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Consider a flatbed truck containing a crane modeled as a long thin rod pivoted at its end. The rod is resting on the cab of the truck as shown while the truck is moving at speed v and suddenly accelerates forward with magnitude a = 5m/s². Assume the rod is L = 2 m long, weights m = 50 kg, and leans at an angle 0 = 60 deg. as shown. ING/O= (v- ¹aG/O = (a Öl sin 0 01 2 Part A: Assuming the inertial reference frame oriented as shown, verify (by showing all interme- diate steps) that the inertial velocity and acceleration of the center of mass point G are: 0²1 2 B O' •B bG sin 0) ²₁+ ( 01 cos 0) 12 Öl cos) ₁ + (cos v a Ö = (Nx sine - Ny cos 0 + N₂ sin 0) 6 ml 8²1 2 sin 0) 2₂ Part B: Using Euler's 2nd Law, show that the equation of motion for the angle of the crane is where N is the magnitude of the horizontal reaction force at B and Rx, Ry are the components of the reaction force at the pin O'. Part C: Consider Euler's 1st Law, along with your previous results, show that the normal force at B is 16.60 N if the crane is at rest ( = 8 = 0). Part D: If the acceleration is sufficiently large, the normal force at B goes to zero and the crane will begin to tip away from the wall of the truck. Show that the acceleration at which this occurs is amax = 5.66 m/s².

Consider a flatbed truck containing a crane modeled as a long thin rod pivoted at its end. The rod is resting on the cab of the truck as shown while the truck is moving at speed v and suddenly accelerates forward with magnitude a = 5m/s². Assume the rod is L = 2 m long, weights m = 50 kg, and leans at an angle 0 = 60 deg. as shown. ING/O= (v- ¹aG/O = (a Öl sin 0 01 2 Part A: Assuming the inertial reference frame oriented as shown, verify (by showing all interme- diate steps) that the inertial velocity and acceleration of the center of mass point G are: 0²1 2 B O' •B bG sin 0) ²₁+ ( 01 cos 0) 12 Öl cos) ₁ + (cos v a Ö = (Nx sine - Ny cos 0 + N₂ sin 0) 6 ml 8²1 2 sin 0) 2₂ Part B: Using Euler's 2nd Law, show that the equation of motion for the angle of the crane is where N is the magnitude of the horizontal reaction force at B and Rx, Ry are the components of the reaction force at the pin O'. Part C: Consider Euler's 1st Law, along with your previous results, show that the normal force at B is 16.60 N if the crane is at rest ( = 8 = 0). Part D: If the acceleration is sufficiently large, the normal force at B goes to zero and the crane will begin to tip away from the wall of the truck. Show that the acceleration at which this occurs is amax = 5.66 m/s².

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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Consider a flatbed truck containing a crane modeled as a long thin rod pivoted at its end. The rod is resting on the cab of the truck as shown while the truck is moving at speed v and suddenly accelerates forward with magnitude a = 5m/s². Assume the rod is L = 2 m long, weights m = 50 kg, and leans at an angle 0 = 60 deg. as shown. ING/O ¹ac/o = (a Öl 2 Ö Part A: Assuming the inertial reference frame oriented as shown, verify (by showing all interme- diate steps) that the inertial velocity and acceleration of the center of mass point G are: = (v ხვე sin 0 ėl 2 0²1 2 •B b₁G (0 'O' sin 0)2₁ + ( 01 2 - cos 0) 12 V a cos)i + (cos-sin) i₂ 12 2 Part B: Using Euler's 2nd Law, show that the equation of motion for the angle of the crane is 6 ml (Nx sine - Ny cos 0 + N₂ sin ) where NB is the magnitude of the horizontal reaction force at B and Ry, Ry are the components of the reaction force at the pin O'. Part C: Consider Euler's 1st Law, along with your previous results, show that the normal force at B is 16.60 N if the crane is at rest (Ö = 0 = 0). Part D: If the acceleration is sufficiently large, the normal force at B goes to zero and the crane will begin to tip away from the wall of the truck. Show that the acceleration at which this occurs is amax = 5.66 m/s².
Transcribed Image Text:Consider a flatbed truck containing a crane modeled as a long thin rod pivoted at its end. The rod is resting on the cab of the truck as shown while the truck is moving at speed v and suddenly accelerates forward with magnitude a = 5m/s². Assume the rod is L = 2 m long, weights m = 50 kg, and leans at an angle 0 = 60 deg. as shown. ING/O ¹ac/o = (a Öl 2 Ö Part A: Assuming the inertial reference frame oriented as shown, verify (by showing all interme- diate steps) that the inertial velocity and acceleration of the center of mass point G are: = (v ხვე sin 0 ėl 2 0²1 2 •B b₁G (0 'O' sin 0)2₁ + ( 01 2 - cos 0) 12 V a cos)i + (cos-sin) i₂ 12 2 Part B: Using Euler's 2nd Law, show that the equation of motion for the angle of the crane is 6 ml (Nx sine - Ny cos 0 + N₂ sin ) where NB is the magnitude of the horizontal reaction force at B and Ry, Ry are the components of the reaction force at the pin O'. Part C: Consider Euler's 1st Law, along with your previous results, show that the normal force at B is 16.60 N if the crane is at rest (Ö = 0 = 0). Part D: If the acceleration is sufficiently large, the normal force at B goes to zero and the crane will begin to tip away from the wall of the truck. Show that the acceleration at which this occurs is amax = 5.66 m/s².
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