2007-09-28 02:54:25 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
if you have a pyramid and a cube with the same size base, which one is easier to flip over?
2007-09-28 02:56:06 · update #1
if you have a pyramid and a cube with the same size base, which one is easier to flip over and why?
2007-09-28 02:56:40 · update #2
If we assume that both are of the same height and same material, and if we assume that both are hinged at one bottom base edge, and that the force on the cube is applied at the upper edge diagonally opposite of the bottom hinge while the force on the pyramid is applied at the apex, then it's the pyramid that's easier to knock over. Why? Because for one thing, it has only 1/3 the mass of the cube. Given that the center of mass of the cube is at 1/2 its height and that the center of the mass of the pyramid is at 1/4 its height, and given that the mass of the cube is W and the mass of the pyramid is (1/3)W, then the forces required to lift (tilt) it are W/(2√2) and W/(3√6) respectively. Thus, it's easier to tilt the pyramid.
2007-09-28 03:50:21 · answer #1 · answered by Scythian1950 7 · 1⤊ 0⤋
Hai brennan m,
I presume the heights are also identical.
Then, the cube is easier to flip over.
That's because the center of Gravity of cube will be at an higher elevation compared to pyramid, thus resulting in faster shifting of center of Gravity.
2007-09-28 03:06:04 · answer #2 · answered by WishInvestor 3 · 1⤊ 0⤋
It is not possible to give a correct answer based on given data.
Though bases are equal , their heights could be differ rent, which adds endless possibilities.
Among first 5 answers given above, answerer-5 appears to have better knowledge about 'overall relations of a pyramid' and the basis on which final answer is given is better known to him/her
Considering the pyramid has 'same height' of cube and both said solids are rotated by 45 degrees (towards same side) by keeping base-edges fairly parallel, we can find that...
1) center of gravity of cube is on a vertical plane passing through edge on it stands. A more than 45 degree rotation it fall to its own adjacent face.
2) As regards pyramid, its mass is concentrated towards base of it and so 'center of gravity too'. Therefore more than 45 degree turning is needed to bring center of gravity to a vertical pane and then falling to one of its slant faces!
Conclusion is, for same height cube and pyramids (with equal bases) a cube turns over first, if both solids (of equal gravity) are rotated in same direction (from respective base resting positions and when both bodies rests on a plane)!
Regards
2007-09-28 06:48:24 · answer #3 · answered by kkr 3 · 0⤊ 0⤋
The cube for sure, because it has as much mass at the top as it does at the bottom- making the center of gravity much higher.
If you have a full glass of milk and a glass with just a little milk in it, which one is easier to tip over?
2007-09-28 02:59:04 · answer #4 · answered by Anonymous · 0⤊ 0⤋
The cube...
By the time it is 46 degrees, the center of gravity is not supported by base
(PS, full glass is heavier and harder to knock over ... but both topple at same angle. not the same)
2007-09-28 03:04:02 · answer #5 · answered by wizebloke 7 · 0⤊ 0⤋
A pyramid is lighter but has a lower centre of gravity.
2007-09-28 02:58:46 · answer #6 · answered by Anonymous · 0⤊ 0⤋