Statics, ladder leaning against wall finding friction mass etc. really simple q.

[Gogarty]

This Is really simple I just can't remember what way Sin and Cosine go

Homework Statement

Here is the problem:
7 (b) A uniform ladder rests on rough
horizontal ground and leans against
a smooth vertical wall.
The length of the ladder is 5 m and
its weight is 80 N.
The angle between the ladder and the
ground is 60
The ladder is on the point of slipping.
(i) Show on a diagram all the forces acting on the ladder.
(ii) Calculate the value of the coefficient of friction


right so I realize the weight acts through the center of gravity in this case half way up. but it also acts towards the wall. is it the sin or cos of the angle that acts down. which goes horizontaly? I know how to do the rest just what way do the components of the weight break up? Is it 80 cos(60 or 80 Sin(60 to find the force acting to the right ?

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

This Is really simple I just can't remember what way Sin and Cosine go

Hi Gogarty! Welcome to PF!

If you're asking about components of force, it's always cos of the angle between the direction of the force and the direction in which you're taking components.

The only time you use sin is when that angle is already called (90º - θ) … so you use cos(90º - θ), which is sinθ.

If you're asking about moments, use the distance from the point to the line (of force).

right so I realize the weight acts through the center of gravity in this case half way up. but it also acts towards the wall. is it the sin or cos of the angle that acts down. which goes horizontaly? I know how to do the rest just what way do the components of the weight break up? Is it 80 cos(60 or 80 Sin(60 to find the force acting to the right ?

Sorry, I'm not understanding this …

how can weight act towards the wall? …

and why would you want to break the weight into components?

Just find the normal force, then find the friction force …

what do you get? ​

 

[pongo38]

Look for a point about which you can take moments to reveal an equation which gives you the answer you want. In my experience, people often get their sins and coses the wrong way round. and I try to avoid them by using geometrical ratios and similar triangles. But try the moment equation first.

 

[silv3rbullet]

the force you're talking about acting against the wall is the normal force, and it is perpendicular to the point of contact.

as for the weight, in the X direction it should be mgsin(60) and the Y -mgcos(60)

 

[DeeNos]

To solve this problem, we first need to understand the concept of statics. Statics is the branch of mechanics that deals with bodies at rest or in a state of constant motion. In this problem, we have a ladder that is leaning against a wall and is on the point of slipping. This means that the ladder is in a state of constant motion, therefore we can apply the principles of statics to solve this problem.

To begin, we need to draw a free body diagram of the ladder, showing all the forces acting on it. These forces include the weight of the ladder, the normal force from the ground, and the frictional force from the ground. The weight of the ladder acts downward through its center of gravity, which is halfway up the ladder. This means that the weight can be broken down into two components, one acting vertically downwards and one acting horizontally towards the wall.

Now, to determine which component is the sine and which is the cosine, we need to remember the basic trigonometric identities. In this case, since the angle between the ladder and the ground is 60 degrees, the sine component will be acting vertically downwards and the cosine component will be acting horizontally towards the wall. This is because the sine function represents the opposite side (vertical) and the cosine function represents the adjacent side (horizontal) in a right triangle.

To find the value of the coefficient of friction, we can use the fact that the ladder is on the point of slipping. This means that the frictional force is equal to the product of the coefficient of friction and the normal force. We can use this relationship to solve for the coefficient of friction.

In summary, to solve this problem we need to draw a free body diagram, use trigonometric identities to determine the components of the weight, and use the relationship between the frictional force and the normal force to find the coefficient of friction. I hope this helps clarify the solution to this problem.