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Crupler22
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thanksHello and thanks to anyone in advance. So I have this physics project that me and a partner have to do. We are suposed to construct a lab for the situation he gives us. Ours is: a dart hits a block hanging on a string which causes it to reach a max height. So we are suposed to figure out the initial velocity of the dart by finding the height it reached. So I started writing an equation. It goes like this:
I first used the momentum equation.
m1v1 + m2v2= (m1+m2)v3 -so the blocks not moving so you can take the second part out.
m1v1=(m1+m2)v3 - divided both sides by (m1+m2) to get v3 alone, so
m1v1
-------- = v3
(m1+m2)
Then science all the energy is sent in a circular path I substatuted v3 into the Centripital Force equation. Fc=(mv^2)/r so
mass that's rotating-->(m1+m2) * ((m1v1)/(m1+m2))^2r so stuff cancels, and I get:
(m1v1)^2/(m1+m2)r
k so that's force so now I figure since its traveling a distance its work (W=F*D)
D is going to be the arc length of the circular path that it takes, so its (Theta* r)
W= (m1^2)(v1^2)
---------------- * theta r = W so the r's cancel
(m1+m2)r
and then I realize all this kenetic energy that is done when its at its top height is equal to the potenial energy. so
(m1+m2)gh = (m1^2)(v1^2)
--------------- *Theta
(m1+m2)
so then I solve for V1 which is the inital velocity of the dart.
v1 = srq( (m1+m2)^2gh
------------------
m1^2 * theta )
But my teacher said that he never saw that before and said there is an easier way which I know now. But is this right?
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