How does energy change as a rock falls in a vacuum chamber?

AI Thread Summary
The discussion focuses on calculating the total energy of a falling rock in a vacuum chamber, emphasizing the relationship between gravitational potential energy (Eg) and kinetic energy (Ek) during its fall. The rock, with a mass of 0.5 kg, falls from a height of 78.4 cm over 4 seconds, starting with zero kinetic energy at the top and zero potential energy at the bottom. Participants suggest using kinematic equations to determine the rock's velocity at various points during its descent, which is necessary for calculating energy at 1-second intervals. The conversation highlights the conservation of energy principle, indicating that total energy remains constant throughout the fall. Understanding these concepts is crucial for solving the problem effectively.
vincent142
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Homework Statement


use an imaginary scenario of a falling rock in a tall vacuum chamber. suppose the rock has a mass of 0.5 kg, and it falls from a height of 78.4, the falling time from the top to the bottom of the chamber is 4.0 sec. the kinetic energy of the rock is zero (Ek = 0) at the top of the chamber and the gravitational potential energy of the rock (Eg = 0) at the bottom of the chamber.

h = 78.4 cm
mass = 0.5kg
time= 4 sec

PROVE that Etotal = Eg + Ek during falling time. use 1.0 sec interval to calculate total energy of the rock at different height

Homework Equations



Ek = 1/2 mv^2
Eg = mgh

The Attempt at a Solution



i am not sure how to find velocity... because it changes when it falls down (Accelerates) :S
 
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Use kinematics. You have v_initial, the height, the acceleration, and the time it takes to fall. You've got more than enough information to calculate the final velocity when it reaches the ground and the velocity at any point during its fall.
 
ahh :D
i see i see =p
thanks Snazzy =]
 
they want you to use the formulas for movement with constant acceleration

<br /> x = x_0 + v_0 t + (1/2) a t^2<br />
and
<br /> v = v_0 + a t<br />

to find the height and the velocity at time t, and then use these to calculate the total energy at time t and find out that it is constant.
 
Usually with those you can use the kinematic equations to help solve conservation of energy problems.
 
yup i got it :P
 
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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