cos 60 instead of sin 60?
 
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  • #2
because the angle created by the rope holding the block and the slanted thinger is 30 degrees (right triangles). So instead of putting sin 30 they just put cos 60 because sin 30 = cos 60. i hope you understand what I'm talking about
 
Last edited:
  • #3


I would like to clarify the use of cosine in this solution. In this scenario, the rod and the tie rope are in equilibrium, meaning that the forces acting on them are balanced and there is no acceleration. This can be represented by the sum of the forces in the vertical and horizontal directions being equal to zero. The tension in the tie rope can be calculated using the equation T = mg/cosθ, where T is the tension, m is the mass of the hanging object, g is the acceleration due to gravity, and θ is the angle between the tie rope and the vertical direction. In this case, the angle θ is 60 degrees, and since we are looking for the tension in the tie rope, we can rearrange the equation to T = mg/cos60 = 2.5 kg x 9.8 m/s^2 / cos60 = 24.5 N. Cosine is used instead of sine because in this scenario, the angle θ is measured from the horizontal direction, not the vertical direction. Therefore, we use cosine to determine the component of the weight of the hanging object that is acting in the horizontal direction, which is the tension in the tie rope.
 

1. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis to the point where the force is applied.

2. How is torque related to equilibrium?

In order for an object to be in equilibrium, the sum of all torques acting on the object must be equal to zero. This means that the clockwise torques must balance out the counterclockwise torques, resulting in no net torque on the object.

3. What factors affect torque?

The two main factors that affect torque are the magnitude of the force applied and the distance from the axis to the point where the force is applied. The angle at which the force is applied also plays a role in determining the torque.

4. How is torque measured?

Torque is typically measured in units of Newton-meters (N*m) in the SI system or foot-pounds (ft-lb) in the English system. A device called a torque wrench is commonly used to measure torque in mechanical systems.

5. What is the difference between static and dynamic equilibrium?

In static equilibrium, an object is at rest and there is no net force or torque acting on it. In dynamic equilibrium, an object is moving at a constant velocity in a straight line and there is no net force or torque acting on it. Both types of equilibrium require the sum of all forces and torques to be equal to zero.

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