# Ladder on a wall held in place by a peg

• Jacobiam
In summary, a 10 m long uniform ladder weighing 400 N is resting against a frictionless vertical wall with its lower end supported by a peg. The ladder is at a 30 degree angle with the horizontal. The magnitude of the force exerted on the peg by the ladder is 470N. The forces acting on the ladder include normal force, weight, force from the wall, and force from the peg. The force of the ladder on the peg is equal in magnitude and opposite in direction according to Newton's third law.
Jacobiam

## Homework Statement

Figure attached
A uniform ladder is 10 m long and weighs 400 N. It rests with its upper end against a frictionless vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground. The ladder makes a 30 degree angle with the horizontal. The magnitude of the force exerted on the peg by the ladder is:
W = 400N
L = 10m

Torque = r x F

## The Attempt at a Solution

Calculating torque about the lower end, I was able to find force exerted by the wall
Tweight = Twall
400N(5cos30) = Fwall(10sin30)
Fwall = 346.4N

the forces I have so far are: normal force, weight and force from the wall.
Are there two other forces from the peg(perpendicular to the ladder going down) and the force of the ladder on the peg(perpendicular to ladder up)?

#### Attachments

• Screen Shot 2017-01-08 at 8.02.38 PM.png
7.1 KB · Views: 764
Jacobiam said:
Are there two other forces from the peg(perpendicular to the ladder going down) and the force of the ladder on the peg(perpendicular to ladder up)?
You can thonk of the force from the peg as a single force or as composed of two forces at right angles to each other; in the latter choice, you could use vertical and horizontal or perpendicular and parallel to the ladder.
I suggest using vertical and horizontal.

CWatters
Jacobiam said:

## Homework Statement

Figure attached
A uniform ladder is 10 m long and weighs 400 N. It rests with its upper end against a frictionless vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground.

In your figure, the peg looks as part of the ladder and perpendicular to the leg of the ladder. But the peg should stand out from the ground, probably vertical. Was the figure attached to the problem, or have you drawn it yourself?
Jacobiam said:
the forces I have so far are: normal force, weight and force from the wall.
Are there two other forces from the peg(perpendicular to the ladder going down) and the force of the ladder on the peg(perpendicular to ladder up)?
You have to collect the forces acting on the ladder, and their sum should result zero. Determine the force of the peg on the ladder. The force of the ladder on the peg is equal in magnitude and of opposite direction according to Newton's third law.

The usual form of this problem has friction with the ground rather than a peg preventing it slipping. Unless there is additional info in the original problem statement I would solve the peg version the same way. eg assume the peg can only provide a horizontal force.

## 1. How does the peg keep the ladder in place?

The peg works by creating a firm hold between the ladder and the wall. It is inserted into a hole at the bottom of the ladder and wedged against the wall, providing stability and preventing the ladder from sliding.

## 2. What material is the peg made of?

The material used for pegs can vary, but common materials include metal (such as steel or aluminum), plastic, or wood. The chosen material will depend on factors such as durability, weight, and cost.

## 3. How do you ensure the ladder is safe when using a peg?

It is important to properly inspect the peg and ladder before use. Make sure the peg is securely inserted into the hole and the ladder is placed at the correct angle against the wall. Always follow the weight and height limits specified for the ladder. It is also recommended to have a spotter or someone to hold the ladder in place while in use.

## 4. Can the peg be used on any type of wall?

The peg can be used on most types of walls, including drywall, concrete, brick, and wood. However, it is important to consider the weight and height limits of the ladder, as well as the strength and stability of the wall. For example, a thin or weak wall may not be able to support a heavy ladder.

## 5. Is the peg necessary for using a ladder on a wall?

No, the peg is not necessary for using a ladder on a wall. There are other options such as a ladder stabilizer or standoffs that can also provide stability and safety. However, the peg is a popular and cost-effective choice for holding a ladder in place.

Replies
4
Views
6K
Replies
5
Views
2K
Replies
12
Views
1K
Replies
5
Views
2K
Replies
2
Views
2K
Replies
23
Views
14K
Replies
2
Views
3K
Replies
11
Views
3K
Replies
4
Views
2K
Replies
1
Views
1K