Level 1 - Physics Paper 1

A delivery drone travels horizontally at \(11.0\,\mathrm{m\,s^{-1}}\) when it releases a \(0.750\,\mathrm{kg}\) instrument package. The release point is \(28.0\,\mathrm{m}\) above level ground. Air resistance is negligible until the package reaches a foam capture pad.

A calibration flywheel has moment of inertia \(0.620\,\mathrm{kg\,m^2}\) about its axle. A light cord is wrapped around a drum of radius \(0.180\,\mathrm{m}\) fixed to the flywheel. A technician pulls the free end of the cord with a constant force of \(24.0\,\mathrm{N}\). A bearing friction torque of magnitude \(1.10\,\mathrm{N\,m}\) opposes the rotation.

A laboratory rig uses a stretched string and a diffraction grating in the same alignment test. The string has length \(0.640\,\mathrm{m}\), is fixed at both ends, and has linear density \(2.40\times10^{-3}\,\mathrm{kg\,m^{-1}}\). Its fundamental resonance is \(220\,\mathrm{Hz}\). A laser of wavelength \(532\,\mathrm{nm}\) is incident normally on a grating with \(500\,\mathrm{lines\,mm^{-1}}\). A screen is \(1.80\,\mathrm{m}\) from the grating.

A floating environmental buoy contains a vertical spring-mass accelerometer. The oscillating sensor mass is \(0.450\,\mathrm{kg}\), the spring constant is \(18.0\,\mathrm{N\,m^{-1}}\), and the linear damping coefficient is \(0.180\,\mathrm{kg\,s^{-1}}\). After a wave passes, the sensor is displaced by \(0.0600\,\mathrm{m}\) from equilibrium and released from rest. The complete buoy, including the sensor, has mass \(3.65\,\mathrm{kg}\) and a vertical cylindrical hull of cross-sectional area \(3.00\times10^{-2}\,\mathrm{m^2}\). The damping rate is \[ \beta=\frac{b}{2m} \] and the damped angular frequency is \[ \omega_d=\sqrt{\omega_0^2-\beta^2}. \] For underdamped motion, the amplitude envelope is \[ A(t)=A_0e^{-\beta t}. \]