Question

Please answer these two questions, thx.

Astronaut X Astronaut Y 70 60 50 Z 40 30 20 10 Figure 1 Astronaut X Astronaut Y 0.1 0.2 0.3 0.4 Spring Length (m) Figure 2 36. The graph above shows the force exerted by a spring as a function of the length of the spring. A block on a frictionless table is pushed against the spring that is fastened to a wall. The spring is compressed until its length is 20 cm. The block is then released. Which of the following values is closest to the kinetic energy with which the block leaves the spring? 35. Two astronauts are connected by a taut cable and are initially at rest with respect to a nearby space station. Astronaut X throws a large container to Astronaut Y. Figure I above shows the astronauts immediately after the container is thrown by Astronaut X, and Figure 2 shows the astronauts immediately after the container is caught by Astronaut Y. Which of the following describes the motion of Astronaut Y in Figures 1 and 2? (A) 3J (B) 6J (C) 12J (D) 151 Eigure 2 Moves to the right Moves to the right Does not move Eigure I (A) Does not move (B) Moves to the left (C) Does not move (D) Moves to the leftDoes not move

Answer 1

35. For an isolated system, as the external force is zero, the center of mass cannot accelerate. Hence in any situation, it will remain in it's initial state of motion. As our system is at rest initially, it's center of mass is also at rest. Finally, in figure 2, when astronaut Y catches the container, everything should be at rest again. So in figure 2, Y does not move. In figure 1, when the container is thrown to the right, both astronauts have to move towards the left such that the center of mass remains at the same point. Hence D is the correct answer.

36. Force is zero for a spring when it is at it's natural length (zero displacement). Hence natural length is 0.3 m (from graph). Reducing the length to 0.2 m amounts to a displacement x = 0.1 m. Work done is equal to area under F-x curve. Which is a triangle here.

W = (1/2)Fx = (1/2) x 60 x 0.1 = 3 J