A 15 kg sphere of 20 cm radius and moment of inertia I = 0.500 kgm2 rolls down a slope, starting from rest at a height of 2.0 m above the bottom. The speed of the sphere at the bottom is closest to … (ignore drag and friction!)
A. 1.7 m/s B. 3.3 m/s C. 4.6 m/s D. 5.4 m/s E. 6.3 m/s
Please give some explanation not just an answer. Thank you.
A. 1.7 m/s B. 3.3 m/s C. 4.6 m/s D. 5.4 m/s E. 6.3 m/s
Please give some explanation not just an answer. Thank you.
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KE = PE
1) ½mV² + ½Iw² = mgh
Noting that w = V/R, (1) simplifies to
V² = gh/[½ + I/2mR²] or
V = 4.62 m/s
BTW, the greatest value of I for a 15 kg sphere of .2 m radius is I = (2/3)*15*(0.2)² = 0.4 kg∙m²
1) ½mV² + ½Iw² = mgh
Noting that w = V/R, (1) simplifies to
V² = gh/[½ + I/2mR²] or
V = 4.62 m/s
BTW, the greatest value of I for a 15 kg sphere of .2 m radius is I = (2/3)*15*(0.2)² = 0.4 kg∙m²