11. 0/2 points | Previous Answers FRKestenCP1 8.P.064 My Notes Calculate the fin

Question

11. 0/2 points | Previous Answers FRKestenCP1 8.P.064 My Notes Calculate the final speed of a uniform, solid sphere of radius 8 cm and mass 5 kg that starts with a translation a speed of 5 m/s at e o an incline plane at S· g and tilted at an angle of 31° with the horizontal. Assume the sphere rolls without slipping down the ramp. 5.007 A uniform, solid sphere of radius 8 cm and mass 5 kg starts with a translational speed of 5 m/s at the top of an inclined plane of length 4 m tilted at an angle of 31° with the horizontal. The sphere rolls without slipping down the ramp. We can calculate the final speed of the cylinder through conservation of energy. All of the initial gravitational potential energy, translational kinetic energy, and rotational kinetic energy is converted into both rotational kinetic energy and translational kinetic energy. m/s eBook

Explanation / Answer

Here,

let the final speed of the sphere is v

for rolling , v = r * w

Using conservation of energy

change in kinetic energy = decrease in potential energy

m * 9.8 * 4 * sin(31 degree) = final kinetic energy - initial kinetic energy

m * 9.8 * 4 * sin(31 degree) = 0.50 * m * v^2 + 0.50 * 2/5 * m * r^2 * (v/r)^2 - (0.50 * m * 5^2 + 0.50 * 2/5 * m * r^2 * (5/r)^2)

9.8 * 4 * sin(31 degree) = 0.50 * v^2 + 0.50 * 2/5 (v)^2 - (0.50* 5^2 + 0.50 * 2/5* (5)^2)

solving for v

v = 7.34 m/s

the speed of the sphere at the ground is 7.34 m/s

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