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V W = h cc BY UBC Engineering A 1.4 m by 1.4 m thin plate is used as target practice at a firing range where participants are shooting for sport. If the plate has a mass of mplate = 16 kg and is pinned at point O, determine the angular velocity of the plate just after a 5 g bullet, shot at a velocity of Ubullet = 480, is embedded in it. The bullet hits a vertical distance h = 1.05 m away from point O. m 8 rad

V W = h cc BY UBC Engineering A 1.4 m by 1.4 m thin plate is used as target practice at a firing range where participants are shooting for sport. If the plate has a mass of mplate = 16 kg and is pinned at point O, determine the angular velocity of the plate just after a 5 g bullet, shot at a velocity of Ubullet = 480, is embedded in it. The bullet hits a vertical distance h = 1.05 m away from point O. m 8 rad

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Target Plate Angular Velocity Calculation In this scenario, a 1.4 m by 1.4 m thin plate is used as a target practice at a firing range where participants are engaged in a shooting sport. The given parameters for this problem are as follows: - Mass of the plate (\( m_{plate} \)): 16 kg - The plate is pinned at point \( O \) - A 5 g bullet is shot at the plate - The velocity of the bullet (\( v_{bullet} \)): 480 m/s - The bullet hits the plate at a vertical distance \( h \): 1.05 m away from point \( O \) Given these details, the task is to determine the angular velocity (\( \omega \)) of the plate just after the bullet, which embeds itself in the plate upon impact. ### Diagram Explanation The accompanying diagram depicts: 1. The thin plate of dimensions 1.4 m by 1.4 m, which is suspended and can rotate around point \( O \). 2. A bullet approaching the plate with velocity \( v \), intending to hit a point vertically distant \( h \) from point \( O \). ### Calculation Task The goal is to find the angular velocity (\( \omega \)) of the plate after it is hit by the bullet. The formula for angular velocity (\( \omega \)) in radians per second (rad/s) should be determined based on the given conditions and constraints. ### Note To solve this problem practically, one would use the principles of conservation of angular momentum or impulse-momentum theorem, taking into consideration the combined inertia of the plate and the bullet after impact. Finally, solve for: \[ \omega = \frac{\text{no answer provided in image}}{\text{rad/s}} \] #### Source This educational scenario is adapted from UBC Engineering resources.
Transcribed Image Text:### Target Plate Angular Velocity Calculation In this scenario, a 1.4 m by 1.4 m thin plate is used as a target practice at a firing range where participants are engaged in a shooting sport. The given parameters for this problem are as follows: - Mass of the plate (\( m_{plate} \)): 16 kg - The plate is pinned at point \( O \) - A 5 g bullet is shot at the plate - The velocity of the bullet (\( v_{bullet} \)): 480 m/s - The bullet hits the plate at a vertical distance \( h \): 1.05 m away from point \( O \) Given these details, the task is to determine the angular velocity (\( \omega \)) of the plate just after the bullet, which embeds itself in the plate upon impact. ### Diagram Explanation The accompanying diagram depicts: 1. The thin plate of dimensions 1.4 m by 1.4 m, which is suspended and can rotate around point \( O \). 2. A bullet approaching the plate with velocity \( v \), intending to hit a point vertically distant \( h \) from point \( O \). ### Calculation Task The goal is to find the angular velocity (\( \omega \)) of the plate after it is hit by the bullet. The formula for angular velocity (\( \omega \)) in radians per second (rad/s) should be determined based on the given conditions and constraints. ### Note To solve this problem practically, one would use the principles of conservation of angular momentum or impulse-momentum theorem, taking into consideration the combined inertia of the plate and the bullet after impact. Finally, solve for: \[ \omega = \frac{\text{no answer provided in image}}{\text{rad/s}} \] #### Source This educational scenario is adapted from UBC Engineering resources.
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