# Solving Student's Ladder Homework Problem

• ledphones
In summary, the problem involves a student standing on a ladder with specific dimensions and weight, and the question is asking for the tension in a tie-rod and the components of the force of the ground on the ladder at various points. The solution involves setting up equations for force and torque and solving for the unknown variables. It is also possible to determine some of the components using geometry.
ledphones

## Homework Statement

A student is standing on a ladder as shown in the figure to the right. Each leg of the ladder is 2.6 m long and is hidged at point C. The tie-rod (BD) attached halfway up and is 0.79 m long. The student is standing at a spot 1.95 m along the leg and her weight is 510 N. (You may ignore the weight of the ladder and any minor friction between the floor and the legs.)

a) What is the tension in the tie-rod?
TR = N

b) What is the vertical component of the force of the ground on the ladder leg at point A?

c) What is the horizontal component of the force of the ground on the ladder leg at point A?
d) What is the vertical component of the force of the ground on the ladder leg at point E?

## Homework Equations

Na is normal force at point A
Ne is normal force at point E
Fcy is the force at point C in the Y direction
Fcx is the force at point C in the X direction
L is the length of one side
l is the length of the tie

## The Attempt at a Solution

I set up my equations like this:
1) Left side in the x: T-Fcx=0 same as on the right
2)Left side in the y: Na+Fcy-mg=0
3)Right side in the y: Ne-Fcy=0
4) Na-Ne-mg=0 (for the system)
5) torque about the point c: Fy*0+Fx*0-T*(L/2)*cos(theta)+Ne*l/2

to find theta i took the inverse sin of (.395/1.3)
so for torque i found .395Ne=1.24T
or T=.3189Ne

but when I tried to solve for my 5 unknowns I keep going in a never ending circle. I think once i find the Tension I can find parts b) c) and d)

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ledphones said:
...
I set up my equations like this:
1) Left side in the x: T-Fcx=0 same as on the right
2)Left side in the y: Na+Fcy-mg=0
3)Right side in the y: Ne-Fcy=0
4) Na-Ne-mg=0 (for the system)
5) torque about the point c: Fy*0+Fx*0-T*(L/2)*cos(theta)+Ne*l/2
...
I think once i find the Tension I can find parts b) c) and d)

Have you kept your force direction assumptions consistent? A free body diagram would help if you haven't completed one. In equation 3, you assume that Ne is positive (up I assume, but in equation 4 it is negative (down). I haven't checked everything.

It isn't necessary to solve in order. From geometry, you can pretty easily determine parts b and d. Part c is rather trivial (I think).

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## What is the "Student's Ladder Homework Problem"?

The Student's Ladder Homework Problem is a mathematical problem that involves calculating the length of a ladder needed to reach a certain height on a wall. It is a common problem given to students in geometry or physics classes.

## What are the steps to solve the "Student's Ladder Homework Problem"?

The steps to solve the Student's Ladder Homework Problem are as follows:

1. Draw a diagram of the problem.
2. Label the known and unknown values.
3. Use the Pythagorean Theorem to create an equation.
4. Solve the equation for the unknown value.
5. Check your answer and round to the appropriate number of significant figures.

## What is the Pythagorean Theorem and how is it used to solve the "Student's Ladder Homework Problem"?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In the "Student's Ladder Homework Problem", the hypotenuse is the length of the ladder, and the other two sides are the height of the wall and the distance from the base of the wall to the base of the ladder.

## What are some common mistakes students make when solving the "Student's Ladder Homework Problem"?

Some common mistakes students make when solving the Student's Ladder Homework Problem include:

• Forgetting to label the known and unknown values correctly.
• Using the wrong formula (such as the Pythagorean Theorem for a non-right triangle).
• Not rounding to the appropriate number of significant figures.
• Making calculation errors.

## Are there any tips or tricks for solving the "Student's Ladder Homework Problem"?

One helpful tip for solving the Student's Ladder Homework Problem is to draw a clear and accurate diagram of the problem. This can help you visualize the situation and label the known and unknown values correctly. Another tip is to double check your calculation and units to ensure you have the correct answer. Finally, it can be helpful to practice similar problems to become more familiar with the steps and concepts involved.

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