Can anyone help me solve this question?? A small circular object with mass m and

Question

Can anyone help me solve this question??

A small circular object with mass m and radius r has a moment of inertia given by I = cmr2 The object rolls without slipping along the track shown in the figure. The track ends with a ramp of height R = 2.19 111 that launches the object vertically. The object starts from a height H = 5.41 m . To what maximum height will it rise after leaving the ramp if c = 0.221 ? Please include a multiplication sign (*) to indicate that two units are being multiplied. h max = 4.637 [Num] m [Units]

Explanation / Answer

kinetic enrgy of the object KE = 0.5*m*v^2 + 0.5*I*w^2 = 0.5*m*v^2 + 0.5*c*m*r^2*w^2 = 0.5*m*v^2 + 0.5*0.221*m*v^2 (here v = r*w) = 0.6105*m*v^2 when it goes from H to R its potential energy decreases and kinetic enrgy increases KE = m*g*(H-R) 0.6105*m*v^2 = m*g*(H-R) v = sqrt(g*(H-R)/0.6105) = sqrt(9.8*(5.41-2.19)/0.6105) = 7.19 m/s height raised by the ball from R h = v^2/(2*g) = 2.637 m toatl height from ground, hmax = R+h = 2.19 + 2.637 = 4.827 m

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