Two identical spheres of mass m and radius R are shot vertically with the same kinetic energy K . The first sphere is not spinning about its axis. The second sphere is spinning about its axis at angular frequency ω . What are the maximum heights of each sphere. The acceleration of gravity is g downward.
2007-10-25 17:14:04 · 6 answers · asked by Nik 1 in Science & Mathematics ➔ Physics
I would rather you say how to find the answer than to give me the answer and not tell me which is which
2007-10-25 17:25:13 · update #1
Kinetic Energy (provided by shooting) = Potential Energy + Rotational energy (both at the highest point of the trajectory)
For 1st ball
1/2 * m *v^2 = mgh
h = v^2 / 2g
For 2nd ball
1/2 * m * v^2 = mgh + 1/2 * I * w^2
where I is the moment of inertia of the spherical ball and w is angular velocity.
I for a sphere spinning about its central axis = 2/5 * m * r^2
where r is the radius.
so
1/2 * m * v^2 = mgh + 1/2 * m * r^2 * w^2
( v^2 - r^2.w^2 ) / 2g = h
NOTE of course that h is the height reached by the centre of the balls.
2007-10-25 21:29:58 · answer #1 · answered by gauravragtah 4 · 1⤊ 1⤋
Are ignoring friction from the atmosphere?
Are we reducing the upward force of the second ball by the energy required to spin it?
Are we assuming that the ball has uniform density?
2007-10-25 17:26:15 · answer #2 · answered by Skeptic 7 · 1⤊ 1⤋
2 and 6. I will not say which number is for which sphere.
2007-10-25 17:16:44 · answer #3 · answered by Anonymous · 1⤊ 1⤋
Kinetic skill of sphere at backside = ½*m*v² the skill skill on the precise of the incline is comparable to the KE on the backside.PE = m*g*h mgh = ½m * 4.9² h = 0.5* 24.01/9.8 h = a million.225m the sector will upward thrust to a million.225m
2016-12-18 17:33:56 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Go away! You hurt my head!
2007-10-25 17:17:33 · answer #5 · answered by Bunts 6 · 1⤊ 1⤋
There is no answer
2007-10-25 17:19:03 · answer #6 · answered by Dylan 2 · 1⤊ 1⤋