Title: InkPhysics / Mechanics
On every note of this deck, unless a note says otherwise:
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Front: RECALL
State the effect of air resistance on a projectile.
Back: It lowers the maximum height, shortens the range and makes the descent steeper than the ascent.

Front: RECALL
State what the area under an acceleration-time graph represents.
Back: The change in velocity.

Front: DEFINITION
Define: Power.
Back: The rate of doing work, equivalently the rate of energy transfer: P = ΔW/Δt.

Front: RECALL
State how P = Fv is derived from W = Fs.
Back: Divide the work done by the time taken: P = W/t = Fs/t, and s/t is the speed v.

Front: RECALL
State where the centre of mass of a uniform regular solid lies.
Back: It lies at the geometric centre of the solid.

Front: RECALL
State the condition at a vehicle's maximum speed.
Back: The driving force equals the total resistive force, so the resultant force and the acceleration are zero.

Front: RECALL
Explain where the constant-acceleration condition enters the SUVAT derivation.
Back: At the step that sets the average velocity equal to ½(u + v). That is true only while the velocity climbs at a steady rate, which is why the four fail the moment the acceleration varies.

Front: DEFINITION
Define: Describe how to find the centre of gravity of an irregular lamina.
Back: Hang it freely from a hole near the edge, hang a plumb line from the same pin and rule the line it marks; repeat from a second hole. The centre of gravity is where the lines cross.

Front: DEFINITION
Define: Newton's second law.
Back: The resultant force on an object equals the rate of change of its momentum; for constant mass this becomes F = ma.

Front: RECALL
State what a balance measures.
Back: It compares the object with standard masses, so it reads mass and gives the same result anywhere.

Front: RECALL
State the condition for equilibrium of coplanar forces at a point.
Back: The resultant force is zero: drawn tip to tail, the forces form a closed triangle.

Front: DEFINITION
Define: Work.
Back: Energy transferred by a force: the force multiplied by the distance moved in the direction of the force, W = Fs cos θ.

Front: DEFINITION
Define: Centre of mass.
Back: The single point at which the whole mass of an object can be taken to be concentrated.

Front: SPOT THE ERROR
Say what is wrong with this claim: When something stops, its momentum simply vanishes.
Back: Momentum does not vanish when something stops; it is transferred to another body. Momentum is conserved: only an external force can change the total momentum of a system.

Front: RECALL
State how the kinetic energy formula is derived.
Back: W = Fs with F = ma gives W = mas; v^2 = u^2 + 2as starting from rest makes as = ½v^2, so the work done is ½mv^2.

Front: DEFINITION
Define: Efficiency.
Back: The ratio of useful output power (or energy) to total input power (or energy); it can never exceed 1.

Front: EQUATION · NOT ON THE DATA SHEET
Momentum:
p = ?\(p = \, ?\)p = ?
Back: p = mv\(p = mv\)p = mv

Front: DEFINITION
Define: Weight.
Back: The gravitational force acting on an object's mass: W = mg, a vector.

Front: SPOT THE ERROR
Say what is wrong with this claim: SUVAT always works.
Back: The SUVAT equations are derived assuming constant acceleration, so that is the only place they apply. When acceleration varies, the graphs still work: gradient and area never stop being true.

Front: DEFINITION
Define: Couple.
Back: A pair of equal and opposite coplanar forces whose lines of action do not coincide.

Front: RECALL
State what the area under a force-displacement graph represents.
Back: The work done by the force, valid however the force varies.

Front: DEFINITION
Define: Terminal speed.
Back: The constant speed a falling object reaches when the resistive forces have grown to equal its weight.

Front: RECALL
State the components of a vector F at angle θ to an axis.
Back: F cos θ along the axis and F sin θ perpendicular to it.

Front: RECALL
Explain how to add two perpendicular vectors.
Back: Pythagoras gives the magnitude of the resultant and tan θ gives its direction.

Front: RECALL
State the kinetic energy of a particle in terms of its momentum.
Back: E_k = p^2/(2m). Substituting v = p/m into ½mv^2 gives it in two lines, and being built on ½mv^2 it holds only at non-relativistic speeds.

Front: DEFINITION
Define: Resultant force.
Back: The single force equivalent to the vector sum of all the forces acting on an object.

