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ira [324]
3 years ago
14

A solid sphere has a radius of 0.200 m and a mass of 150.0 kg. how much work is required to get the sphere rolling with an angul

ar speed of 50.0 rad/s on a horizontal surface? assume that the sphere starts from rest and rolls without slipping.
Physics
1 answer:
Allisa [31]3 years ago
7 0

Here in this case we can use work energy theorem

As per work energy theorem

Work done by all forces = Change in kinetic Energy of the object

Total kinetic energy of the solid sphere is ZERO initially as it is given at rest.

Final total kinetic energy is sum of rotational kinetic energy and translational kinetic energy

KE = \frac{1}{2}Iw^2 +\frac{1}{2} mv^2

also we know that

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

w= \frac{v}{R}

Now kinetic energy is given by

KE = \frac{1}{2}(\frac{2}{5}mR^2)w^2 +\frac{1}{2} m(Rw)^2

KE = \frac{1}{5}mR^2w^2 +\frac{1}{2} mR^2w^2

KE = \frac{7}{10}mR^2w^2

KE = \frac{7}{10}*150*(0.200)^2(50)^2

KE = 10500 J

Now by work energy theorem

Work done = 10500 - 0 = 10500 J

So in the above case work done on sphere is 10500 J

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Master of physics needed
Delicious77 [7]
Hey JayDilla, I get 1/3.  Here's how:
Kinetic energy due to linear motion is:
E_{linear}= \frac{1}{2}mv^2
where
v=r \omega
giving
E_{linear}= \frac{1}{2}mr^2 \omega ^2

The rotational part requires the moment of inertia of a solid cylinder
I_{cyl} =  \frac{1}{2}mr^2
Then the rotational kinetic energy is
E_{rot}= \frac{1}{2}I \omega ^2= \frac{1}{4}mr^2 \omega ^2
Adding the two types of energy and factoring out common terms gives
\frac{1}{2}mr^2 \omega ^2(1+ \frac{1}{2})
Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part.  Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.

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The angular acceleration of a rotating object is given by
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