SACE STAGE 2 PHYSICS - TOPIC 1 - Motion and Relativity - worded questions

Explain qualitatively that the maximum range occurs at a launch angle of 45 degrees for projectiles that land at the same height from which they were launched.

At 45 degrees, the horizontal and vertical components of velocity are equal. This results in the greatest horizontal displacement.

Describe the relationship between launch angles that result in the same range.

When a projectile is launched from the ground, two angles that add up to 90 degrees will result in the same range.

Describe and explain the effect of launch height, speed, and angle on the time of flight, maximum height, and the maximum range of a projectile.

Assuming that velocity and launch angle are kept constant, as launch height increases, the distance the projectile falls increase, this results in the time of flight of the projectile to increase and hence the maximum range of the projectile increases.

If launch height and launch angle are kept constant, then as the initial launch velocity of a projectile is increase, then both the time of flight and maximum range of a projectile increases. This is because the vertical component of velocity is increases, and hence the time of flight of the projectile is increases. Additionally, the horizontal component of velocity is increased, and therefore, both of these factors, leads to an increases maximum range of the projectile.

As launch height increases, the launch angle required for maximum range decreases. A smaller launch angle results in a larger component of horizontal velocity when the projectile reaches its original launch height, therefore range is increases as it has more time ti fall at this faster horizontal velocity. The higher the launch height, the smaller the angle required to achieve maximum range of a projectile

Explain the effects of speed, cross-sectional area of the body, and density of the medium on the drag force on a moving body.

Drag force is proportional to speed (v) squared. Bodies moving faster are more affected by the drag force.

Increasing the cross-sectional area of a body increases the number of collisions that air particles have with a body, these air particles apply a drag force opposite the motion of the body. Therefore, increasing cross sectional area increases drag force on the body.

Increasing the density of a medium increases the number of collisions that body has with the medium, the particles in the medium apply a drag force opposite the motion of the body. Therefore, increasing density increases drag force on the body.

Explain that terminal velocity occurs when the magnitude of the drag force results in zero net force on the moving body.

Terminal velocity occurs when the force due to drag and the force due to gravity are balanced, therefore there is no net force acting on the body, which means that the body can no longer accelerate and hence has reached its fastest speed, known as terminal velocity.

Describe situations (such as skydiving and the maximum speed of racing cars) where terminal velocity is achieved.

When a skydiver jumps out of a plane, the force due to gravity pulls them towards Earth, drag force opposes the motion of the sky diver and applied a drag force upwards. As the skydiver falls, it is accelerated towards earth and speeds up. As the skydiver speeds up, the drag force acting on them increases. Eventually the skydiver reaches its maximum speed (terminal velocity) where they will no longer accelerate as the force due to gravity and the force due to drag are balanced, resulting in a zero net force and hence, constant terminal velocity

Racing cars also reach a kind of terminal velocity. As a car accelerates, the engine’s thrust increases its speed until the aerodynamic drag, rolling resistance, and frictional forces grow large enough to counterbalance the engine power. Once these forces are equal, the car can no longer accelerate further, and it achieves a maximum constant speed. This balance of forces determines the top speed that the car can sustain under specific racing conditions.

Describe and explain the effects of air resistance on the vertical and horizontal components of the velocity, maximum height, and range of a projectile.

Air resistance causes a drag force that is applied opposite the motion of a body and therefore decreases both the horizontal and vertical components of velocity. If this is an angled launch, this will reduce the maximum height reached because drag force will cause the body to decelerate reducing the vertical component of velocity and hence, reduce the time of flight and maximum height it can reach. Air resistance will reduce the range of a projectile as range is proportional to horizontal component of velocity and time of flight. As explained above, air resistance causes a drag force that is applied opposite the motion of a body and therefore decreases both the horizontal and vertical components of velocity. As both horizontal and vertical components are reduced and proportional to range, range will be reduced.

Describe and explain the effects of air resistance on the time for a projectile to reach the maximum height or to fall from the maximum height.

