Physics
21.12.2021 04:49
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A480n sphere 40.0cm in radius rolls without slipping 1200cm down a ramp that is

A480n sphere 40.0cm in radius rolls without slipping 1200cm down a ramp that is inclined at 53 0 with the horizontal. what is the angular speed of the sphere at the bottom of the slope if it starts from rest?
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kianakilbourn8
kianakilbourn8
5,0(16 marks)

As we know that sphere roll without slipping so there is no loss of energy in this case

so here we can say that total energy is conserved

Initial Kinetic energy + initial potential energy = final kinetic energy + final potential energy

\frac{1}{2}mv_i^2 + mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2+ mgh'

as we know that ball start from rest

v_i = 0

height of the ball initially is given as

h = Lsin\theta

h = 1200sin53 = 960 cm

also we know that

I = \frac{2}{5}mR^2

also for pure rolling

v = r\omega

also we know that

480 = m*9.8

m = 49 kg

now plug in all data in above equation

480*9.60 + 0 = \frac{1}{2}*49*(0.40*\omega)^2 + \frac{1}{2}*\frac{2}{5}*49*(0.40)^2\omega^2 + 0

4608 = 3.92\omega^2 + 1.568\omega^2

\omega^2 = 839.65

\omega = 29 rad/s

So speed at the bottom of the inclined plane will be 29 rad/s

tinajackson6534
tinajackson6534
4,6(10 marks)
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