Difficult Force Problem with changing angle ( )

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SUMMARY

The discussion focuses on a physics problem involving a crate of mass m subjected to a force F on a surface with a coefficient of static friction. The angle theta starts at 0 degrees and is gradually increased, requiring the force F to be adjusted to keep the crate on the verge of sliding. Key tasks include plotting the ratio F/mg versus theta, determining the angle theta sub infinite at which this ratio approaches infinity, and analyzing the effect of lubricating the floor on theta sub infinite for coefficients of static friction of 0.70 and 0.60.

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  • Understanding of static friction and its coefficient
  • Knowledge of force diagrams and vector components
  • Familiarity with the relationship between force, mass, and gravity (F = mg)
  • Basic skills in plotting graphs and analyzing mathematical relationships
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  • Learn how to derive and plot the relationship between F/mg and theta using trigonometric functions
  • Study the effects of varying coefficients of static friction on force dynamics
  • Explore the concept of limiting angles in static friction scenarios
  • Investigate the impact of surface lubrication on frictional forces and angles
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Students studying physics, particularly those focusing on mechanics, as well as educators and tutors assisting with force and friction problems.

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Difficult Force Problem with changing angle (please help!)

1. A force F is applied to a crate of mass m on a floor where it has a coefficeint of static friction . Angle theta is intially 0 degrees but is gradually increased so that the force vector rotates clockwise in the figure. During the rotation the magnitude F of the force is continuously adjusted so that the crate is always on the verge of sliding. For coeff. of static friction = 0.70 (a) plot the ratio F/mg versus theta and (b) determine the theta sub infinite at which the ratio approaches an infinite value. (c) Does lubricating the floor increase or deacrease theta sub infinite or is the value unchanged? (d) what is theta sub infinite if the coefficient = 0.60?






3. Please help me set up the problem! I am very confused and don't comprehend the question. If you can just help me start the problem I can probably take it from here. We are having an emergency study session w/ our class tonight and none of us understand this.
 
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DJWise said:
1. A force F is applied to a crate of mass m on a floor where it has a coefficeint of static friction . Angle theta is intially 0 degrees but is gradually increased so that the force vector rotates clockwise in the figure. During the rotation the magnitude F of the force is continuously adjusted so that the crate is always on the verge of sliding. For coeff. of static friction = 0.70 (a) plot the ratio F/mg versus theta and (b) determine the theta sub infinite at which the ratio approaches an infinite value. (c) Does lubricating the floor increase or deacrease theta sub infinite or is the value unchanged? (d) what is theta sub infinite if the coefficient = 0.60?

3. Please help me set up the problem! I am very confused and don't comprehend the question. If you can just help me start the problem I can probably take it from here. We are having an emergency study session w/ our class tonight and none of us understand this.

One way to approach understanding this problem is to draw a force diagram and write things in terms of the Forces. For instance the x component of force is balanced out by the weight and the y component of the force times u.

Then rearrange your formula with F/mg = ...?

You can then evaluate this relationship as theta varies and as to how you might vary u.
 

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