- #1
x2017
- 84
- 1
Homework Statement
Homework Equations
ΣFx=max
The Attempt at a Solution
I drew a free body diagram for the box and set up the equation to solve for θ, but I'm not sure how to do it without μ
At What Angle Will This Box Begin to Slide?
In summary, the conversation discusses a problem involving a box on a surface with a given frictional force. The attempt at a solution involves setting up an equation using the sum of forces in the x-direction, but initially forgetting to include the given frictional force. After realizing the mistake, the solution is found to be θ=30°. The mistake is deemed reasonable since in reality, the friction force would depend on the normal force, which is affected by the angle of the surface.
ΣFx=max
I drew a free body diagram for the box and set up the equation to solve for θ, but I'm not sure how to do it without μ
- #2
Suraj M
Gold Member
- 597
- 39
I don't think you need to substitute
##F_{friction}## with ##μ F_N##
They want you to use the frictional force they themselves have provided in the question.
##F_{friction}## with ##μ F_N##
They want you to use the frictional force they themselves have provided in the question.
- #3
x2017
- 84
- 1
Suraj M said:
Oh my goodness I can't believe I missed that... Thank you!
ΣFx=max
mgx-Ffx=max
mgsinθ-Ffx=max
(100)(9.81)sinθ-490.5=(100)(0)
981sinθ=490.5
θ=sin-1(490.5/981)
θ=30°
Wow, that was an embarrassing mistake!
- #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
- 11,892
- 1,484
In a way, your mistake is one that is reasonable to make.x2017 said:
In an actual situation, the friction force does depend upon the normal force, which depends upon the angle the surface make with the horizontal.
Having the friction force be a fixed value, is not realistic.
Related to At What Angle Will This Box Begin to Slide?
1. What factors determine at what angle a box will begin to slide?
The angle at which a box will begin to slide depends on several factors, including the weight and mass of the box, the friction between the box and the surface it is resting on, and the force acting on the box (such as gravity).
2. Is there a specific formula to determine the angle at which a box will begin to slide?
Yes, there is a formula known as the "sliding angle" formula that can be used to calculate the angle at which a box will begin to slide. It takes into account the weight and mass of the box, the coefficient of friction between the box and the surface, and the force acting on the box.
3. How does the coefficient of friction affect the angle at which a box will begin to slide?
The coefficient of friction is a measure of the amount of resistance between two surfaces in contact. The higher the coefficient of friction, the more difficult it is for the box to slide. Therefore, a higher coefficient of friction would result in a higher sliding angle.
4. Can the shape of the box affect the angle at which it will begin to slide?
Yes, the shape of the box can definitely affect the angle at which it will begin to slide. For example, a box with a wider base will have a lower sliding angle compared to a box with a narrower base, as the wider base provides more stability and resistance against sliding.
5. What are some practical applications of understanding the sliding angle of a box?
Understanding the sliding angle of a box is important in various industries, such as construction, engineering, and transportation. It can help in determining the stability of structures and vehicles, as well as ensuring the safety of workers and passengers. It is also useful in everyday tasks, such as packing and storing items to prevent them from sliding or tipping over.
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