Question

Part A A uniform solid sphere is rolling without slipping along a horizontal surface with a speed of 4.10 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal. What is the speed of the sphere after it has rolled 3.00 m up the ramp, measured along the surface of the ramp? 0+1.37i m/s 0+1.57i m/s 0+0.783i m/s 0+0.979i m/s 0+1.17i m/s Request Answer Submit

Answer 1

here,

for solid sphere

the moment of inertia of solid sphere , I = 0.4 * m * r^2

the initial speed of sphere , u = 4.1 m/s

theta = 25 degree

the length of ramp , s = 3 m

let the final speed of the sphere be v

using conservation of mechanical energy

KEi + PEi = KEf + PEf

(0.5 * m * u^2 + 0.5 * I * w0^2) = (0.5 * m * v^2 + 0.5 * I * w^2) + m * g * s * sin(theta)

(0.5 * m * u^2 + 0.5 * (0.4 * m * r^2) * (u/r)^2) = (0.5 * m * v^2 + 0.5 * (0.4 * m * r^2) * (v/r)^2) + m * g * s * sin(theta)

(0.7 * m * u^2 ) = (0.7 * m * v^2 ) + m * g * s * sin(theta)

(0.7 * u^2 ) = (0.7 * v^2 ) + g * s * sin(theta)

(0.7 * 4.1^2 ) = (0.7 * v^2 ) + 9.81 * 3 * sin(25)

solving for v

v = 0.979 i m/s

the final speed of solid sphere is 0.979 i m/s