A large solid sphere rolls without slipping across a horizontal surface, as show
ID: 2199442 • Letter: A
Question
A large solid sphere rolls without slipping across a horizontal surface, as shown. The sphere has a mass of 5.17 kg, and a radius of 0.24 m. The sphere approaches and rolls up the incline without slipping. How far from the right-hand edge of the ramp does the ball land?
A large solid sphere rolls without slipping across a horizontal surface, as shown. The sphere has a mass of 5.17 kg, and a radius of 0.24 m. The sphere approaches and rolls up the incline without slipping. How far from the right - hand edge of the ramp does the ball land?Explanation / Answer
Sphere's Total kinetic energy at the ground= 1/2 * I * w^2 + 1/2 * M * v^2= 1/2 * (2/5 * 5.17*.24^2) * (10/.24 )^ 2 + 1/2 * 5.17 * 10^2= 103.4 + 258.5 = 361.9 J. its PE at the top of the ramp= mgh= 5.17 * 10 * 3 = 155.1 J.......................... hence total KE= 361.9 - 155.1 J = 206.8 J which is divided in rotati0onal and Translational KE. Solve for v since you know the total KE= 206.8 and then once you have v, ...........then 3 = 1/2* 10*t^2 , implies t= 0.77 sec...........Hence distance to the right edge of incline= 0.77 * v
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