- #1
Arixal
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Homework Statement
In the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h1 = 4.5 cm and h2 = 1.00 cm. With what speed must the ball be shot at point P for it to land at d = 3.5 cm?
Homework Equations
E'=E
Translational KE = mv^2/2
Rotational KE = Iω^2/2
y = y0 + v0T + aT^2/2
The Attempt at a Solution
(0.5)mv0^2 = (0.5)mv'^2 + mgh1
Which simplifies to v0 = sqrt(2gh1 + v'^2) (1)
To find v': d = v'T => v' = d/T
To find T: h2 = (0.5)gT^2 => T = sqrt(2h2/2)
So, v' = d/sqrt(2h2/2) which is approximately 0.77 m/s.
Plugging this into (1) v0 = 1.217 m/s.
However, this is not the right answer.
So, I then attempted it again this time taking into account that the moment of inertia of a solid sphere is (2/5)mR^2.
(0.5)(2/5)(mR^2)ω0^2 = (0.5)(2/5)(mR^2)ω'^2 + mgh1
v = rω
(1/5)(mR^2)v0^2/R^2 = (1/5)(mR^2)v'^2/R^2 + mgh1
v0^2 = v'^2 + 5gh1
v0 = sqrt(v'^2 + 5gh1)
Then v' is the same in this attempt as the previous, so v0 = 1.67 m/s.
However, this is also not the right answer.
It appears there is not enough information to take into account energy lost to friction so I'm assuming that's negligible. So, I'm at a loss.