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Questions and Answers
What is the speed at which a steel ball hits the ground for the first time when thrown down with a speed of 3.0 m s−1 from a height of 2.0 m, retaining 70% of its energy on each bounce?
What is the speed at which a steel ball hits the ground for the first time when thrown down with a speed of 3.0 m s−1 from a height of 2.0 m, retaining 70% of its energy on each bounce?
Calculate using kinematics and energy conservation.
What is the maximum height a steel ball reaches after the 4th bounce if it retains 70% of its energy on each bounce?
What is the maximum height a steel ball reaches after the 4th bounce if it retains 70% of its energy on each bounce?
Calculate using the energy retention formula.
How long will a fully charged cycle computer last in direct sunlight if it lasts 10 hours at night and receives additional power from a solar panel?
How long will a fully charged cycle computer last in direct sunlight if it lasts 10 hours at night and receives additional power from a solar panel?
Calculate using power consumption ratios.
At what angle would a cyclist lean over if they went round a corner at 15 km h−1, knowing they lean at an angle of 12◦ at 10 km h−1?
At what angle would a cyclist lean over if they went round a corner at 15 km h−1, knowing they lean at an angle of 12◦ at 10 km h−1?
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What is the ratio of the centripetal acceleration of Io and Europa if Europa takes twice as long as Io to complete an orbit?
What is the ratio of the centripetal acceleration of Io and Europa if Europa takes twice as long as Io to complete an orbit?
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What is the largest ratio of masses for which an equal angle condition can occur in an elastic collision?
What is the largest ratio of masses for which an equal angle condition can occur in an elastic collision?
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What is the largest angle of deflection, θ, for a stationary particle of mass m2 in an elastic collision with a moving particle of mass m1?
What is the largest angle of deflection, θ, for a stationary particle of mass m2 in an elastic collision with a moving particle of mass m1?
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Determine the coefficient of friction μ for a body projected up a plane inclined at an angle α, returning with half its initial speed.
Determine the coefficient of friction μ for a body projected up a plane inclined at an angle α, returning with half its initial speed.
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Provide an expression for the force F1 on the area A surrounding the top liquid in a cylinder of n different liquids.
Provide an expression for the force F1 on the area A surrounding the top liquid in a cylinder of n different liquids.
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What expression relates the force F2 on the second liquid down from the top in terms of F1?
What expression relates the force F2 on the second liquid down from the top in terms of F1?
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Calculate the thrust T applied to a rocket of mass 5000 kg with a fuel expulsion rate of 50 kg/s at a speed of 2000 m s−1.
Calculate the thrust T applied to a rocket of mass 5000 kg with a fuel expulsion rate of 50 kg/s at a speed of 2000 m s−1.
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What is the time after launch at which the weight of an astronaut will have appeared to double?
What is the time after launch at which the weight of an astronaut will have appeared to double?
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Find the temperature reached when 2.4% of oil spills out due to heating, given the volume coefficient of expansion.
Find the temperature reached when 2.4% of oil spills out due to heating, given the volume coefficient of expansion.
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Calculate the speed of an aircraft from two bearings and ranges recorded five minutes apart.
Calculate the speed of an aircraft from two bearings and ranges recorded five minutes apart.
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What are the SI base units in which constants a and b are expressed in the gas equation?
What are the SI base units in which constants a and b are expressed in the gas equation?
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Calculate the work done when particle B is brought toward charged particle A until they are in neutral equilibrium.
Calculate the work done when particle B is brought toward charged particle A until they are in neutral equilibrium.
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Determine how long it takes for a capacitor of value 1.0 F to discharge to 1% of its initial value through a varying resistance circuit.
Determine how long it takes for a capacitor of value 1.0 F to discharge to 1% of its initial value through a varying resistance circuit.
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Determine the kinetic energy of an emitted α-particle during the decay of 23892U.
Determine the kinetic energy of an emitted α-particle during the decay of 23892U.
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For what range of incident angles will light emerge from face AC of a prism with refracting angle 75.0◦?
For what range of incident angles will light emerge from face AC of a prism with refracting angle 75.0◦?
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What diameter telescope is needed to resolve two stars separated by 0.00593 light years in a binary star system 2140 light years away?
What diameter telescope is needed to resolve two stars separated by 0.00593 light years in a binary star system 2140 light years away?
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Study Notes
BPhO Round 1 Section 1
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Question 1(a) A steel ball is thrown downwards with an initial velocity of 3.0 m/s from a height of 2.0 m. It retains 70% of its energy on each bounce. Calculate:
- (i) The speed at which the ball hits the ground for the first time.
- (ii) The maximum height reached after the 4th bounce.
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Question 1(b) A cyclist's computer is dual powered and provides energy via battery and solar panel. The solar panel provides 1/3 of the total power consumption while the cyclist is in direct sunlight. Calculate the time a fully charged computer can run in direct sunlight, given that it lasts 10 hours at night (using only battery power).
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Question 1(c) A cyclist leans over at an angle of 12° while cycling around a corner at 10 km/h. Calculate the angle the cyclist must lean over at, when cycling around the same corner at 15 km/h.
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Question 1(d) Io and Europa are moons of Jupiter. Europa takes twice as long as Io to complete an orbit. Determine the ratio of centripetal acceleration of Io to Europa using the given relationship ⍵²r³ = constant (where ⍵ is angular velocity and r is the orbital radius).
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Question 1(e) A particle of mass m₁ and initial speed u collides elastically with a stationary particle of mass m₂. They scatter at equal angles θ either side of the initial direction of m₁. Calculate:
- (i) The maximum ratio of m₁/m₂ for which the equal angle condition is possible.
- (ii) The largest angle of deflection, θ, for m₁ if m₁ = m₂.
