## Step 1: Identify the formula for the capillary force When two fibers are held together by a liquid drop, the force required to pull them apart is determined by the surface tension force at the contact line. For a cylindrical fiber with radius \( r \), the capillary force contributed by each fiber is: \[ F = 2 \pi r \sigma \cos\theta \] where: - \( \sigma \) = surface tension of the glue - \( r \) = fiber radius - \( \theta \) = contact angle **Explanation:** This formula gives the force per fiber due to surface tension acting at the contact line, resolved along the axis pulling the fibers apart. --- ## Step 2: Plug in the values and calculate the force Given: - \( r \) (fiber radius) - \( R = 3r \) (drop radius, not needed for the force since force is determined at the contact line) - \( \sigma = 30 \) mN/m \( = .030 \) N/m - \( \theta = \pi/6 \) - \( \cos(\pi/6) = \sqrt{3}/2 \) Plug in: \[ F = 2 \pi r \sigma \cos\theta = 2 \pi r \times .030 \times \frac{\sqrt{3}}{2} \] \[ F = \pi r \times .030 \times \sqrt{3} \] **Explanation:** This is the force needed to separate the fibers, expressed in terms of the fiber radius \( r \). --- ## **Final Answer** \[ \boxed{F = .030 \pi r \sqrt{3}} \] Where \( r \) is the fiber radius (in meters). If you want a numerical answer, insert the value of \( r \) in meters.