Topic 2: Mechanics Flashcards
Define: displacement.
The distance in a given direction from a fixed origin. It is a vector quantity.
What is the symbol for displacement?
s
Define: velocity.
Velocity is the rate of change of displacement. It is a vector quantity.
Define: speed.
Speed is the rate of change of distance. It is a scalar quantity.
Define: acceleration.
The rate of change with time of the velocity vector. It is a vector quantity.
What is an instantaneous value of speed?
Speed at a particular moment in time
What is an instantaneous value of velocity?
Velocity at a particular moment in time
What is an instantaneous value of acceleration?
Acceleration at a particular moment in time
What is an average value of speed?
Speed over a period of time.
What is an average value of velocity?
Velocity over a period of time
What is an average value of acceleration?
Acceleration over a period of time
When is an object in free fall?
When an object is falling under the sole influence of gravity or the effects of air resistance are being ignored. In the absence of air resistance, all objects have the same acceleration of free-fall, independent of their mass.
What is terminal velocity?
The point by which the velocity of a falling object remains constant and acceleration is zero.
What effect does terminal velocity have on an object?
- At the start, the object accelerates downwards because of its weight. There is no air resistance. There is a resultant force acting downwards
- As it gains speed, the object’s weight stays the same, but the air resistance on it increases. There is a resultant force acting downwards.
- Eventually, the object’s weight is balanced by the air resistance. There is no resultant force and the object reaches a steady speed, called the terminal velocity.
Define: force.
The cause of a deformation or a velocity change. A force is a vector quantity.
Define: weight.
Gravitational force. The force between objects as a result of their masses.
Define: drag
Forces that oppose the motion of a body through a fluid. They are directed opposite to the velocity of the body and generally depend on the speed of that body.
What effect does a higher speed have on drag force?
Higher speed equals higher drag force.
When will an object experience upthrust?
When it is in a fluid medium.
When will an object float?
When the upthrust force is equal to the weight.
Define: frictional forces.
Forces that oppose the motion of a body.
What does Hooke’s law state?
Up to the elastic limit, the extension, x of a spring is proportional to the tension force, F. The constant of proportionality k is called the spring constant.
Define: resultant force.
The overall force acting on an object when all the individual forces acting on that object have been added together.
State Newton’s First Law of Motion.
An object continues in uniform motion in a straight line or at rest unless a resultant external force acts.
State the condition for translational equilibrium.
If the resultant force of an object is zero; an object that is constantly at rest and an object that is moving with uniform velocity in a straight line must be in equilibrium.
State Newton’s Second Law of Motion.
The net force on a body is proportional to that body’s acceleration and is in the same direction as the acceleration. The rate of change of momentum of a body is equal to the net external force acting on the body.
Define: linear momentum.
A vector quantity - the product of mass and velocity whose direction is the same as that of the velocity of the body.
Define: impulse.
The area under the curve of a force-time graph and equals the total momentum change of the mass.
State the law of conservation of linear momentum.
When no external forces act on a system, the total momentum of the system stays the same.
State Newton’s Third Law of Motion.
If Body A exerts a force F on Body B, then Body B exerts an equal but opposite force on Body A.
FAB = -FBA
Define: work
Work done is the energy transferred. It is a vector quantity.
Define: kinetic energy.
The energy of a body or a system with respect to the motion of the body or of the particles in the system.
E = 1/2 m v^2
Where:
E is kinetic energy in J
m is mass in kg
v is velocity in m s^-1
State the principle of conservation of energy.
Energy cannot be created or destroyed. It can only be transferred from one form to another:
- the total energy of any closed system must be constant
- energy is neither created or destroyed, it only changes form
- there is no change in the total energy of the Universe
What are the nine different forms of energy?
- Chemical
- Kinetic
- Elastic potential
- Electrical
- Thermal
- Sound
- Gravitational potential
- Nuclear
- Light
Define: inelastic collision.
An inelastic collision is where kinetic energy is lost/not conserved.
Define: power.
Power is the rate at which work is done.
Define: efficiency.
The ratio of useful energy to the total energy transferred.
When is an object in static equillibrium?
When it is at rest.
When is an object in dynamic equilibrium?
When it is moving at a constant velocity.
How is energy lost in collisions?
Almost always in reality collisions are inelastic as energy is lost as sound and friction.
Define: elastic collision
An elastic collision is when the total kinetic energy of the objects is the same before and after the collision.
Determine relative velocity in one and in two dimensions.
If two objects are moving in the same straight line but are travelling at different speeds, then we can work out their relative velocities by addition or subtraction.
Define: gravitational force/weight
The force between objects as a result of their masses.
Define: magnetic force
The force between magnets and/or electric currents.
Define: normal reaction
The force exerted when a body touches another body. This force is perpendicular to the body exerting the force. If two surfaces are smooth then this is the only force that acts between them.
