1. calculate it\'s translational speed when it reaches the bottom. 2. calculate

Question

1. calculate it's translational speed when it reaches the bottom. 2. calculate its rotational speed when it reaches the bottom 3. what is the ratio of translational to rotational kinetic energy at the bottom? -Does your answer in part 1 depend on mass or radius of ball? does your answer in part 2 depend on mass or radius of ball? does your answer in part 3 depend on mass or radius of ball? Secure https://sess.on.masteringphysics.com/ Homework 8. Chapter 10.11 Problem 10.73 Problem 10.73 A sphere of radius ro = 25.0 cm and mass m = 1.20kg starts from rest and rolls without slipping down a 40.0 incline that is 14.0 m long.

Explanation / Answer

using law of conservation of energy

energy at the top = energy at the bottom

m*g*H = (0.5*m*v^2)+(0.5*I*w^2)

I is the moment of inertia = (2/5)*m*R^2

w = v/R

then

m*g*H = (0.5*m*v^2) + (0.5*(2/5)*m*R^2*(v/R)^2)

m cancels

g*H = (0.5*v^2) + (0.2*v^2) = 0.7*v^2

but H = L*sin(theta) = L*sin(40)

then

g*L*sin(40) = 0.7*v^2

v = sqrt(g*L*sin(40)/0.7) = sqrt(9.8*14*sin(40)/0.7) = 11.22 m/sec is the translational speed at the bottom

2) rotational speed is w = v/R = 11.22/0.25 = 44.88 rad/s

3) KE _trasn /KE_rot = (0.5*m*v^2)/(0.5*I*w^2) = (0.5*m*v^2)/(0.5*(2/5)*m*R^2*(v/R)^2) = (0.5*m*v^2)/0.2*m*v^2) = 2.5

No,answer in part1) ,part 2) and part 3) does not depend on mass or radius of the ball

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