A classical mechanics problem by my physics teacher
Mass A is released from a height
on this curved, frictionless curve. Mass A will hit mass B and the two will stick together and continue traveling from left to right up the curve. What will be the maximum height of combined masses A and B on the right side of the curve? If the answer can be written in the form
(simplest form), find
.
The answer is 5.
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1 solution
On conservation of energy we get mgh=(1/2)mv^2 Hence we get velocity of block A at lower most point=(2gh)^1/2 On conservation of linear momentum we get m×(2gh)^1/2=2mv* Hence we get velocity of the combined block as v =((2gh)^1/2)/2 And by once again applying conservation of energy we get 1/2×2m×v ^2=2mgh* Hence h*=(1/4)h Thus Ans=4+1=5