A 90 kg astronaut wearing a jet‐black maneuvering suit drifts freely in space

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A 90 kg astronaut wearing a jet‐black maneuvering suit drifts freely in space, initially non-rotating. The astronaut’s moment of inertia about a chosen axis is

I_0 = 25\,\text{kg}\,\text{m}^2

. The astronaut is holding a

2.0\,\text{kg}

tool kit at rest relative to his body, at a distance of

0.80\,\text{m}

from the axis. The tool kit can be approximated as a point mass. The astronaut throws the tool kit tangentially so that it leaves his hand with a speed of

6.0\,\text{m}\!/\!\text{s}

measured in an inertial frame. Assume the throw is completed so quickly that external torques can be neglected. (a) Determine the magnitude of the angular momentum of the tool kit immediately after it leaves the astronaut’s hand, measured about the astronaut’s center of mass. (b) Calculate the astronaut’s resulting angular speed and state the direction of his rotation relative to the throw. (c) After one full revolution, the astronaut decides to stop his rotation by firing small thrusters located at a radius of

0.60\,\text{m}

from the axis. The thrusters produce a constant tangential force of

15\,\text{N}

opposite the astronaut’s motion for

2.0\,\text{s}

. Assuming no other forces act, determine whether the thruster firing duration is sufficient to bring the astronaut to rest. Justify quantitatively.

Related theory

Browse the problem library