As a projectile is reaching its maximum height, the drag force due to air resistance acts opposite the motion of the projectile causing the projectile to reach its maximum height in a smaller time interval.

On the way down, air resistance is now acting upwards, opposing the motion of the projectile. This actually increases the time taken to descend from its maximum height. However, because the time of flight was reduced on the way up, this still results in an overall, reduced time of flight.

Use the conservation of momentum to describe and explain the change in momentum and acceleration of spacecraft due to the emission of gas particles or ionised particles.

Before emitting gas particles, the momentum of the spacecraft system is zero. As the particles are ejected downwards, in order for momentum to be conserved, the momentum of the system is upwards. This means that the change in momentum of the spacecraft is upwards. A change in momentum causes a force to be applied upwards (write equation), this force causes an acceleration, as F = ma, therefore, the emission of particles has causes the spacecraft to accelerate.

Use the conservation of momentum to describe and explain how the reflection of particles of light (photons) can be used to accelerate a solar sail.

Before reflecting photons, the momentum of the solar sail system is zero. As the photons are reflected this causes a change in momentum of the photons, in order for momentum to be conserved, the momentum of the solar sails must act opposite the reflection of the photons. This change in momentum causes a force to be applied (write equation), this force causes an acceleration, as F = ma, therefore, the reflection of photons has causes the solar sail to accelerate.

Explain how a banked curve reduces the reliance on friction to provide centripetal acceleration

A banked curve splits the normal force acting on a vehicle (due to gravity) to be split into a horizontal and a vertical component. The horizontal component of normal force acts towards the centre of the vehicle’s path, this causes a centripetal force that causes centripetal acceleration. This centripetal acceleration causes the vehicle to undergo uniform circular motion (or constant speed in a circular path), thus reducing a vehicle’s reliance on friction.

Explain that the gravitational forces are consistent with Newton’s Third Law.

Newton’s third law states that every action force has an equal in magnitude but opposite in direction reaction force applied. For example, gravitational forces are consistent because the Earth applies a gravitational force on the moon, and the moon applies a gravitational force on the Earth that is equal in magnitude but opposite in direction.

Explain why the centres of the circular orbits of Earth satellites must coincide with the centre of the Earth.

In order for a satellite to orbit Earth, it needs a centripetal force to cause uniform circular motion. The gravitational force acting between the Earth and a satellite acts between the centres of the two masses. Therefore, the satellites must coincide with the centre of the Earth in order for the Earth’s gravitational force to causes the centripetal force on the satellite necessary for centripetal acceleration, and hence, uniform circular motion.

Explain that the speed, and hence the period, of a satellite moving in a circular orbit depends only on the radius of the orbit and the mass of the central body (m₂) about which the satellite is orbiting and not on the mass of the satellite.

Set Gravitational force equal to Centripetal force.

Use Kepler’s first two laws to solve problems involving the motion of comets, planets, moons, and other satellites.

Kepler’s first law is that the planets etc. orbit in an elliptical orbit with the sun at one focus of the ellipse.

Kepler’s second law is that the line joining a planet to the sun sweeps out equal areas in equal amounts of time. This means that when a planet is closer to the sun it will travel faster because it will be travelling a longer distance in the same amount of time as v = s/t. (I would draw an image too).

Explain why a satellite in a geostationary orbit must have an orbit in the Earth’s equatorial plane, with a relatively large radius and in the same direction as the Earth’s rotation.

In order for a geostationary satellite to be stationary above Earth’s surface it must be located high above the equator in order for the Earth to have a period of one day to match the Earth’s period and the satellite must also rotate from west to east to match the rotation of the Earth.

Explain the differences between polar, geostationary, and equatorial orbits. Justify the use of each orbit for different applications.

Polar Orbit: A polar orbit has a path that passes near the Earth’s poles, allowing the satellite to cover nearly every part of the globe as the planet rotates beneath it. This orbit is especially useful for Earth observation, remote sensing, and environmental monitoring since it provides comprehensive, high-resolution imaging of the entire planet over time.

