A small block of mass m slides down a ramp without friction from point `A\', and
ID: 1338721 • Letter: A
Question
A small block of mass m slides down a ramp without friction from point `A', and then begins to climb a circular loop of radius R. When it reaches point `B' at the top of the loop, it has slowed down just enough so that it just barely loses contact with the track. Determine the kinetic energy of the block when it is at the top of the loop. Enter your symbolic answer as a function of m, g, and R, plus physical constants such as 1.0, 0.5, or . As with all symbolic answers, do not ever include units or unit conversion factors. For example, you might enter:
Answer:
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14. [2pt]
Similarly, symbolically determine the height H required for this to occur.
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Explanation / Answer
At the top of the loop two forces acting are N and mg acting downward
SigmaFr =N+mg =mv2/R
N =mv2/R -mg
at the minimum speed N =0 then v2 =gR
multiplying by (1/2) we get (1/2)mgR =(1/2)mv2
Now the minimum kinetic energy is given by KE =(1/2)mgR
The zero level potential energy is at the bottom of the loop
Ui+Ki =Uf+Kf
ki= 0,ui =mgh,kf =(1/2)mgR and Uf =(1/2)mg(2R)
mgH =(1/2)mgR+mg(2R)
therefore H =5R/2