Finding Speed at Point A for Particle on Curved Runway

AI Thread Summary
To find the speed of the particle at point A, both kinetic and potential energy must be considered, as the particle is projected down a curved runway and reaches a maximum height of 4.00 m at point B. At this maximum height, the final velocity is zero, indicating that the particle momentarily stops before descending. The conservation of energy principle can be applied, equating the kinetic energy at point A to the potential energy at the maximum height. This approach allows for the calculation of the initial velocity needed at point A. Understanding these energy transformations is crucial for solving the problem effectively.
Inertialforce
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Homework Statement


A particle, starting from point A in the drawing, is projected down the curved runway. Upon leaving the runway at point B, the particle is traveling straight upward and reaches a height of 4.00 m above the floor before falling back down. Ignoring friction and air resistance, find the speed of the particle at point A.


http://qaboard.cramster.com/answer-board/image/5b5efcf498963c65f5517ad6687243f2.jpg

Homework Equations





The Attempt at a Solution


My question for this question is that I know I have to use an equation that utilizes both kinetic and potential energy since both kinetic and potential energy values are present (or at least things that you would need to find values). I know that I am trying to find the initial velocity but what is the final velocity? Is it zero because the particle reaches a maximum height and then falls back down?
 
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Hi Inertialforce

Inertialforce said:

Homework Statement


A particle, starting from point A in the drawing, is projected down the curved runway. Upon leaving the runway at point B, the particle is traveling straight upward and reaches a height of 4.00 m above the floor before falling back down. Ignoring friction and air resistance, find the speed of the particle at point A.


http://qaboard.cramster.com/answer-board/image/5b5efcf498963c65f5517ad6687243f2.jpg

Homework Equations





The Attempt at a Solution


My question for this question is that I know I have to use an equation that utilizes both kinetic and potential energy since both kinetic and potential energy values are present (or at least things that you would need to find values). I know that I am trying to find the initial velocity but what is the final velocity? Is it zero because the particle reaches a maximum height and then falls back down?

That's right; the velocity at the point 4m above the floor is zero; if it wasn't zero, that point would not be the maximum height because it would still be moving upwards.
 
Last edited by a moderator:
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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