Geostationary Orbit: In a geostationary orbit, a satellite circles Earth at an altitude of about 35,786 kilometers directly above the equator, matching Earth’s rotation so it appears stationary over one spot. This constant positioning makes it ideal for telecommunications, broadcasting, and weather monitoring, as it can provide uninterrupted coverage to a specific region.

Equatorial Orbit: An equatorial orbit lies in the plane of the Earth’s equator, ensuring that the satellite's path remains close to equatorial regions. While a circular equatorial orbit can be geostationary, other forms may be elliptical, providing focused coverage ideal for regional communications or specialized scientific missions that study equatorial phenomena.

Explain the effects of time dilation on objects moving at relativistic speeds.

Time dilation is the effect where time appears to pass more slowly for an object moving at relativistic speeds compared to an observer at rest. Explanation: According to Einstein's theory of Special Relativity, as an object approaches the speed of light, the passage of time slows down for it relative to a stationary observer. This means that a moving clock ticks more slowly than one at rest (from the perspective of the observer). Example: If an astronaut travels in a spaceship at 90% the speed of light and returns to Earth, less time will have passed for the astronaut than for people on Earth.

Explain the effects of length contraction on objects moving at relativistic speeds.

Length contraction is the effect where an object moving at relativistic speeds appears shorter in the direction of motion to a stationary observer. Explanation: To someone watching from rest, the length of the moving object appears contracted (compressed) along the direction it’s travelling. The faster the object moves, the more contracted it looks. Example: A spaceship moving close to the speed of light would appear shorter in length (front to back) to an observer on Earth than it would to someone on board the spaceship.

Newtons two postulates of special relativity.

1. That the speed of light in a vacuum is an absolute constant

2. That the laws of physics are the same in all inertial reference frames

Kepler’s First Law – The Law of Ellipses

"The orbit of a planet is an ellipse with the Sun at one of the two foci."

• This means planets don’t orbit in perfect circles but in oval-shaped paths.

• The Sun isn't in the center of the orbit—it's off to one side, at a focus of the ellipse.

Kepler’s Second Law – The Law of Equal Areas

"A line joining a planet and the Sun sweeps out equal areas in equal intervals of time."

• This means a planet moves faster when it's closer to the Sun and slower when it's farther away.

• So, the planet covers the same area of space in the same amount of time, no matter where it is in its orbit.

Kepler’s Third Law – The Law of Harmonies

"The square of a planet’s orbital period (T²) is proportional to the cube of the semi-major axis of its orbit (R³)."

• Mathematically:

  T2∝R3T^2 \propto R^3T2∝R3

  or

  T2R3=constant\frac{T^2}{R^3} = \text{constant}R3T2​=constant

• TTT is the time it takes for a planet to complete one orbit (in Earth years), and RRR is the average distance from the Sun (in Astronomical Units, AU).

• This law shows that the farther a planet is from the Sun, the longer it takes to orbit it.

Newton’s First Law – Law of Inertia

"An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by a net external force."

• In simple terms:
  Things won’t start, stop, or change direction unless something forces them to.

• Example: A soccer ball won’t move unless you kick it. Once kicked, it keeps rolling until friction or a wall stops it.

Newton’s Second Law – Law of Force and Acceleration

"The acceleration of an object depends on the net force acting on it and its mass."

• Mathematically:

  F=maF = maF=ma

  Where:
  FFF = Force (in newtons)
  mmm = Mass (in kg)
  aaa = Acceleration (in m/s²)

• Bigger force = more acceleration.
  Bigger mass = slower acceleration (if the same force is applied).

• Example: It's harder to push a heavy wheelbarrow than a light one.

Newton’s Third Law – Action and Reaction

"For every action, there is an equal and opposite reaction."

• Forces always come in pairs.

• Example: When you jump, your legs push down on the ground (action), and the ground pushes you up (reaction).

Explain that, in the absence of air resistance, the horizontal component of the velocity is constant.

Air resistance is due to collisions with air particles which apply a force opposite to the motion of an object. Therefore, when air resistance is neglected there is no force acting on the horizontal component of velocity, therefore making it constant.