Torques in equilibrium w/ angle

In summary, to balance a meter stick by pulling upward on one end with a string at a 30 degree angle, we need to consider the torque from the gravitational force and the torque exerted by the center of mass of the stick. The force needed can be calculated using F=-0/(rsin(theta)), where theta is the angle of the string to the vertical. It is important to note the difference between sine and cosine when calculating the force.
  • #1
supercherrie
1
0
on a meter stick the pivot point is placed at 1/4 its length; predict the force needed to balance the meter stick by pulling upward on the end of it with a string making an angle of 30 degrees w/ respect to the vertical.

Me trying to solve it:
sigma T=0
T1+T2=0
T1 = 0 <--this is the pivot point, i think it equals 0 b/c we what to reach equilibrium
T2 = rFsin(theta)
0+rFsin(theta)
F=-0/(rsin(theta)) ?
 
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  • #2
supercherrie said:
T1+T2=0
T1 = 0 <--this is the pivot point, i think it equals 0 b/c we what to reach equilibrium
It's the '=0' in 'T1+T2=0' that says we're to reach equilibrium. T1 is the torque from the gravitational force. Where is the centre of mass of the stick? How far from the pivot point? What torque does it exert?
As for the string, it's 30 degrees to the vertical. Be careful about sine versus cosine. (As a check, I always think to myself, what if the specified angle were zero? Would the force be zero or max?)
 

1. What is the definition of torque in equilibrium?

Torque in equilibrium refers to the state where the net torque on an object is zero, meaning that the object is not rotating. This occurs when the sum of all the forces acting on the object is balanced and there is no net rotational force.

2. How is the angle of an object related to its equilibrium torque?

The angle of an object is directly related to its equilibrium torque. The farther the force is applied from the pivot point, the greater the torque. This means that the greater the angle between the force and the lever arm, the greater the torque and the more likely the object is to rotate.

3. What is the importance of balancing torques in equilibrium?

Balancing torques in equilibrium is important because it ensures that an object remains in a stable and stationary position. If the net torque is not zero, the object will rotate, potentially causing damage or injury.

4. How can the equilibrium of torques be calculated?

The equilibrium of torques can be calculated by using the formula: Στ = rFsinθ, where Στ is the net torque, r is the distance from the pivot point to the point where the force is applied, F is the magnitude of the force, and θ is the angle between the force and the lever arm.

5. What factors affect the equilibrium of torques?

The equilibrium of torques can be affected by several factors, including the magnitude and direction of the forces, the distance from the pivot point to the point where the force is applied, and the angle between the force and the lever arm. These factors must be balanced in order to achieve a net torque of zero and maintain equilibrium.

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