A damp washcloth is hung over the edge of a table to dry. Thus, part (mass = mon) of the washcloth rests on the table and part (mass = moff) does not. The coefficient of static friction between the table and the washcloth is 0.350. Determine the maximum fraction [moff/(mon + moff)] that can hang over the edge without causing the whole washcloth to slide off the table
How did you get 1.35?
thank you!
To determine the maximum fraction [moff/(mon + moff)] that can hang over the edge without causing the whole washcloth to slide off the table, we need to consider the forces acting on the washcloth.
1. The weight of the washcloth acts vertically downward, and it can be broken down into two components:
- The vertical component, which contributes to the normal force between the washcloth and the table.
- The horizontal component, which contributes to the force pushing the washcloth towards the edge of the table.
2. The static frictional force between the washcloth and the table acts in the opposite direction of the horizontal component of the weight. The magnitude of this frictional force can be determined using the equation:
F_static = coefficient of static friction * normal force
3. For the washcloth to remain in static equilibrium (not slide off the table), the frictional force must balance the horizontal component of the weight acting on the hanging part of the washcloth.
Now let's proceed with the calculations:
Let's assume the length of the washcloth hanging over the table is L, and the total length of the washcloth is L_total.
The hanging part of the washcloth has a weight of moff * g, where g is the acceleration due to gravity, and the normal force is mon * g (since the hanging part doesn't contribute to the normal force).
The horizontal component of the weight is (moff * g * sinθ), where θ is the angle between the vertical weight vector and the table.
The static frictional force (F_static) must balance this horizontal component of the weight:
F_static = moff * g * sinθ
Since F_static = coefficient of static friction * normal force, we can substitute these values:
coefficient of static friction * mon * g = moff * g * sinθ
Now, sinθ = (L / L_total), as the washcloth hangs over the edge.
coefficient of static friction * mon * g = moff * g * (L / L_total)
The g term cancels out, and we can rearrange the equation to solve for the maximum fraction [moff/(mon + moff)]:
coefficient of static friction * mon = (L / L_total)
[moff/(mon + moff)] = L / (coefficient of static friction * L_total)
So, to determine the maximum fraction, we need to know the length of the hanging part (L) and the total length of the washcloth (L_total), as well as the coefficient of static friction between the washcloth and the table.
friction force=masson*.350g
force pulling=mass0ff*g
forcepulling=frictionforce
moff*g=.350Mon*g
so massoff=.350mon
so the fraction must be massoff/(mon+moff)
= .350mo/(mo*1.35)=.35/1.35
check that.