An astronaut is performing repairs on the outside of the International Space station. (a) The astronaut needs to remove a nut using a spanner and a torque of 7.0 Nm is required to achieve this. The maximum force that the astronaut can apply is 21 N. (i) In applying this maximum force to the spanner, what two things can the astronaut do to maximise the torque applied to the nut? Explain your answers. (ii) Calculate the minimum length of spanner required to achieve the stated torque using the maximum force. (b) With a final turn of the spanner, a constant angular acceleration of 38 rad s¹ is applied to the nut for 0.40 s. At the end of this time the nut comes free and drifts away, rotating with its final angular speed. The nut can be modelled as a disk of mass M = 17g and radius R = 15 mm, with a moment of inertia given by I=MR². The nut rotates about an axis through its centre and perpendicular to the plane of the disk. (i) Calculate the angular speed of the nut. (ii) Calculate the rotational kinetic energy of the nut. (c) After drifting free, the escaped nut is now in a circular orbit of radius 6.8 x 106 m around the Earth. The only force acting on it is the Earth's gravity. (i) Show that the speed u of the nut in its orbit around the Earth is given by: GmEarth Torbit where mEarth is the mass of the Earth, Torbit is the radius of the orbit, and G is the universal gravitational constant. (ii) Express the rotational kinetic energy of the nut (as calculated in part (b)(ii)) as a percentage of its total kinetic energy.

An astronaut is performing repairs on the outside of the International Space station. (a) The astronaut needs to remove a nut using a spanner and a torque of 7.0 Nm is required to achieve this. The maximum force that the astronaut can apply is 21 N. (i) In applying this maximum force to the spanner, what two things can the astronaut do to maximise the torque applied to the nut? Explain your answers. (ii) Calculate the minimum length of spanner required to achieve the stated torque using the maximum force. (b) With a final turn of the spanner, a constant angular acceleration of 38 rad s¹ is applied to the nut for 0.40 s. At the end of this time the nut comes free and drifts away, rotating with its final angular speed. The nut can be modelled as a disk of mass M = 17g and radius R = 15 mm, with a moment of inertia given by I=MR². The nut rotates about an axis through its centre and perpendicular to the plane of the disk. (i) Calculate the angular speed of the nut. (ii) Calculate the rotational kinetic energy of the nut. (c) After drifting free, the escaped nut is now in a circular orbit of radius 6.8 x 106 m around the Earth. The only force acting on it is the Earth's gravity. (i) Show that the speed u of the nut in its orbit around the Earth is given by: GmEarth Torbit where mEarth is the mass of the Earth, Torbit is the radius of the orbit, and G is the universal gravitational constant. (ii) Express the rotational kinetic energy of the nut (as calculated in part (b)(ii)) as a percentage of its total kinetic energy.