Understanding Toy Rocket Physics: A Comprehensive Analysis

The physics behind toy water rockets demonstrates fascinating principles of pressure, force, and acceleration. This detailed examination breaks down the calculations and concepts from an OCR A Level Physics unified exam June 2019 question involving a water-powered toy rocket system.

Definition: A water rocket operates on Newton's Third Law, using pressurized air to expel water, creating thrust that propels the rocket upward.

When analyzing the rocket's initial conditions, we find a 1.5-liter plastic bottle containing 0.30 liters of water and 1.2 liters of trapped air at 17°C. The air is pressurized to 2.4 × 10⁵ Pa before launch. Calculating trapped air moles in toy rocket requires applying the ideal gas equation PV = nRT, where the volume is 1.2 × 10⁻³ m³ and temperature is 290K, yielding 0.12 moles of trapped air.

The pressure dynamics follow Boyle's Law as the water exits. Using P₁V₁ = P₂V₂, we can determine that the final pressure just before water depletion is 1.9 × 10⁵ Pa. This pressure difference between the trapped air and atmosphere creates the thrust necessary for lift-off.

Optimizing Rocket Performance

The relationship between water volume and maximum height achieved presents an interesting optimization problem. Adding more water creates competing effects on the rocket's performance.

Highlight: Increasing initial water volume:

• Maintains the same upward force if pressure remains constant
• Increases total mass, reducing initial acceleration
• Extends thrust duration due to more water expulsion time
• Creates complex trajectory effects

The final height depends on both the rocket's velocity and its position when water depletion occurs. This demonstrates how real-world physics problems often involve multiple interacting variables that make simple predictions challenging.

Page 6: Data Analysis

The final page covers data analysis of gamma radiation absorption through lead sheets.

Highlight: The relationship between detected radiation (N) and lead thickness (d) follows an exponential decay pattern.

Example: Data table showing radiation counts and their natural logarithms with uncertainties.

Definition: The equation N = N₀e⁻ᵘᵈ describes the relationship between radiation intensity and absorber thickness.

Time-Dependent Behavior of Induced EMF in Mechanical Torches

The relationship between time and induced e.m.f. in a mechanical torch follows a distinctive pattern that reflects the physics of the falling magnet. As shown in experimental data, the e.m.f. generated typically spans about 0.2 seconds, corresponding to the time it takes for the magnet to fall through the coil.

The magnitude of the induced e.m.f. varies significantly during the magnet's fall. This variation occurs because the rate of change of magnetic flux through the coil isn't constant - it depends on both the magnet's velocity (which increases due to gravity) and its position relative to the coil. The maximum e.m.f. is generated when the rate of change of magnetic flux is greatest, typically occurring as the magnet passes through the center of the coil.

Understanding this time-dependent behavior is crucial for optimizing the torch's design. The coil's length, number of turns, and the strength of the magnet all affect the induced e.m.f. and consequently the amount of energy stored in the capacitor. Engineers must balance these parameters to create an efficient device that produces sufficient light from a single mechanical action.

Example: When a magnet falls through a coil for 0.2 seconds, it generates a varying e.m.f. that can charge a capacitor enough to power an LED for several seconds.