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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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2. Given a fourbar linkage (not drawn to scale) with the link lengths L₁ = d = 100 mm, L₂ = a = 40 mm, L3= b = 120 mm, L4 = c = 80 mm, 60°, w₂ = 25 rad/s (CCW), a₂ = 15 rad/s² (CCW). Determine graphically, (with considering inertia effects) i) the forces acting on all the links (including the pins) and the couple on link 2. ii) AG3 = 60 mm 04G4 = 40 mm B G₂ 3 m₂ = 0.15 kg m3 = 0.25 kg m4 = 0.5 kg W₂ = 25 2 IG₂ = 50 kg. mm² a₂ = 15 0₁ T₂ IG₂ = 580 kg. mm² IG₁ = 425 kg. mm² OG₂ O₂ I No Freehand Drawing! 3. Four masses m₁, m2, m3 and m4 are 200 kg, 300 kg, 240 kg and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45°, 75⁰ and 135º. Find (a) graphically and (b) analytically, the position and magnitude of the balance mass required, if its radius of rotation is 0.2 m. 4. A four cylinder vertical engine has cranks 150 mm long. The planes of rotation of the first, second and fourth cranks are 400 mm, 200 mm and 200 mm respectively from the third crank and their Page 2 of 3 reciprocating masses are 50 kg, 60 kg and 50 kg respectively. Find the mass of the reciprocating parts for the third cylinder and the relative angular positions of the cranks in order that the engine may be in complete primary balance. 5. A vee-twin engine has the cylinder axes at right angles and the connecting rods operate a common crank. The reciprocating mass per cylinder is 11.5 kg and the crank radius is 75 mm. The length of the connecting rod is 0.3 m. Show that the engine may be balanced for primary forces by means of a revolving balance mass. If the engine speed is 500 r.p.m. What is the value of maximum resultant secondary force ? 6. The turning moment diagram for a petrol engine is drawn to the following scales: Turning moment, 1 mm = 5 N-m ; crank angle, 1 mm = 1°. The turning moment diagram repeats itself at every half revolution of the engine and the areas above and below the mean turning moment line taken in order are 295, 685, 40, 340, 960, 270 mm². The rotating parts are equivalent to a mass of 36 kg at a radius of gyration of 150 mm. Determine the maximum fluctuation of energy when the engine runs at 1800 r.p.m. G (A) در این مقال 295 B 685 C 40 E 340 Crank angle 960 270
Transcribed Image Text:2. Given a fourbar linkage (not drawn to scale) with the link lengths L₁ = d = 100 mm, L₂ = a = 40 mm, L3= b = 120 mm, L4 = c = 80 mm, 60°, w₂ = 25 rad/s (CCW), a₂ = 15 rad/s² (CCW). Determine graphically, (with considering inertia effects) i) the forces acting on all the links (including the pins) and the couple on link 2. ii) AG3 = 60 mm 04G4 = 40 mm B G₂ 3 m₂ = 0.15 kg m3 = 0.25 kg m4 = 0.5 kg W₂ = 25 2 IG₂ = 50 kg. mm² a₂ = 15 0₁ T₂ IG₂ = 580 kg. mm² IG₁ = 425 kg. mm² OG₂ O₂ I No Freehand Drawing! 3. Four masses m₁, m2, m3 and m4 are 200 kg, 300 kg, 240 kg and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45°, 75⁰ and 135º. Find (a) graphically and (b) analytically, the position and magnitude of the balance mass required, if its radius of rotation is 0.2 m. 4. A four cylinder vertical engine has cranks 150 mm long. The planes of rotation of the first, second and fourth cranks are 400 mm, 200 mm and 200 mm respectively from the third crank and their Page 2 of 3 reciprocating masses are 50 kg, 60 kg and 50 kg respectively. Find the mass of the reciprocating parts for the third cylinder and the relative angular positions of the cranks in order that the engine may be in complete primary balance. 5. A vee-twin engine has the cylinder axes at right angles and the connecting rods operate a common crank. The reciprocating mass per cylinder is 11.5 kg and the crank radius is 75 mm. The length of the connecting rod is 0.3 m. Show that the engine may be balanced for primary forces by means of a revolving balance mass. If the engine speed is 500 r.p.m. What is the value of maximum resultant secondary force ? 6. The turning moment diagram for a petrol engine is drawn to the following scales: Turning moment, 1 mm = 5 N-m ; crank angle, 1 mm = 1°. The turning moment diagram repeats itself at every half revolution of the engine and the areas above and below the mean turning moment line taken in order are 295, 685, 40, 340, 960, 270 mm². The rotating parts are equivalent to a mass of 36 kg at a radius of gyration of 150 mm. Determine the maximum fluctuation of energy when the engine runs at 1800 r.p.m. G (A) در این مقال 295 B 685 C 40 E 340 Crank angle 960 270
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