Solve Dynamics Problem: Find Friction Force at θ=80° & 40°

  • Thread starter springo
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In summary, the problem involves a plate rotating at a constant speed with coefficients of friction of 0.35 and 0.25. The goal is to determine if a mass, E, will move for certain angles and to find the friction force for a specific time. Newton's second law and the equations for acceleration and angular velocity were used to solve the problem.
  • #1
springo
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Homework Statement


I drew this to make it easier to understand:
http://img142.imageshack.us/img142/2729/problemagc0.th.jpg
E (mass: 400g) can move along the semicircle.
ABCD is a plate rotating around (AD) axis at constant speed (14 rad/s).
Coefficients of friction are 0.35 (static) and 0.25 (dynamic).
I need to find out whether E will move for θ = 80º and for θ = 40º. Also I need to find the module and direction of the friction force for t0.

Homework Equations


None.

The Attempt at a Solution


I applied Newton's second law.
Σ Fext = mg + N1 + N2 + f
Where:
mg is E's weight
N1 is the normal force in the (ABC) plane
N2 is the normal force perpendicular to the (ABC) plane
f is the friction force
I did this also so that you understand what I mean -just in case... :)
http://img88.imageshack.us/img88/4488/esquemabr8.th.jpg

Then I think I must use:
aE = aO + aE/O + ωx(ωxOE) + αxOE + 2ωxvE/O
With:
α = dω/dt = 0
ω = 14 j
OE = (0.65 - sin(θ)*0.25) iI hope you can help me out here. Thanks a lot!
 
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  • #2
Bump, anyone?
Thanks again.
 
  • #3
Bump, please give me a hand...
 

What is the friction force at θ=80°?

The friction force at θ=80° can be calculated using the formula:

F = μNcosθ

Where μ is the coefficient of friction, N is the normal force, and θ is the angle of inclination. Simply plug in the values for μ and N to find the friction force at θ=80°.

How do you find the friction force at θ=40°?

The same formula can be used to find the friction force at θ=40°:

F = μNcosθ

Make sure to double check that the values for μ and N are correct before plugging them into the formula.

What is the significance of the coefficient of friction in this problem?

The coefficient of friction, denoted by μ, is a measure of the amount of resistance two surfaces have when in contact with each other. In this problem, the coefficient of friction is used in the formula to calculate the friction force at various angles. It is an important factor to consider in solving dynamics problems involving friction.

How does the normal force affect the friction force?

The normal force, denoted by N, is the force that is perpendicular to the surface of contact between two objects. It is responsible for balancing out the weight of an object and keeping it in place. The friction force is directly proportional to the normal force, meaning that an increase in the normal force will result in an increase in the friction force. This is because a greater normal force means more contact between the two surfaces, leading to more resistance and therefore a higher friction force.

What are some real-life applications of solving dynamics problems involving friction?

Understanding the principles of friction and how it affects the motion of objects is crucial in many real-life scenarios. For example, engineers use this knowledge to design vehicles with proper braking systems, as friction is what allows them to slow down and stop. In construction, friction is taken into account when building structures to ensure stability and prevent slipping or sliding. Additionally, knowledge of friction is useful in sports, such as determining the ideal surface for a specific sport or designing equipment with the right amount of friction for optimal performance.

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