Anyone? Amarble of mass m 624g and radius r- 21 Acm rolls without slipping along

Question

Anyone? Amarble of mass m 624g and radius r- 21 Acm rolls without slipping along the looped rough track of figure below. The loop has a radius of R m 2.03m. is the minimum value of homeasured from the bottom edge of the marble, not the center) ifthe marble is to reach the highest What point of the loop without leaving the track? submit Ail Answers Last Answer: 5,697 m Answer: tries 2/5 Incorrect Hint: The radius of the marble is not negligible relative to the curved track radius, so you need to consider that the marble center of mass is not at the track radius in expressions for gravitational potential energy and centripetal acceleration!

Explanation / Answer

minimum speed at the top of the loop, u = sqrt(g*R)

= sqrt(9.8*2.03)

= 4.46 m/s

let h is the height needed above the top of the loop.

Apply enrgy conservation

m*g*h = 0.5*m*u^2 + 0.5*I*w^2

m*g*h = 0.5*m*u^2 + 0.5*(2/5)*m*r^2*w^2

m*g*h = 0.5*m*u^2 + 0.2*m*v1^2

m*g*h = 0.7*m*u^2

h = 0.7*u^2/g

= 0.7*4.46^2/9.8

= 1.42 m

so H = h + 2*R

= 1.42 + 2*2.03

= 5.48 m from ground <<<<<<<<<<<<<<<------Answer

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