Level 1 - Physics Paper 1

On a level test track, cart \(A\) of mass \(1.80\,\mathrm{kg}\) moves to the right at \(4.00\,\mathrm{m\,s^{-1}}\). It runs into cart \(B\), of mass \(1.20\,\mathrm{kg}\), which is initially at rest. A spring bumper between the carts compresses during the impact, and a catch then holds the carts together. The collision time is short enough that external horizontal impulses can be neglected. The linked carts then enter a rough patch of track of length \(0.800\,\mathrm{m}\).

A uniform inspection boom of length \(3.00\,\mathrm{m}\) and mass \(18.0\,\mathrm{kg}\) is hinged to a wall and held horizontal. A \(10.0\,\mathrm{kg}\) camera module is fixed \(2.40\,\mathrm{m}\) from the hinge. A cable is attached \(2.20\,\mathrm{m}\) from the hinge. The cable is \(50.0^\circ\) above the horizontal boom, and its horizontal projection is \(20.0^\circ\) sideways from the boom, so the cable force is not in the boom's vertical plane.

A teaching spectrometer uses a narrow adjustable slit, a thin converging lens, and a removable diffraction grating. Green laser light of wavelength \(532\,\mathrm{nm}\) is normally incident on the slit unless stated otherwise.

A fluid-density sensor consists of a \(0.850\,\mathrm{kg}\) probe on a vertical spring of constant \(34.0\,\mathrm{N\,m^{-1}}\). In a test fluid the motion is lightly damped, with damping coefficient \(b=0.680\,\mathrm{kg\,s^{-1}}\). The probe is a sealed cylinder of diameter \(42.0\,\mathrm{mm}\) and length \(180\,\mathrm{mm}\), fully submerged during measurement. 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 \[ A(t)=A_0e^{-\beta t}. \]