DP IB Physics: SL

A. Space, time and motion

A.3 Work, Energy and Power

DP IB Physics: SL A. Space, time and motion A.3 Work, Energy and Power Linking questions:
a)	Which other quantities in physics involve rates of change?
b)	How is the equilibrium state of a system, such as the Earth’s atmosphere or a star, determined?
c)	How do travelling waves allow for a transfer of energy without a resultant displacement of matter?
d)	Why is the equation for the change in gravitational potential energy only relevant close to the surface of the Earth, and what happens when moving further away from the surface?
e)	Where do the laws of conservation apply in other areas of physics? (NOS)

a) Which other quantities in physics involve rates of change?
Solution:
The following are other physics quantities that entail rates of change in addition to displacement, velocity, and acceleration:
Velocity:
Rate of change of displacement with respect to time
[math]v = \frac{dx}{dt}[/math]
Acceleration:
Rate of change of velocity with respect to time.
[math]a = \frac{dv}{dt}[/math]
Power:
This has to do with the idea of power, which is the speed at which energy is transferred or work is completed.
[math]P = \frac{dE}{dt}[/math]
Force:
Force, or the rate at which momentum varies, is connected to the rate of change of momentum.
[math]F = \frac{dp}{dt}[/math]
Current:
Electric current, or the flow of electric charge, is connected to the rate of change of electric charge.
[math]I = \frac{dq}{dt}[/math]
Rate of change of magnetic charge:
The idea of induced electromotive force (EMF), or a voltage produced by a fluctuating magnetic field, is connected to the rate of change of the magnetic field.
[math]\varepsilon = -\frac{d\Phi_B}{dt}[/math]
Rates of change are present in many different physical quantities; these are but a few examples. The essential idea is that a rate of change characterizes the relationship between a quantity and another quantity, usually time or some physical variable.
b) How is the equilibrium state of a system, such as the Earth’s atmosphere or a star, determined?
A balance of competing forces or effects determines a system’s equilibrium state. It is the equilibrium between the outward pressure from nuclear fusion and the inward pull of gravity for a star.
It is the equilibrium between gravity and the pressure-gradient force in Earth’s atmosphere. Generally speaking, equilibrium is reached when the system can no longer change.
⇒ Hydrostatic Equilibrium (Stars and Atmospheres):
Stars:
When the outward pressure from nuclear fusion in the core of a star balances the inward pull of gravity, the star is said to be in hydrostatic equilibrium.
The star is kept from collapsing under its own gravity by this pressure, which is produced by the extreme heat and density found in its core.
Earth’s Atmosphere:
Hydrostatic equilibrium also exists in the Earth’s atmosphere. As altitude increases, the air pressure drops, producing an upward force known as the pressure-gradient force.
The downward pull of gravity balances this force, keeping the atmosphere confined to the Earth and preserving the pressure variations with height.
⇒ Thermodynamic Equilibrium:
Closed Systems:
When the system’s entropy reaches a maximum and there is no more energy available to perform productive work, equilibrium is reached in a closed system—one that doesn’t interchange matter or energy with its surroundings.
For instance:
A system in which heat is transferred until every component reaches the same temperature or in which volumes are adjusted until every component is at the same pressure are two examples.
⇒ Chemical Equilibrium:
Reacting Systems:
When the forward and reverse reaction rates in a chemical system are equal, equilibrium is achieved. This indicates that there isn’t a net change in the reactant or product concentrations.
⇒ Open Systems:
Equilibrium of Inputs and Outputs (Earth’s Energy Budget)
When inputs (like incoming solar radiation) and outputs (like outgoing infrared radiation) are equal, open systems—like the Earth’s energy budget—are in a state of balance.
A comparatively steady climate is maintained in part by this equilibrium.
Figure 1 The sun and stellar structure
c) How do travelling waves allow for a transfer of energy without a resultant displacement of matter?
Solution:
By disturbing a medium and causing its particles to fluctuate around their equilibrium locations, travelling waves transmit energy.
Without causing any net movement of the particles themselves, these oscillations create a ripple effect that spreads across the medium by transferring energy from one particle to its neighbor.
Disturbance:
