Fera Academy

Paper 1

Time2 hours

Marks60

SetSet 3

PaperLevel 1 - Physics Paper 1

Information

Section A: Mechanics
Section B: Waves and Optics
Section C: Oscillations and Collisions, Conservation and Fields

Candidate name

Candidate number

Instructions

Attempt all questions.
All main questions carry the same number of marks.
Show enough working to make the model, assumptions, and sign conventions clear.
Begin each main question on a new page when working on paper.
Use the constants printed in this paper where relevant.
Answer spaces are provided after each question part.

Constants

Gravitational acceleration	\( g=9.81\,\mathrm{m\,s^{-2}} \)
Speed of light	\( c=3.00\times10^8\,\mathrm{m\,s^{-1}} \)
Elementary charge	\( e=1.60\times10^{-19}\,\mathrm{C} \)
Electron mass	\( m_e=9.11\times10^{-31}\,\mathrm{kg} \)
Planck constant	\( h=6.63\times10^{-34}\,\mathrm{J\,s} \)
Permittivity of free space	\( \epsilon_0=8.85\times10^{-12}\,\mathrm{F\,m^{-1}} \)
Magnetic constant	\( \mu_0=1.26\times10^{-6}\,\mathrm{N\,A^{-2}} \)
Boltzmann constant	\( k_B=1.38\times10^{-23}\,\mathrm{J\,K^{-1}} \)

Section A: Mechanics

1. Spring-bumper carts and a rough patch

[15 marks]

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) Find the common speed immediately after the catch engages, and find the impulse delivered to cart \(B\) during the collision.

[4 marks]

b) The spring bumper has stiffness \(720\,\mathrm{N\,m^{-1}}\). Estimate its maximum compression, assuming negligible energy loss before maximum compression.

[4 marks]

c) The linked carts leave the rough patch at \(1.60\,\mathrm{m\,s^{-1}}\). Use work-energy to infer the coefficient of kinetic friction on the patch.

[4 marks]

d) After the patch, the carts move onto a rubber stopping strip with coefficient of kinetic friction \(0.360\). Find the additional stopping distance.

[3 marks]

2. Off-axis support cable and inspection boom

[15 marks]

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) Use torque equilibrium about the hinge to find the cable tension.

[4 marks]

b) Find the three components of the hinge force and its magnitude.

[4 marks]

c) The cable is suddenly cut. Calculate the angular acceleration of the boom immediately after release.

[4 marks]

d) Explain why the angular acceleration and hinge force do not remain equal to their initial-release values as the boom falls.

[3 marks]

Section B: Waves and Optics

3. Spectrometer slit, lens, and grating checks

[15 marks]

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) With no grating in place, a lens of focal length \(0.750\,\mathrm{m}\) forms the far-field diffraction pattern in its focal plane. The central maximum is \(3.80\,\mathrm{mm}\) wide. Find the slit width.

[4 marks]

b) The slit is then used as an object for a \(12.0\,\mathrm{cm}\) focal-length lens. The slit is \(30.0\,\mathrm{cm}\) from the lens and its illuminated height is \(1.50\,\mathrm{mm}\). Find the image distance and image height.

[4 marks]

c) A \(600\,\mathrm{lines\,mm^{-1}}\) grating is inserted. Check whether an observed first-order angle of \(18.7^\circ\) is consistent with \(532\,\mathrm{nm}\) light, and find the second-order angle.

[4 marks]

d) If the source is changed to \(650\,\mathrm{nm}\) red light without changing the apparatus, find the new central maximum width and first-order grating angle. Comment on the scaling.

[3 marks]

Section C: Oscillations and Collisions, Conservation and Fields

4. Damped spring sensor in a fluid

[15 marks]

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 \[ A(t)=A_0e^{-\beta t}. \]

a) Find the damped oscillation frequency of the sensor.

[3 marks]

b) The probe is displaced and released with initial envelope amplitude \(18.0\,\mathrm{mm}\). Find the envelope amplitude after four complete oscillations.

[4 marks]

c) Estimate the mechanical energy lost to the fluid over those four oscillations.

[3 marks]

d) Find the volume of fluid displaced by the submerged probe.

[2 marks]

e) When the probe is immersed, its static spring extension is \(62.0\,\mathrm{mm}\) smaller than in air. Infer the fluid density.

[3 marks]

END