Answer:3.49 m/s
Explanation:
Given
Speed of marble at Bottom [tex]v=4.22 m/s[/tex]
Diameter of loop [tex]d=28.6 cm[/tex]
As Energy is conserved therefore Energy at top is equal to energy at bottom
[tex]E_T=E_B[/tex]
[tex]\frac{mv^2}{2}+mgh=\frac{mv_0^2}{2}[/tex] ,where [tex]v_0[/tex] is the velocity at bottom
[tex]\frac{v^2}{2}+gh=\frac{v_0^2}{2}[/tex]
[tex]v_0^2=v^2+2gh[/tex]
[tex]v^2=v_0^2-2gh[/tex]
[tex]v=\sqrt{v_0^2-2gh}[/tex]
[tex]v=\sqrt{4.22^2-2\times 9.8\times 0.286}[/tex]
[tex]v=\sqrt{17.8084-5.6056}[/tex]
[tex]v=3.49 m/s[/tex]