Front: RECALL
State how the gravitational potential energy formula is derived.
Back: Raising a mass at constant speed needs an upward force mg acting along the displacement Δh, so W = Fs gives the work as mgΔh, and that is what the store gains.

Front: RECALL
State how the four constant-acceleration equations are derived.
Back: From a = (v − u)/t, which gives v = u + at, and from s = average velocity × t = ½(u + v)t. Substituting the first into the second gives s = ut + ½at^2; eliminating t between them gives v^2 = u^2 + 2as.

Front: RECALL
State the velocity of a projectile at the top of its arc.
Back: The vertical component is zero but the horizontal component remains, so the speed is not zero.

Front: RECALL
State how to find a change in a vector quantity.
Back: Subtract the initial vector from the final one, Δv = v − u, treating both as vectors, so a straight rebound at unchanged speed gives a change of twice the speed.

Front: DEFINITION
Define: Moment of a couple.
Back: One of the two forces multiplied by the perpendicular distance between their lines of action.

Front: DEFINITION
Define: Kinetic energy.
Back: The energy of a moving object: E_k = ½mv^2.

Front: RECALL
State what a newton meter measures.
Back: It measures force directly through a stretched spring, so it reads weight and its reading changes with g.

Front: SPOT THE ERROR
Say what is wrong with this claim: Falling objects just keep speeding up.
Back: Drag grows with speed, so a falling object cannot speed up forever: eventually drag equals weight, the resultant force is zero, and the object continues at that terminal speed.

Front: RECALL
State the unit of mass.
Back: The kilogram, kg.

Front: DEFINITION
Define: Principle of conservation of energy.
Back: Energy cannot be created or destroyed, only transferred from one form to another.

Front: RECALL
State what the area under a velocity-time graph represents.
Back: The displacement, with area below the time axis counting as negative.

Front: RECALL
State how drag depends on speed.
Back: Drag increases with speed: the faster an object moves through a fluid, the larger the resistive force.

Front: DEFINITION
Define: Principle of moments.
Back: For a body in equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that point.

Front: SPOT THE ERROR
Say what is wrong with this claim: Mass and weight are two words for the same thing.
Back: Mass and weight are different quantities. Mass, in kilograms, is the same everywhere; weight is the gravitational force on that mass, W = mg, in newtons, so it changes with g.

Front: RECALL
State the effect on kinetic energy of doubling the speed.
Back: It quadruples, because kinetic energy is proportional to the square of the speed.

Front: RECALL
Explain why crumple zones reduce injury.
Back: They increase the time taken for the momentum change, so the average force F = Δ(mv)/Δt is smaller.

Front: SPOT THE ERROR
Say what is wrong with this claim: Something must keep pushing a projectile forwards.
Back: Nothing pushes a projectile along. With air resistance neglected the only force is gravity, straight down, so horizontal velocity stays constant. Motion needs no force to continue, only to change.

Front: DEFINITION
Define: Scalar.
Back: A quantity with magnitude only, such as speed, distance, energy or temperature.

Front: RECALL
State the initial gradient of the velocity-time graph for an object dropped from rest.
Back: It equals g, because at zero speed there is no drag and the resultant force is the full weight.

Front: DEFINITION
Define: Momentum.
Back: The product of an object's mass and its velocity: p = mv, a vector.

Front: RECALL
State the relationship between impulse and momentum change.
Back: The impulse of a force equals the change in momentum it produces: FΔt = Δ(mv).

Front: DEFINITION
Define: Friction.
Back: The resistive force between solid surfaces in contact that opposes relative motion, or attempted motion, between them.

Front: RECALL
Explain how to subtract one vector from another.
Back: Reverse the second and add it: A − B means A + (−B), joined tip to tail. Drawn from a common starting point, A − B runs from the tip of B to the tip of A.

Front: DEFINITION
Define: Mass.
Back: A measure of an object's resistance to acceleration: its inertia.

Front: SPOT THE ERROR
Say what is wrong with this claim: Energy gets used up.
Back: Energy is never used up; it is transferred, usually ending as internal energy spread into the surroundings. Dissipated energy is not destroyed, just no longer usefully collected.

Front: RECALL
State the unit of momentum.
Back: The kilogram metre per second, kg m s^−1, equivalent to the newton second, N s.

Front: RECALL
State what the gradient of a displacement-time graph represents.
Back: The velocity; the gradient of the tangent at a point is the instantaneous velocity.