A wave starts when there is a disturbance in a medium, such air, water, or a solid.
Oscillation:
The disturbance causes the medium’s particles to oscillate, or vibrate, about their resting positions.
Energy Transfer:
A neighboring particle receives energy from an oscillating particle, which causes it to begin oscillating as well.
Ripple Effect:
The ripple effect is when energy moves from one particle to another, forming a wave that moves across the medium.
No Net Displacement:
The particles do not follow the wave’s path even if they are moving. They only move in a circular motion around their initial locations.
Wave Form Propagation:
Energy is transported from the source to a new site by the wave form, which is the pattern of crests and troughs, as it moves through the medium.
For instance,
The water particles around a pebble will rise and fall when you toss it into a pond. Energy is transferred by these motions, causing ripples to appear on the water’s surface.
The wave pattern keeps moving outward as the individual water particles return to their starting locations.
Figure 2 Travelling waves for a transfer of energy
d) Why is the equation for the change in gravitational potential energy only relevant close to the surface of the Earth, and what happens when moving further away from the surface?
Solution:
Because the gravitational field intensity is roughly constant across short distances, the conventional equation for gravitational potential energy change (ΔU = mgh) is correct at the Earth’s surface.
Gravitational Field Strength:
The strength of the gravitational attraction at a certain location in space is described by the gravitational field strength.
The force of gravity per unit mass at that location is its definition. In essence, it indicates the weight that an object would have if it were positioned there.
– Near the surface, [math]g = 9.8 m/s^2[/math]
– This works well for small height changes compared to Earth’s radius
[math]g = \frac{GM}{r^2}[/math]
Figure 3 Gravitational field strength
Uniform gravitational field:
A zone with a uniform gravitational field is one in which the gravitational force acting on an item is constant throughout, both in strength and direction.
Consequently, the acceleration caused by gravity, commonly denoted as ‘g’, remains constant throughout.
Because the distances involved are so tiny in relation to the Earth’s radius, the gravitational field is frequently estimated to be uniform at the Earth’s surface.
Figure 4 Uniform gravitational field
The straightforward approach loses accuracy as one gets farther away from Earth. Rather, we apply the gravitational potential energy universal formula:
[math]E_p = -\frac{GMm}{r}[/math]
⇒ Implications at greater distances:
Not simply height, but also the change in distance from Earth’s center determines the change in potential energy as one gets farther away.
Understanding orbital energy, space flight, and satellite motion all depend on this.
e) Where do the laws of conservation apply in other areas of physics? (NOS)
Solution:
Fundamental concepts in physics that are applicable to many fields, such as particle physics, thermodynamics, and electromagnetic, are conservation laws, such as the conservation of energy, momentum, and angular momentum.
According to these rules, even when matter or energy undergoes change, some quantities in a system must stay constant across time.
Conservation rules in particle physics guarantee the preservation of basic quantities during particle interactions, such as charge, baryon number, lepton number, and strangeness. comprehension how subatomic particles behave and interact requires a comprehension of these rules.
Comprehension energy transitions and system behavior in thermodynamics requires a comprehension of the law of conservation of energy.
In a heat engine, for instance, energy is transformed from one form to another (heat to mechanical work), but the system’s overall energy stays constant.
A fundamental concept of electromagnetism is the conservation of charge, which states that the net charge in an isolated system must always be constant.
⇒ Law of conservation of angular momentum:
According to the rule of conservation of angular momentum, a system’s angular momentum stays constant in the absence of any net external torque.
Put more simply, the system’s overall “spin” remains constant if no external forces are twisting it. This implies that a system’s angular velocity, or speed of rotation, will adapt to maintain a constant angular momentum if its moment of inertia, or resistance to rotational change, varies.
Figure 5 Law of conservation of angular momentum