A square shaped block of mass travels to the right with velocity on a frctionless table surface. The block has side-length
. The block hits a very small, immovable obstacle on the edge of the table and starts to tip.
The block has moment of inertia
about an axis through its center of mass and perpendicular to its face.
What is the magnitude of angular momentum
of the block with respect to the two reference point shown in the figure? Answer in terms of some or all of the variables , , , and
.
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What is the magnitude of the angular velocity
of the block immediately after the collision?
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Quiz 12, Problem 6 (B)
(1 point possible)
To what maximum height
above the table will the block's center-of-mass rise? Assume the block does not tip over the edge of the table. Answer in terms of , , and
.
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To find the magnitude of angular momentum of the block with respect to the two reference points, we need to consider the moment of inertia of the block and its angular velocity.
Angular momentum (L) is given by the equation L = Iω, where I is the moment of inertia and ω is the angular velocity.
The moment of inertia of a square block rotating about an axis through its center of mass and perpendicular to its face is given by I = (1/6) * m * a^2, where m is the mass of the block and a is the length of its side.
To find the angular velocity immediately after the collision, we need to consider the conservation of angular momentum. Since the block is on a frictionless surface, there are no external torques acting on it, so angular momentum is conserved. Thus, we can use the initial angular momentum equal to the final angular momentum.
The initial angular momentum (L_initial) can be calculated using the initial velocity of the block before hitting the obstacle and the initial moment of inertia.
The final angular momentum (L_final) can be calculated using the final angular velocity and the final moment of inertia.
To calculate the maximum height above the table that the block's center of mass will rise, we need to use conservation of mechanical energy. The initial kinetic energy of the block converts into potential energy as it rises.
The maximum height (h) can be calculated using the formula h = (1/2) * (v^2) / g, where v is the initial velocity of the block before hitting the obstacle and g is acceleration due to gravity.