Conservation of Energy problem

AI Thread Summary
The discussion centers on a physics problem involving the conservation of energy and momentum for two blocks, M1 and M2, on a frictionless circular path. The user derived the velocity of block M2 as it exits the circular path using energy conservation, resulting in v(21) = SQRT(2gR). They then applied momentum conservation to find the relationship between the velocities of M1 and M2, ultimately arriving at the equation V2 = M1[SQRT(2gR)]/(M1 + M2). However, there was a discrepancy noted when M1 equals M2, where the expected result is V2 = SQRT(gR). The discussion highlights the importance of correctly applying conservation laws in solving physics problems.
a9211l
Messages
22
Reaction score
0

Homework Statement



If there is a frictionless circular path with radius R cut into a block of mass M1 and a block of mass M2 slides down the path, what is the velocity of mass M2 as it leaves the block?

There is no friction between M1 and the ground.

M2=mass of falling block
M1=mass of
v(21)=velocity of M2 with respect to M1
v(1)=velocity of M1 with respect to the earth
v(2)=velocity of M2 with respect to the earth

Homework Equations



I know that this is a conservation of momentum problem, so I used the equations. E(initial)=E(final) and P(initial)=P(final)

The Attempt at a Solution



By using conservation of energy, I found the velocity of the mass M2 with respect to M1 as it leaves the circular path. Since it falls a distance R, I set

(M2)gR=m[v(21)]^2/2

And found v(21)=SQRT(2gR)

Since the system began with no momentum and momentum must be conserved:

0=(M2)(V2)+(M1)(V1)

What I'm trying to find is V2, I know that V2=V21+V1, so substituting V1=V2-V21 into the momentum equation...

0=(M2)(V2)+(M1)(V2-V21)=(M2)(V2)+(M1)(V2-[SQRT(2gR)])

Now the final answer I got was that V2=M1[SQRT(2gR)]/(M1+M2).

But the answer hint was that if M1=M2, that V2=SQRT(gR) which wasn't what my answer would get.
 
Physics news on Phys.org
just kidding, I got it.
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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}...
Back
Top