Max Angle for Block to Roll Without Slipping: 29.24°

In summary, the homework statement states that if a solid cylinder is fashioned from the same material as a sliding block, the maximum angle at which it will roll without slipping on the plane is 29.24 degrees.
  • #1
Anya91
3
0
1. Homework Statement
A block of a certain material begins to slide on an inclined plane when the plane is inclined to an angle of 15.64°. If a solid cyclinder is fashioned from the same material, what will be the maximum angle at which it will roll without slipping on the plan

2. Homework Equations

tan θ = μ
tan 15.64 = 0.28 = μ
Now let's assume a solid cylinder with mass M and radius R on an inclination θ
Translatory motion, (a is acceleration of CM)
Mg sinθ - μMgcosθ = Ma
g sinθ - μgcosθ = a ...(1)

Rotational motion,
μMgcosθ(R) = Iα (α is angular acceleration)
μMgcosθ (R) = MR²/2(α)
μ g cosθ = R/2 (α) ...(2)

for pure rolling,
αR = a

μ g cosθ = a / 2
Replace a with the expression in (1)
μ g cosθ = g sinθ - μgcosθ
μ cosθ = sinθ - μ cosθ
2(μ cosθ) = sinθ
μ = tanθ / 2

θ = arc tan (2μ) = arc tan(0.56) = 29.24 deg

3. The Attempt at a Solution
I got incorrect answer for that problem?? I don't know why I got it wrong??
 
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  • #2
Hi Anya91! :smile:
Anya91 said:
μ g cosθ = a / 2
Replace a with the expression in (1)
μ g cosθ = g sinθ - μgcosθ

You dropped the 2. :redface:

(btw, you could also have done τ = Iα about the centre of rotation :wink:)
 
  • #3
thank you so much :) I got correct answer now =)
 
  • #4
i am so confused.. how can you find the "arc" that you are plugging into "arc tan(0.56) = 29.24 deg" i tried this and i am LOST! helppp!
 
  • #5
hi slk011! :smile:
slk011 said:
.. how can you find the "arc" that you are plugging into "arc tan(0.56) = 29.24 deg"

arctan is the same as tan-1

use the tan-1 button on your calculator, and it gives you the angle whose tan is 0.56 :wink:

(you may need to click "2nd" to turn the tan button into tan-1)
 
  • #6
Thank you for the help! ... i am using eq (3 tanθ)(tan-1 (3tanθ) and its not working :( what am i doing wrong?
 
  • #7
nevermind! got it! it was (3 tanθ)+(tan-1 (3tanθ)!
 

FAQ: Max Angle for Block to Roll Without Slipping: 29.24°

What does "Max Angle for Block to Roll Without Slipping: 29.24°" mean?

"Max Angle for Block to Roll Without Slipping: 29.24°" refers to the maximum angle at which a block can be placed on a surface without slipping. In other words, it is the steepest incline on which the block can be placed and still roll without any slipping motion.

How is the max angle for block to roll without slipping calculated?

The max angle for block to roll without slipping is calculated using the coefficient of static friction between the block and the surface it is resting on. This coefficient is a measure of the amount of friction between the two surfaces and is used in a formula to determine the maximum angle. The formula is given by tanθ = μs, where θ is the maximum angle and μs is the coefficient of static friction.

Why is it important to know the max angle for block to roll without slipping?

Knowing the max angle for block to roll without slipping is important for understanding the behavior of objects on inclined planes. It is crucial in engineering and physics applications where objects may need to be placed on inclines or ramps without slipping to avoid accidents or malfunctions. Additionally, it can help determine the stability of a structure on an inclined surface.

What factors can affect the max angle for block to roll without slipping?

The max angle for block to roll without slipping can be affected by several factors, including the surface material and roughness, the weight and shape of the block, and the magnitude of the applied force. Additionally, the coefficient of static friction can vary depending on the temperature and moisture of the surface.

Can the max angle for block to roll without slipping be greater than 90 degrees?

No, the max angle for block to roll without slipping cannot be greater than 90 degrees. This is because a 90 degree angle would mean the block is placed vertically and is no longer rolling, but rather falling. The maximum angle for rolling without slipping is always less than 90 degrees.

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