Define: friction
The force that opposes the relative motion of two surfaces and acts along the surfaces.
Define: tension
The force that arises in any body when it is stretched. When a string (or a spring) is stretched, it has equal and opposite forces on its ends pulling outwards. The tension force is the force that the end of the string applies to another object.
Define: electrostatic force
The force between objects as a result of their electric charges.
Define: compression.
When a rod is compressed it has equal and opposite forces on its ends pushing inwards. The compression force is the force that the ends of the rod applies to another object. This is the opposite of tension.
Define: upthrust
The upward force that acts on an object when it is submerged in a fluid. It is the force that causes some objects to float in water.
Define: lift
Can be exerted on an object when a fluid flows over it in an asymmetrical way.
Define: totally inelastic collision
A collision where a large amount of mechanical energy is lost but momentum is conserved.
An object is projected upwards at an angle of θ to the ground. What is the total horizontal range when it hits the floor?
2t (u cos θ)
Define: translational equilibrium
When an object is either at rest or moving at a constant velocity (not just constant speed)
What forces are acting on an object at translational equilibrium (at rest or constant velocity)?
From Newton’s I and II laws, as there is no change in velocity, there must be no resultant force acting on the object, i.e. all forces are in balance.
Define: static friction
Friction when there is no relative movement between the surfaces
Define: dynamic friciton
Friction when there is relative movement between the objects
What does the amount of friction depend on?
The two surfaces, not just one.
What does the dynamic friction equation show?
The frictional force is constant and, according to simple theory, is not thought to be dependant on the relative speed between the two surfaces.
What is resistance in a fluid (gas or liquid) called?
Drag (force)
What is terminal velocity?
When the velocity is maximised i.e. no more acceleration - forces are balanced and the object is at translational/dynamic equilibrium.
Define: elastic potential energy
After a force has acted on an object to change its shape, some materials are able to revert back to their original shape by storing the required energy after the force is removed.
At what point does an object reach terminal velocity?
When the drag force is equal to weight (mg)
When speed doubles what typically happens to the drag force?
It increases by at least a factor of four.
NB: this is only a generalisation and not entirely accurate
What is one joule in terms of force?
One joule is one newton metre
or
One joule is one newton of force through a distance of 1 metre
As work done is in the direction of the force, what must you do if the force acts at an angle to the movement?
Multiply the work done by cos θ where θ is the angle between the force direction and the direction of movement.
What is the area underneath a force-displacement graph?
The work is done, as W = Fs
Derive the kinetic energy equation
acceleration is a = F/m (Newton’s II law)
therefore v = 0 + (F/m)T (SUVAT)
so, after rearranging, F = (mv)/T
the distance travelled, s = (v+0)T/2 (SUVAT)
Work done, W = Fs, is the kinetic energy so:
EK = mv/T x vT/2
EK = mv2/2 = 1/2(mv2)
What type of force is the gravitational force?
Conservative, as they conserve energy
ANSWER:
A snowboarder is moving down a curved slope starting from rest (u = 0). The vertical change in height of the slope is Δh = 50m.
What is the speed of the snowboarder at the bottom of the slope?
Air resistance and friction are negligible.
As air resistance and friction are negligible, the decrease in GPE is equal to the increase in KE.
mgΔh = 1/2(mv2)
(50)(9.81) = 1/2v2
v2 = 2 x 50 x 9.81
v = √(2x50x9.81)
v = 31 ms-1
How is GPE related to work done?
GPE is the work done when an object is raised at a constant speed through a change in height of Δh.
Work done = force x distance
GPE = mg x Δh
How should you approach this type of question:
“A snowboarder is moving down a curved slope starting from rest (u = 0). The vertical change in height of the slope is Δh = 50m.
What is the speed of the snowboarder at the bottom of the slope?”
Use GPE and KE equations.
Do NOT use SUVAT equations, despite they may give the same answer for this question. The examiner WILL discount your answer as the physics is incorrect.
What is the area below a force-extension graph?
Work done extending the spring.
What is the thermal energy produced when loading and unloading a spring?
Thermal energy produced = work done (loading) - work done (unloading)
or the area under loading graph - area under unloading graph.
Where is the elastic limit of a spring shown on a diagram?
As force-extension graphs follow a linear line, once the line curves/flatten/inverses, the elastic limit has been reached.
How is momentum transferred?
Through collisions
In an elastic collision of two objects with identical mass, what happens to the relative velocity of both objects?
As the first object approaches the second, stationary object, it has a velocity of u.
As no energy is lost (elastic collision), all the kinetic energy is transferred to the second object.
As the second object has the same mass, it will travel as a velocity v, which is identical to u.
Momentum is conserved.
What is conserved in elastic collisions:
- momentum?
- total energy?
- kinetic energy?
- momentum is conserved
- total energy is conserved
- kinetic energy is not conserved (some lost to heat)
