Conservation of Momentum initial velocity curved path

AI Thread Summary
The discussion revolves around a physics problem involving conservation of momentum and motion along a curved path. A 1 Kg lump of putty collides with a stationary 4 Kg block on a frictionless track, and the goal is to find the initial speed of the putty given the normal force at a specific point. The user initially struggles with applying the energy equation but eventually realizes that the velocity at the bottom of the arc can be determined using the relationship between normal force, weight, and centripetal acceleration. By correctly applying the equations of motion and momentum, they arrive at the solution of 70 m/s for the initial speed of the putty. The discussion highlights the importance of understanding forces acting on objects in motion along curved paths.
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Homework Statement


The frictionless track is made of a straight horizontal section and a quarter-circle with radius R = 5 m. A 1 Kg lump of putty is thrown toward the stationary 4 Kg block, and the block starts to slide with the putty stuck on it after the collision. If the normal force acting on the block/putty from the track is 98 N at point B, find the initial speed v0 of the putty.

Homework Equations


m1v0=(m1+m2)(vf)
...energy equation?

The Attempt at a Solution


I have been trying to use the energy equation to solve this problem but I am getting nowhere. The answer is 70 m/s. I can't seem to figure out what the velocity would be at the bottom of the arc. According to a(norm)=v^2/R, I found that v=9.8995 but don't know what to do with that...
 

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Well depending on where B is the velocity would be different.

But say B is just at the bottom of the arc, then on the arc the forces acting are the Normal force R and the weight W. The resultant of these two gives mv^2/r

\frac{mv^2}{r}=R-W

so find v from that.

Then put that into the momentum equation.
 
Ok I got it now. Thanks for the help.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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