A small block of mass 2kg initially rests at the bottom of a fixed vertical circular track of radius 1m. A bullet of mass 1 kg strikes the block horizontally with initial speed m/s and remains embedded in the block. Assume no friction between block and circular track. What is the normal force (in N) exerted by track at θ = 60°.

Engineering

Physics

Collision

Circular Motion in Vertical Plane

Question

A small block of mass 2kg initially rests at the bottom of a fixed vertical circular track of radius 1m. A bullet of mass 1 kg strikes the block horizontally with initial speed $v_{0} = \sqrt{990}$ m/s and remains embedded in the block. Assume no friction between block and circular track. What is the normal force (in N) exerted by track at θ = 60°.

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3mv = mv₀

$u = \frac{u_{0}}{3} = \sqrt{110}$

$(1 - \cos θ) = \frac{1}{2} \times (v_{1}^{2} - 110)$

$- 10 \times \frac{1}{2} = \frac{1}{2} (v_{1}^{2} - 110)$

$v_{1}^{2} = 100$

v₁ = 10

$N - 3 mgcos 60 = \frac{3 {mv}^{2}}{R}$

$N = \frac{3 mg}{2} + \frac{3 {mv}^{2}}{R}$

$= \frac{3}{2} \times 10 + \frac{3 \times 1 \times 100}{1} = 315 N$