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# webct7 - astronaut 1 An astronaut of mass M = 100...

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astronaut 1. An astronaut of mass M = 100 kg (including all equipment) who was having a space walk suddenly finds out that the cable that was supposed to keep her safely attached to the spaceship is broken. The distance between the astronaut and the spaceship is d = 12 m and their relative velocity is zero. She realizes that she needs to be back in no more than 2 minutes because her air supply is running short. She grabs the heaviest of the tools in her belt (1500 g) and throws it in the direction opposite to where the spaceship is. At what minimum speed does she need to throw the tool in order to make it safely to the spaceship? The minimum speed required for the astronaut to reach the spaceship in 2 min is 12 m 0.1 m/s 60 s 2 min 1 min d v t = = = When the astronaut throws the tool in the direction opposite to where the spaceship is, since there are no external forces acting on her in the space, s he will move towards the spaceship with some constant speed because of conservation of linear momentum. Initial momentum: 0 (astronaut and tool at rest) Final momentum: astronaut astronaut tool tool M v m v Conservation of linear momentum: astronaut astronaut astronaut tool tool tool astronaut tool 0 M M v m v v v m = = Since the speed of the astronaut should be at least 0.1 m/s, astronaut tool astronaut tool 100 1.5 (0.1 m/s) 6.57 m/s 1.5 M v v m = =

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CM 1. Find the position of the center of mass for the following systems. System 1: Three pointlike masses. a = 2.0 cm. Enter x CM , in cm. CM (1 kg)0 (2 kg)2 (3 kg)3 13 4.3 cm 6 kg 6 a a x a + + = = = 2. Enter y CM for system 1, in cm. All the masses have y = 0 , so y CM = 0. 3. System 2: Three pointlike masses. a = 2.0 cm.
Enter x CM , in cm. CM (1 kg)0 (2 kg)0 (3 kg)2 6 2 cm 6 kg 6 a x a + + = = = 4. Enter y CM for system 2, in cm. CM (1 kg) (2 kg)0 (3 kg)0 1 0.33 cm 6 kg 6 a y a + + = = = 5. System 3: Three identical uniform rectangles of sides a and b and mass m forming a U. a = 2 cm, b = 10 cm.

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