What is the critical value of mu_s in this static friction problem?

In summary, the conversation discusses a problem involving a woman pushing a box up a ramp with coefficients of friction. The critical value of mu_s is calculated using the maximum value of mu_s and the equations involving F, N, and acceleration. The equations are solved to obtain the value of mu_s.
  • #1
Lalo1985
3
0
Hi, I'm having trouble solving this problem:

A woman attempts to push a box of books that has mass up a ramp inclined at an angle (alpha) above the horizontal. The coefficients of friction between the ramp and the box are (mu_k) and (mu_s). The force F applied by the woman is horizontal.

If (mu_s) is greater than some critical value, the woman cannot start the box moving up the ramp no matter how hard she pushes. Calculate this critical value of (mu_s).

I know that the maximum value of mu_s is f_mu/N. So, using F(y) = ma(y), I got: N - F*Gcos(alpha) - F*Gsin(alpha) = 0. Therefore, making N = F*Gcos(alpha) + F*Gsin(alpha). That's it. I don't know what to do next. Any ideas?
 
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  • #2
You have to resolve F in two directions: parallel to the incline and perpendicular to it. This will give you two equations, both involving F and one involving the normal reaction N, friction force f and acceleration a. Since the mass (of books) does not move up or down the incline, the acceleration a = 0. So this problem reduces to

[tex]\sum F_{x} = 0[/tex]

[tex]\sum F_{y} = 0[/tex]

where x and y are the directions parallel and perpendicular to the incline.

You should get the following equations as a result

[tex]F\cos\alpha - mg\sin\alpha - f_{s} = 0[/tex]
[tex]N - mg\cos\alpha - F\sin\alpha = 0[/tex]

Solve them to get the value of [tex]\mu_{s}[/tex] using the fact that [tex]f_{s} = \mu_{s}N[/tex].

Hope that helps...

Cheers
Vivek

EDIT--The above equations are valid iff F is applied in the horizontal direction (i.e. in a direction parallel to the base of the incline).
 
Last edited:
  • #3


To solve this problem, we can use the concept of static friction and its relationship with the coefficient of friction. When an object is at rest, the force of static friction is equal to the applied force, up to a maximum value determined by the coefficient of friction. In this case, the applied force is the horizontal force F applied by the woman, and the maximum value of static friction is mu_s*N, where N is the normal force exerted by the ramp on the box.

To find the critical value of mu_s, we need to determine the maximum value of N. From the free body diagram, we can see that the normal force N is equal to the weight of the box, which is given by m*g, where m is the mass of the box and g is the acceleration due to gravity.

Therefore, the maximum value of N is m*g. Substituting this into our equation for N, we get:

m*g = F*Gcos(alpha) + F*Gsin(alpha)

Now, we can solve for the critical value of mu_s by rearranging the equation:

mu_s = (m*g - F*Gcos(alpha)) / (F*Gsin(alpha))

This is the critical value of mu_s that the woman cannot exceed in order to start the box moving up the ramp. Any value of mu_s greater than this will result in the box remaining at rest.

I hope this helps you solve the problem. Remember to always carefully consider the forces acting on an object and their relationships in order to solve physics problems. Good luck!
 

1. What is static friction?

Static friction is the force that prevents an object from moving when a force is applied to it. It occurs between two surfaces that are in contact with each other and are not moving relative to one another.

2. How is static friction different from kinetic friction?

Static friction occurs when two surfaces are not moving relative to each other, while kinetic friction occurs when two surfaces are moving relative to each other. The force of static friction is usually greater than the force of kinetic friction.

3. What factors affect the strength of static friction?

The strength of static friction is affected by the mass of the object, the roughness of the surfaces, and the normal force exerted on the object. Additionally, the coefficient of static friction, which is a measure of the roughness of the surfaces, also plays a role in determining the strength of static friction.

4. How is the coefficient of static friction determined?

The coefficient of static friction can be determined experimentally by measuring the maximum force required to move an object across a surface, divided by the normal force exerted on the object. It can also be calculated by dividing the force of static friction by the normal force.

5. How can the problem of static friction be overcome?

The problem of static friction can be overcome by increasing the applied force or by decreasing the coefficient of static friction. This can be achieved by using lubricants or by changing the materials of the surfaces in contact. Additionally, reducing the mass of the object can also help reduce the strength of static friction.

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