Calculate Work Needed to Stop Rolling Cylinder

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To calculate the work needed to stop a rolling cylinder, both translational and rotational kinetic energy must be considered. The translational kinetic energy is calculated using the formula 0.5 * mass * velocity^2, resulting in 115 J for the given cylinder. Additionally, the rotational kinetic energy is determined using the moment of inertia and angular velocity, which requires calculating omega and I. The total kinetic energy is the sum of both translational and rotational energies, leading to the correct work needed to stop the cylinder. Thus, the total work required to stop the cylinder is the sum of these two energy components.
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A homogeneous cylinder of radius 30cm and mass 40kg is rolling without slipping along a horizontal floor at 2.4m/s. How much work is needed to stop the cylinder?

work = delta_KE in this case so oi figured .5 *40 * 2.4^2 = 115 J but this is not right, what should i do with the cylinder?
 
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i still can not figure this one out.
 
Besides KE of the center-of-mass moving in translation (linear),
you also have KE of the extended mass moving AROUND the c.o.m.

KE_rotation = 1/2 I (omega)^2
 
i did this and found omega to be 8 rad/s and I to be 1.8 then i found the KE to be 57.6 this is now right either.
 
"Besides" the old linear KE there's now rotational KE, ALSO.
The total KE is the SUM : KE_linear + KE_rotation
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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