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8.3. Find the velocity and acceleration of the center of mass of a system consisting of the following two objects at t = 0 and 1 = 10 s. m, = 2 kg, r, = 28 + 3j + 41°k m, = 4 kg, r, = ri + sj + 6rk

8.3. Find the velocity and acceleration of the center of mass of a system consisting of the following two objects at t = 0 and 1 = 10 s. m, = 2 kg, r, = 28 + 3j + 41°k m, = 4 kg, r, = ri + sj + 6rk

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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Number 8.7 and 8.8 please and 8.3

8.3. Find the velocity and acceleration of the center of mass of a system consisting of the following two objects at t = 0 and 1 = 10 s. m, = 2 kg, r, = 2î + 3j + 41°k m, = 4 kg, r, = 11 + 5j + 62°k %3D 8.4. A projectile of mass m is fired with a velocity of 50 m/s at an angle of 60° with the horizontal. At the top (maximum height), it explodes into two fragments, creating an additional energy E, with the result that one fragment is observed to be moving directly upward. What is the direction of the other fragment? Calculate the velocity of both fragments. 8.5. A projectile of mass M (=m, + m2) is fired with velocity v making an angle 0 with the horizontal. At the top it explodes into two masses, m, and m,, creating an additional energy E. Show that the two fragments strike the ground at a distance apart equal to v sin 0 1 + | 1/2 m, m2
Transcribed Image Text:8.3. Find the velocity and acceleration of the center of mass of a system consisting of the following two objects at t = 0 and 1 = 10 s. m, = 2 kg, r, = 2î + 3j + 41°k m, = 4 kg, r, = 11 + 5j + 62°k %3D 8.4. A projectile of mass m is fired with a velocity of 50 m/s at an angle of 60° with the horizontal. At the top (maximum height), it explodes into two fragments, creating an additional energy E, with the result that one fragment is observed to be moving directly upward. What is the direction of the other fragment? Calculate the velocity of both fragments. 8.5. A projectile of mass M (=m, + m2) is fired with velocity v making an angle 0 with the horizontal. At the top it explodes into two masses, m, and m,, creating an additional energy E. Show that the two fragments strike the ground at a distance apart equal to v sin 0 1 + | 1/2 m, m2
332 System of Particles: Conservation Laws and Collisions Chap. 8 8.6. If a projectile explodes at the top (maximum height) with an additional energy E, under what cir- cumstances will one of the fragments land at the starting position? 8.7. A fire boat draws water from a bay through a vertical inlet and sprays it out at a rate of 10 m/s. The diameter of the nozzle of the fire hose is 20 cm. Calculate the horizontal force from the propellers necessary to keep the boat stationary. The density of water is 1020 kg/m³. 8.8. A bucket of 0.5 kg is placed on a spring scale and water is added to it from a height of 2 m at a rate of 5 ml/s. Find the scale reading as a function of time. 8.9. A chain of length L and mass M is held vertically so that the bottom of the chain just touches the horizontal table top, as shown in Fig. P8.9. If the upper end of the chain is released, determine the force on the table top, as the function of the length of the chain above the table top, while it is falling.
Transcribed Image Text:332 System of Particles: Conservation Laws and Collisions Chap. 8 8.6. If a projectile explodes at the top (maximum height) with an additional energy E, under what cir- cumstances will one of the fragments land at the starting position? 8.7. A fire boat draws water from a bay through a vertical inlet and sprays it out at a rate of 10 m/s. The diameter of the nozzle of the fire hose is 20 cm. Calculate the horizontal force from the propellers necessary to keep the boat stationary. The density of water is 1020 kg/m³. 8.8. A bucket of 0.5 kg is placed on a spring scale and water is added to it from a height of 2 m at a rate of 5 ml/s. Find the scale reading as a function of time. 8.9. A chain of length L and mass M is held vertically so that the bottom of the chain just touches the horizontal table top, as shown in Fig. P8.9. If the upper end of the chain is released, determine the force on the table top, as the function of the length of the chain above the table top, while it is falling.
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