Front: RECALL
State what the gradient of a velocity-time graph represents.
Back: The acceleration.

Front: DEFINITION
Define: Inelastic collision.
Back: A collision in which momentum is conserved but some kinetic energy is transferred to other forms, such as internal energy.

Front: EQUATION · NOT ON THE DATA SHEET
Weight from mass:
W = ?\(W = \, ?\)W = ?
Back: W = mg\(W = mg\)W = mg

Front: RECALL
State what the area under a force-time graph represents.
Back: The impulse of the force, equal to the change in momentum it produces.

Front: DEFINITION
Define: Newton's third law.
Back: When body A exerts a force on body B, body B exerts a force on A of equal magnitude, opposite direction and the same type.

Front: RECALL
State how to find the change in gravitational potential energy.
Back: ΔE_p = mgΔh, where Δh is the vertical height change.

Front: DEFINITION
Define: Newton's first law.
Back: An object remains at rest or continues at constant velocity unless a resultant external force acts on it.

Front: DEFINITION
Define: Moment of a force.
Back: The force multiplied by the perpendicular distance from the line of action of the force to the pivot.

Front: SPOT THE ERROR
Say what is wrong with this claim: Adding forces means adding the numbers.
Back: Forces are vectors, so magnitudes cannot simply be added: the resultant depends on the angle between them. Only forces, or components, along the same line add as plain numbers.

Front: RECALL
State the unit of weight.
Back: The newton, N, because weight is a force.

Front: RECALL
State the energy budget when resistive forces act.
Back: The initial energy equals the final useful energy plus the work done against resistive forces.

Front: DEFINITION
Define: Vector.
Back: A quantity with both magnitude and direction, such as velocity, displacement, force or momentum.

Front: RECALL
State the quantity shared by the two motions of a projectile.
Back: Time: found from one direction, it is spent in the other.

Front: RECALL
State the unit of power.
Back: The watt, W: one joule of energy transferred per second.

Front: SPOT THE ERROR
Say what is wrong with this claim: Work means effort.
Back: Effort is not work. Work is done only when a force moves its point of application through a distance in the direction of the force; with no displacement, no work is done.

Front: RECALL
State the work done by a force perpendicular to the motion.
Back: Zero: W = Fs cos θ and cos 90° = 0, so no energy is transferred.

Front: DEFINITION
Define: Drag.
Back: The resistive force on an object moving through a fluid, acting opposite to the motion.

Front: RECALL
Explain why a suspended body hangs with its centre of gravity below the pivot.
Back: In any other position the weight has a moment about the pivot, which turns the body until that moment is zero, and it is zero only when the two are vertically in line.

Front: SPOT THE ERROR
Say what is wrong with this claim: Weight and the normal force are an action-reaction pair.
Back: Weight and the normal force act on the same body, so they are not a third-law pair. The partner of your weight is your gravitational pull on the Earth; third-law pairs act on different bodies.

Front: RECALL
State the unit of the moment of a force.
Back: The newton metre, N m.

Front: SPOT THE ERROR
Say what is wrong with this claim: If the forces are equal, it balances.
Back: Equal forces can still turn an object: a couple has zero resultant force and a definite moment. Balance needs both resultant force and resultant moment to be zero.

Front: RECALL
State the weight components on a slope at angle θ.
Back: W sin θ acts down the slope and W cos θ presses perpendicular into the surface.

Front: RECALL
State whether mass changes with location.
Back: An object's mass is unchanged by location: it is the same anywhere in the universe.

Front: DEFINITION
Define: Gravitational field strength g.
Back: The gravitational force per unit mass at a point: g = W/m, in N kg^−1.

Front: DEFINITION
Define: Lift.
Back: The component of the force from a fluid on an object that acts perpendicular to the direction of flow.

Front: RECALL
Explain how conservation of momentum is applied in two dimensions.
Back: Momentum is a vector, so resolve every momentum into components and conserve it along each axis separately: one equation for the x-components and one for the y-components.

Front: DEFINITION
Define: Elastic collision.
Back: A collision in which kinetic energy is conserved as well as momentum.

Front: DEFINITION
Define: Centre of gravity.
Back: The single point at which the whole weight of a body may be taken to act; where the gravitational field is uniform across the body it coincides with the centre of mass.

Front: DEFINITION
Define: Impulse.
Back: The product of a force and the time for which it acts: impulse = FΔt.