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Question 1(f) A body is projected up an incline at an angle α with velocity v. When it returns to the starting point, its speed is half the initial speed. Determine the coefficient of friction, μ, in terms of the angle of the plane.
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Question 1(g) A cylindrical container holds equal volumes of n different liquids, which do not mix and form horizontal layers of height h. The densities of the liquids are 𝜌, 2𝜌, 3𝜌... with the lowest liquid having a density of n𝜌. The curved surface area of the cylinder enclosing each liquid is A. Calculate:
- (i) The force F₁ on the area A surrounding the top liquid.
- (ii) The force F₂ on the area A surrounding the second liquid down from the top, in terms of F₁.
- (iii) The force Fₙ on the area A surrounding the nth liquid at the bottom, in terms of F₁.
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Question 1(h) A rocket of mass mᵣ contains fuel of mass m₀. When ignited, 50 kg of hot gas is expelled downwards each second at a speed of 2000 m/s. Calculate:
- (i) The thrust, T, applied to the rocket.
- (ii) The acceleration of the rocket, a, in terms of its total mass, m, T, and g.
- (iii) The acceleration of the rocket as a function of time, t, in terms of T, g, mᵣ, m₀, and t₀ (total thrust time).
- (iv) The time after launch when an astronaut's apparent weight doubles.
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Question 1(i) A steel drum is completely filled with oil at 5.0°C. On a warmer day, 2.4% of the oil spills out. Calculate the final temperature, given the volume coefficient of expansion of oil is 7.0 × 10⁻⁴ °C⁻¹ and the linear coefficient of expansion of steel is 1.2 × 10⁻⁵ °C⁻¹.
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Question 1(j) An airplane is observed from a tower. Its bearing and range are measured at two different times. Calculate:
- (i) The airplane's speed in m/s.
- (ii) Its bearing and range 10 minutes after the second sighting.
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Question 1(k) A gas follows the equation p(V-b) = nRTexp(-a/nRTV), where:
- p is pressure
- V is volume
- n is the number of moles
- R is the molar gas constant
- a and b are constants
Determine:
- (i) The SI units for a and b.
- (ii) The ideal gas equation approximation when b << V and a << nRTV. Determine the temperature Tₓ in terms of a, b, n, and R.
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Question 1(l) A thin rod is balanced in a smooth hemispherical bowl touching both the interior and rim. The rim of the bowl remains horizontal. Determine the radius of the bowl, r, in terms of the length of the rod, l, and the angle θ.
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Question 1(m) A circuit with three cells, each with an emf of 5.0 V and internal resistance of 5.0 Ω, is connected to three external resistors, each with a resistance of 5.0 Ω. Determine:
- (i) The switch arrangement for maximum current.
- (ii) The switch arrangement for minimum non-zero current.
- (iii) The current in each case.
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Question 1(n) A circuit with four resistors and a switch is analyzed. The current through the 5 kΩ resistor is Io when the switch is open and Ic when it is closed. Determine the ratio of Ic to Io, expressed as a ratio of two integers.
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Question 1(o) The Stefan-Boltzmann law relates the emitted power of a blackbody sphere (P) to its radius (R) and absolute surface temperature (T) as P ∝ R²T⁴. Wien's displacement law states that the peak wavelength 𝜆max of the emitted power spectrum is inversely proportional to the absolute surface temperature. The Sun currently has a peak wavelength of 500 nm. Calculate the new peak wavelength when it becomes a red giant, given its radius and power output increase by 200 and 4000 times respectively.
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Question 1(p) A spectral line in hydrogen is caused by photons with an energy of 2.55 eV. The line is redshifted by 5.4 nm in the spectrum of a distant galaxy. Calculate:
- (i) The wavelength of the photon.
- (ii) The speed of recession of the galaxy.
- (iii) The distance to the galaxy in megaparsecs (Mpc) using the Hubble constant, H₀ = 70 km/s/Mpc.
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Question 1(q) A car with 800 kg mass sinks 1.8 cm when four 80-kg passengers enter. The car is driven on a road with depressions spaced 8.0 m apart. Estimate the speed at which the car's ride becomes very uncomfortable.
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Question 1(r) A pendulum clock is designed to have a period of 1.00 seconds but runs slow by ten minutes each day. Determine the percentage change required in the pendulum's length to correct its timing.
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Question 1(s) A binary star system is 2140 light years away and has two Sun-like stars with an average separation of 0.00593 light years. Determine the diameter of a telescope required to resolve the two stars at a visible wavelength of 550 nm.
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Question 1(t) A glass prism with a refracting angle of 75.0° and refractive index of 1.40 is illuminated by light from air. Determine the range of incident angles for which light emerges from the prism and illustrate your result with a diagram.
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Question 1(u) A charged particle A of mass m and charge Q is suspended by an insulating thread. Another particle B with negligible mass and positive charge +q is brought towards A, resulting in repulsion. When B reaches A's initial position, the system is in equilibrium. Determine the work done in terms of m, g, l, q, Q, and k (where k = 1/4πε₀).
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Question 1(v) A 1.0 F capacitor discharges through a device whose resistance (R) varies linearly with applied voltage (V) according to R = AV + B, where A and B are constants. The device has resistance 10.0 Ω at 6.0 V and 4.0 Ω at 0.06 V. The capacitor is initially charged to 6.0 V. Calculate the time required for the capacitor to discharge to 1% of its initial value.
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Question 1(w) The 238U decays into 234Th and 4He. Calculate the kinetic energy of the emitted α-particle in MeV using the given nuclear masses.
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Description
Test your knowledge of physics with this BPhO Round 1 quiz. It covers topics including energy conservation, power calculations, and motion dynamics. Challenge yourself with a variety of problems related to mechanics and orbital motion.
