Conservation of Mechanical Energy

AI Thread Summary
A uniform solid ball rolls up a ramp inclined at 19.0 degrees, momentarily stopping after rolling 2.20 m. The initial speed can be calculated using the acceleration derived from gravitational forces and kinematic equations. An alternative approach involves using the conservation of energy, equating the gain in gravitational potential energy to the loss in kinetic energy. Participants confirm that both methods yield the same result, simplifying the problem-solving process. The discussion highlights the effectiveness of different physics principles in solving mechanical energy conservation problems.
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Homework Statement



A uniform solid ball rolls smoothly along a floor, then up a ramp inclined at 19.0 degrees. It momentarily stops when it has rolled 2.20 m along the ramp. What was its initial speed?

Homework Equations



Kinematic Equations
Conservation of Momentum

The Attempt at a Solution



I used a=(5/7)g*sin(theta)

then used V^2 - Vo^2 = 2a(x-xo) and solved for Vo. My answer is correct but I'm wondering if there is another approach to solving this problem?
 
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You can use conservation of energy.

ehild
 
Calculate the vertical height that the ball has gain, that's the gain in Gravitational Potential energy. There will be a equivalent lose of kinetic energy. Equate those them together solve for V.

delzac
 
Ah ok, yes I got the same answer as I did before utilizing the rotational kinetic energy, kinetic energy and potential energy. Not as hard as I was making it out to be.
 
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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