A block of mass M travels over a frictionless horizontal surface at 3.00 m/s. Th

Question

A block of mass M travels over a frictionless horizontal surface at 3.00 m/s. The block encounters frictionless incline as shown in Figure below. What vertical distance up the incline does the block travel before coming momentarily to rest? Suppose a solid sphere of identical mass is rolling without slipping a rough surface and encounters a rough incline. If the velocity of the center of mass of the sphere is the same as that of the block how far up the incline does it roll? Determine the acceleration of the block and sphere objects if the angle is 20 Degree and kinetics' friction coefficient Mu =.25.

Explanation / Answer

Initial potential Energy = Final Potential Energy
1/2*mv^2 = m*g*h
h = (1/2*3^3)/9.8 m
h = 1.38 m

Rotational Kinetic Energy = 1/2*I*w^2
Rotational Kinetic Energy = 1/2 * 2/5 * m*r^2 * v^2/r^2
Rotational Kinetic Energy = 1/5 *m*v^2

Rotational Kinetic Energy + Kinetic Energy = Final Potential Energy
1/5 * mv^2 + 1/2*mv^2 = m*g*h
1/2*3.0^2 + 1/2 * 3.0^2 = 9.8*h
h = 0.918 m

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