# Torque/Static Equilibrium Problems

• blackice552
In summary, the first problem involves finding the magnitude of a perpendicular force needed to prevent a stick from rotating, given the length of the stick, the angle and distance of the initial force, and the distance of the new force from the pivot. The second problem involves finding the magnitude of the torque on a wrench, given the magnitude and angle of the applied force and the distance from the pivot. The equations used are torque = force * perpendicular distance and perpendicular distance = distance * sin(theta).

#### blackice552

1. Homework Statement :
I have 2 problems:
1. We have a stick of length 30cm. The stick has a pivot point in its left end. We have a force 3.3N acting at angle 0.7rads and a distance 16.1cm from the pivot. What is the MAGNITUDE of the force we must apply perpendicular to the stick at a distance 5.0cm from the pivot so that the stick does NOT rotate?

2.I am applying a force 2.4N on a wrench at an angle 0.5rads from the horizontal. If the point of application of the force is 7.8cm from the pivot, what is the MAGNITUDE of the torque about the pivot?

2. Homework Equations :
Torque = Force * Perpendicular Distance
Perpendicualr Distance = distance * sin(theta)
Note: I'm not sure if it matters in problem one that the distances aren't the end of the object.

3. The Attempt at a Solution :
1.
Torque1 +Torque2 = 0
Torque1 = .161 m * (3.3 N) * (sin (.7)) = 3.422
Torque2 = -3.422 = F(.5)(sin (pi/2)) = .5F
-6.844 = F
Mag. F = 6.844 N

2.Perpendicular Distance = .078 m * sin(.5) = .037
Torque = 2.4 N * .037 m= .09 Nm

blackice552 said:
Torque2 = -3.422 = F(.5)(sin (pi/2)) = .5F

I'm not sure why you used the sine here, since the distance is perpendicular? Or am I missing something?

I would like to point out a few things about these torque/static equilibrium problems. First, it is important to note that torque is a vector quantity, meaning it has both magnitude and direction. In these problems, we are given the magnitude of the force and the distance from the pivot, but we also need to consider the direction of the force in order to calculate the torque correctly.

In problem 1, we are given a force acting at an angle from the pivot, so we need to use the perpendicular component of the force (3.3N * sin(0.7) = 2.911N) to calculate the torque. Additionally, we need to consider the direction of the perpendicular force, which is counterclockwise in this case. So our equation should be: Torque1 + Torque2 = 0, where Torque1 is the torque from the given force and Torque2 is the torque from the perpendicular force we are trying to find. This will give us the correct magnitude and direction of the force needed to keep the stick from rotating.

In problem 2, we need to be careful with the units. The distance from the pivot is given in centimeters, but we need to convert it to meters in order to use the equation Torque = Force * Perpendicular Distance. Also, the given force is already perpendicular to the wrench, so we don't need to calculate the perpendicular component. Our equation should be: Torque = 2.4N * 0.078m = 0.1872 Nm.

Overall, these problems require careful consideration of both magnitude and direction in order to calculate the correct torque and solve for the unknown force. It is important to pay attention to units and use the correct equations to get an accurate solution.

## 1. What is torque?

Torque is a measure of the rotational force acting on an object. It is calculated by multiplying the force applied to an object by the distance from the fulcrum (pivot point) to the point where the force is applied.

## 2. How is torque related to static equilibrium?

In static equilibrium, the net torque acting on an object is equal to zero. This means that the object is not rotating or moving, and the forces acting on it are balanced. The concept of torque helps us understand how different forces can act on an object to keep it in static equilibrium.

## 3. How do I calculate torque in a problem?

To calculate torque, you need to know the magnitude of the force acting on an object and the distance from the fulcrum to the point where the force is applied. The formula for torque is T = F * d * sin(theta), where T is torque, F is the force, d is the distance, and theta is the angle between the force and the lever arm.

## 4. What is the difference between clockwise and counterclockwise torque?

Clockwise torque is when the force causes the object to rotate in a clockwise direction, while counterclockwise torque causes the object to rotate in a counterclockwise direction. The direction of the torque depends on the direction of the force and the position of the fulcrum.

## 5. How do I determine the equilibrium condition in a torque problem?

In order for an object to be in static equilibrium, the net torque acting on the object must be equal to zero. This means that the sum of all the clockwise torques must be equal to the sum of all the counterclockwise torques. If the net torque is not equal to zero, the object will either rotate or translate in the direction of the greater torque.