2. A box with sides of length 2 m slides along a smooth horizontal floor at speed 4 m/s and strikes a low-lying "curb' about which it could flip over. The radius of gyration about the cube's center-of-gravity is 3 m. Determine the angular speed of the box immediately after striking the curb.
2. A box with sides of length 2 m slides along a smooth horizontal floor at speed 4 m/s and strikes a low-lying "curb' about which it could flip over. The radius of gyration about the cube's center-of-gravity is 3 m. Determine the angular speed of the box immediately after striking the curb.
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Question
Transcribed Image Text:**Problem 2: Angular Speed Calculation of a Box**
A box with sides of length 2 m slides along a smooth horizontal floor at a speed of 4 m/s and strikes a low-lying ‘curb’ about which it could potentially flip over. The radius of gyration about the cube's center of gravity is 3 m. Determine the angular speed of the box immediately after striking the curb.
**Explanation of Diagram/Equations:**
In the lower right corner, a small mathematical notation appears which likely represents an equation used to solve for the angular speed (\(\omega\)). The notation includes terms for variables like mass (m) and length (l) of the box, as well as possibly incorporating the radius of gyration and linear speed. The details of the equation have been cut off in the image, making a precise transcription of the equation not fully visible.
Expert Solution
Step 1
We can use conservation of energy :
As the particle move then the kinetic energy it gain = 1/2 m v2 = 1/2 m 42
= 1/2m16 J=8m J.
As falls down the curb and it attains rotational kinetic energy = 1/2 I 2 after it flip over the curb.
This energy must be equal to 8m J. by conservation of energy.
hence we write that 1/2 I 2= 8m
( Moment of inertia of box of length l and of mass m about one side
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