With two fingers, you hold an ice cream cone motionless upside down, as shown in

Question

With two fingers, you hold an ice cream cone motionless upside down, as shown in Fig. 2.28. The mass of the cone is m, and the coefficient of static friction between your fingers and the cone is mu, when viewed from the side, the angle of the tip is 2 theta. What is the minimum normal force you must apply with each finger in order to hold up the cone? In terms of theta, what is the minimum value of mu that allows you to hold up the cone? Assume that you can supply as large a normal force as needed.

Explanation / Answer

The forces along X cancel out.

The total force along y will be:

2 u F cos(theta) = mg + 2 F sin(theta)

F = mg/2[u cos(theta) - sin(theta)]

for the value of u:

2(u cos(theta) - sin(theta)) = 0

u = sin(theta)/cos(theta) = tan(theta)

Hence, u = tan(theta)

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