Placing rock under ladder to stop it from slipping

In summary, the conversation is about explaining the solutions to parts (a) and (b) of a problem. There is confusion about where the value of 5.77 cm came from, and someone suggests using similar triangles to solve the problem. They also mention drawing a diagram to better understand the problem. Eventually, it is understood that the value of 5.77 cm was obtained through the use of similar triangles.
  • #1
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Homework Statement
Please see below
Relevant Equations
Please see below
For part(a) and (b),
1675394717684.png

The solution is,
1675394798329.png

Can someone please explain the solutions to (a) and (b) to me? I don't understand where they got 5.77 cm from.

Many thanks!
 
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  • #2
They used b to get a.

What answer did you get ?
 
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  • #3
hmmm27 said:
They used b to get a.

What answer did you get ?
Thanks for your reply @hmmm27 ! The got 5.77 cm. But don't you think that is a little strange using (b) to get (a)?

I still don't understand (b). Many thanks!
 
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  • #4
So, what answer did you get ? and how did you arrive at it.
 
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  • #5
hmmm27 said:
So, what answer did you get ? and how did you arrive at it.
I did't get an answer @hmmm27. I am wondering how the solutions arrived at their anwser.
 
  • #6
Callumnc1 said:
is a little strange using (b) to get (a)?
Not at all. The answer to part b) is the explanation of how they arrived at the solution to a). Presumably this uses ideas earlier in the chapter, but I do not have the book.
Draw a diagram showing the ladder in both positions. Label the right-hand foot of the ladder P (the pivot point), the right-hand top of the tilted ladder B, the right-hand top of the upright ladder B', the left-hand bottom of the tilted ladder A, the left-hand bottom of the upright ladder A'.
Drop a vertical from A' to meet the sloping ground.
Draw a horizontal from B to meet PB'.
Spot similar triangles.
 
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  • #7
haruspex said:
Not at all. The answer to part b) is the explanation of how they arrived at the solution to a). Presumably this uses ideas earlier in the chapter, but I do not have the book.
Draw a diagram showing the ladder in both positions. Label the right-hand foot of the ladder P (the pivot point), the right-hand top of the tilted ladder B, the right-hand top of the upright ladder B', the left-hand bottom of the tilted ladder A, the left-hand bottom of the upright ladder A'.
Drop a vertical from A' to meet the sloping ground.
Draw a horizontal from B to meet PB'.
Spot similar triangles.
Thank you @haruspex , I will try that!
 
  • #8
Callumnc1 said:
Can someone please explain the solutions to (a) and (b) to me? I don't understand where they got 5.77 cm from.

Many thanks!
I don’t see a reason for translating tilting into angle and back to vertical displacement of the left leg.
Are you familiar with similar triangles?

https://www.mathsisfun.com/geometry/triangles-similar.html

If so, I would draw a 0.41 x 0.41 square at the bottom of the rectangle formed by the ladder dimensions.
The horizontal displacement of the top corners of that square should be equal to the vertical one, and both should be proportional to the horizontal displacement of the top of the ladder.
 
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  • #9
Lnewqban said:
I don’t see a reason for translating tilting into angle and back to vertical displacement of the left leg.
Are you familiar with similar triangles?

https://www.mathsisfun.com/geometry/triangles-similar.html

If so, I would draw a 0.41 x 0.41 square at the bottom of the rectangle formed by the ladder dimensions.
The horizontal displacement of the top corners of that square should be equal to the vertical one, and both should be proportional to the horizontal displacement of the top of the ladder.
Thank you for your reply @Lnewqban ! Yeah I'm familiar with similar triangles.
 
  • #10
Callumnc1 said:
Thank you for your reply @Lnewqban ! Yeah I'm familiar with similar triangles.
You are welcome. :smile:
Then, you now understand where they got 5.77 cm from.

We have two triangles that are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Please, see scaled drawing representing our problematic ladder.
 

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  • #11
Lnewqban said:
You are welcome. :smile:
Then, you now understand where they got 5.77 cm from.

We have two triangles that are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Please, see scaled drawing representing our problematic ladder.
That is very helpful @Lnewqban ! Thank you for your help!
 
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Related to Placing rock under ladder to stop it from slipping

Why does placing a rock under a ladder help prevent it from slipping?

Placing a rock under a ladder helps prevent it from slipping by providing additional friction and stability. The rock acts as a wedge, increasing the contact area between the ladder's feet and the ground, which reduces the chances of the ladder moving or sliding.

What type of rock should be used to stop a ladder from slipping?

It is best to use a flat, stable rock that can provide a solid base. The rock should be large enough to cover the area under the ladder's feet and have a rough surface to maximize friction. Avoid using rounded or smooth rocks, as they may not provide adequate stability.

Is placing a rock under a ladder a safe and reliable method?

While placing a rock under a ladder can improve stability, it is not the most reliable or safest method. It is recommended to use ladder stabilizers or anti-slip devices specifically designed for this purpose. Always ensure the ladder is set up on a stable and level surface.

Can placing a rock under a ladder damage the ladder?

If done carefully, placing a rock under a ladder should not damage the ladder. However, if the rock is too sharp or uneven, it may cause wear or damage to the ladder's feet over time. It is important to choose a suitable rock and check the ladder for any signs of damage regularly.

Are there any alternatives to using a rock to prevent a ladder from slipping?

Yes, there are several alternatives to using a rock to prevent a ladder from slipping. These include using ladder stabilizers, anti-slip mats, ladder levelers, and securing the ladder with ropes or straps. These methods are generally safer and more effective than using a rock.

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