# What Angle Allows a Right Angle Ruler to Hang in Equilibrium?

• joemama69
In summary, in this conversation, the topic is about finding the angle at which a right angle ruler made of uniform sheet metal will hang in equilibrium. The equation used is F(y) = P - .75mg, and the force P must equal mg, not .75mg. The final equation to solve is .25 = tanQ, where Q represents the angle.
joemama69

## Homework Statement

the right angle ruler shown in the figure hangs from a peg . it is made of unifrom sheet metal. let lambda equal the leiner dinsity. one arm is Lcm long and the other is 2L cm long. find the angle theta at which it will hang in equilibrium

## The Attempt at a Solution

I believe ij ust sum the forces, that is the forces in the y direction equal zero as well as the torqs. i don't think i need the x right?

F(y) = 0 = P - .5mg - mg = P - .75mg

F(torque) = 0 = .5Amg - Bmg hwere A = .5LcosQ and B = LsinQ

F = 0 = .5(.5LcosQ)mg - (LsinQ)mg = .25cosQ - sinQ = 0

is this correct, how do i solve this

#### Attachments

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you are on track, but you have the force P equal to .75mg, where instead, it must equal mg, where mg is the total weight of the right angled metal. It doesn't make much difference, though...note that sin theta/cos theta =tan theta, when you solve your equation for theta.

something is not right

.25cosQ = sinQ
cosQ = 4sinQ
0 = 4tanQ

Q = 0

what did i do wrong

joemama69 said:
something is not right

.25cosQ = sinQ
cosQ = 4sinQ
0 = 4tanQ

Q = 0

what did i do wrong

if .25cosQ = sinQ, then divide both sides of the equation by cosQ, which yields

.25cosQ/cosQ = sinQ/cosQ, or
.25 = tanQ

Solve for the angle, Q.

## 1. What is a right angle equilibrium?

A right angle equilibrium refers to a situation where two or more forces acting on an object are balanced in such a way that the resultant force is at a right angle to the direction of motion.

## 2. How is right angle equilibrium achieved?

Right angle equilibrium is achieved when the vector sum of all the forces acting on an object is equal to zero. This means that the forces are balanced and the object will remain in a state of rest or constant motion.

## 3. What are some examples of right angle equilibrium?

One example of right angle equilibrium is a book resting on a table. The weight of the book is balanced by the normal force exerted by the table, and the resultant force is at a right angle to the surface of the table.

Another example is a person holding a weight at the end of a rope. The weight of the object is balanced by the tension force in the rope, and the resultant force is at a right angle to the direction of motion.

## 4. How is right angle equilibrium different from regular equilibrium?

In regular equilibrium, the resultant force is equal to zero, but the direction of the force is not necessarily at a right angle to the direction of motion. In right angle equilibrium, the resultant force is also equal to zero, but the direction of the force is specifically at a right angle to the direction of motion.

## 5. Why is right angle equilibrium important?

Right angle equilibrium is important because it ensures that an object remains in a state of rest or constant motion. It is also a key concept in understanding the forces acting on an object and how they can be balanced or unbalanced.

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