Static friction of a block on an incline?

In summary, we were dealing with a block on an incline that could be altered by changing the angle. We found that the critical angle at which the block just begins to slide can be used to write an equation for the coefficient of static friction. In this equation, the coefficient is equal to the tangent of the angle at which the block begins to slide. This is derived from the equation Fs=μ*n, where n is the normal force and μ is the coefficient of static friction. We also found that the maximum frictional force is equal to the product of the coefficient of static friction and the normal force, and that if there is no sliding, the frictional force must be less than or equal to the maximum frictional force.
  • #1
Tim Wellens
20
0

Homework Statement


We are dealing with a block on an incline that you can alter the angle with.

The inclination angle was increased until we reached a certain angle(critical angle) that the block just begins to slide at. Use this critical angle and your previous answers for the normal force and frictional force at rest to write an equation for the coefficient of static friction. Equation should be in terms of the angle when the block begins to slide and if needed other measurable quantities.

Homework Equations


F=ma[/B]

The Attempt at a Solution


I figured out for the normal force of this block at an inclination at rest, the equation would be n=mgcos(θ)I think that the magnitude of the frictional force of this block at an inclination at rest (in terms of m, g, and theta), would be Fs=tan(θ)(mgcos(θ). I got this from the equation Fs=μ*n. We had already found what n would be, so I inputted that. The question wants it in terms of theta, so I think the coefficent of static friction would have to be tan(θ). So, I believe the magnitude of the friction force would be Fs=tan(θ)(mgcos(θ)). But I'm not positive.So, writing an equation for the coefficient of static friction for the point of inclination when the block just begins to slide, using this angle... I think the equation would be... μ=F/N > μ= tanθ(mgcosθ)/mgcosθ. If the mgcosθ cancel.. we would be left with μ= tanθ. But I'm just not sure if this is correct with what the question is looking for and if my previous equations make sense?
 
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  • #2
Hi Tim, I think you did just fine. Your explanation is taking a few shortcuts (where the ##\tan\theta## comes from isn't made explicit) but you get the benefit of the doubt from me. Up to you to guess if teacher will be equally benevolent ...

Note that ##F_{s,{\rm max}} = \mu N##. If there is no sliding then ##F_{s} \le \mu N##.
 

Related to Static friction of a block on an incline?

1. What is static friction?

Static friction is the force that prevents two surfaces from sliding against each other when there is no relative motion between them. It is the resistance force that acts in the opposite direction of the applied force.

2. How is static friction different from kinetic friction?

Static friction occurs when there is no relative motion between two surfaces, while kinetic friction occurs when there is relative motion between two surfaces. Kinetic friction is typically smaller than static friction.

3. How is the static friction of a block on an incline calculated?

The static friction force is equal to the coefficient of static friction multiplied by the normal force, which is the force perpendicular to the surface of contact. In the case of a block on an incline, the normal force is equal to the weight of the block multiplied by the cosine of the angle of the incline.

4. What factors affect the static friction of a block on an incline?

The coefficient of static friction, the weight of the block, and the angle of the incline are the main factors that affect the static friction of a block on an incline. Other factors such as the surface roughness and the presence of any lubricants can also affect the value of static friction.

5. How can the static friction of a block on an incline be minimized?

The static friction of a block on an incline can be minimized by decreasing the coefficient of static friction, reducing the weight of the block, or decreasing the angle of the incline. Additionally, using a lubricant between the surfaces can also help reduce the static friction force.

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