AQA Physics: Conservation Laws - Mechanics 3

Flashcards covering the fundamentals of work, energy, power, and momentum conservation based on the Mechanics 3 lecture transcript.

How is work done calculated when a force acts at an angle to the direction of motion?

$W = Fs \cos(\theta)$ where $\theta$ is the angle between the force ($F$) direction and the displacement ($s$) direction.

What does the area under a force-displacement graph represent?

The work done.

State the Principle of Conservation of Energy.

The total energy in an isolated system always remains constant. Energy is not created nor destroyed, just transferred from one store to another.

What are the formulas for kinetic energy ($E_k$) and the change in gravitational potential energy ($\Delta E_p$)?

$E_k = \frac{1}{2}mv^2$ and $\Delta E_p = mg\Delta h$.

Define power in terms of energy transfer and in terms of force and velocity.

$P = \frac{\Delta W}{\Delta t}$ (rate of energy transfer) and $P = Fv$ (for an object moving at velocity $v$ in the direction of force $F$).

What is the formula for efficiency?

$\text{efficiency} = \frac{\text{useful output power}}{\text{input power}}$ (or energy), often expressed as a percentage.

How much energy is contained in one kilowatt-hour ($kWh$)?

$1\,kWh = 3.6 \times 10^6\,J$.

Define linear momentum and state its units.

Momentum is the product of mass and velocity ($p = mv$). Its units are $kg\,ms^{-1}$.

How is force defined in terms of momentum?

Force is the rate of change of momentum: $F = \frac{\Delta p}{\Delta t}$.

What is impulse and how is it related to a force-time graph?

Impulse is the change in momentum ($Impulse = F\Delta t = \Delta mv$), and it is equal to the area under a force-time graph.

State the Principle of Conservation of Momentum.

The total momentum of an isolated system is constant ($\sum mv_{\text{before}} = \sum mv_{\text{after}}$).

How do safety features like crumple zones or airbags reduce injury?

They increase the collision time ($\Delta t$) over which the change in momentum occurs, which reduces the resultant force ($F$) experienced ($F = \frac{\Delta p}{\Delta t}$).

What defines an elastic collision?

A collision in which both total momentum and total kinetic energy are conserved.

What is the difference between inelastic and super-elastic collisions?

In an inelastic collision, total kinetic energy is reduced (transferred to heat/sound/deformation); in a super-elastic collision, total kinetic energy is increased.

In an elastic collision between two equal masses where one is initially stationary, what happens after impact?

The first mass comes to a complete rest ($v_1 = 0$) and the second mass moves off with the initial velocity of the first ($v_2 = u$).

What is the relationship between Newton’s Third Law and momentum conservation?

Every action has an equal and opposite reaction; the change in momentum of object A will be equal and opposite to the change in momentum of object B, meaning the total change in momentum of the system is zero.