Mechanics Flashcards
Describe the difference between scalar and vector quantities
A scalar quantity just takes into account magnitude (size) whereas a vector quantity takes into account both the magnitude and the direction they are going
Give 5 examples each of both scalar and vector quantities
Scalar - mass, time, temperature, speed, distance
Vector - displacement, velocity, acceleration, force/weight, momentum
In what circumstances are the 2 different methods to add vectors/find the resultant vector used
Scale drawings- used when the vectors are not at right angles to eachother
Pythagoras/Trig - can be used when the vectors are at right angles to eachother
A woman walks 3m on a bearing of 055 degrees, then 4m east. How would you find the magnitude and direction of her displacement
- Displacement gives her final position relative to her starting point
- Draw a scale diagram e.g. 1cm = 1m, where you connect the vectors tip to tail
- To do this, you would draw the first arrow, which is a distance of 3cm from the start point, at a bearing of 055 from north line
- Then draw the second arrow from the tip of the first one, which is 4cm and east from the tip
- Then draw the resultant vector from the tail of the first vector to the tip of the second (from the start of her journey to the end) and measure its length and bearing to the north line. convert back to metres at the end
Jemima walks 3m north and 4m east. Find the magnitude and direction of her displacement
- Displacement is position from starting point. Her distance travelled is 7m but she isn’t 7m from her starting point
- Draw the vectors tip to tail
- Draw a resultant vector from the starting point to the end point
- Use Pythagoras to calculate the magnitude of the vector (5m)
- Use trig to find the bearing from the north line tanx=4/3 so x = 053 degrees
Explain the process of resolving vectors
- It is the opposite of adding vectors
- Instead you split a resultant vector into 2 different vectors at right angles to each other
- You are finding its horizontal and vertical components
Why is resolving the weight of the block on a slope useful
You can resolve its weight parallel and perpendicular to the slope, and these 2 forces do not affect each other so you can deal with them separately
What is a free body force diagram
A diagram which shows all the forces acting on a body, including magnitude and direction
What does it mean for a body to be in equilibrium
- The sum of all the forces acting on the body = 0
- The object has no resultant force acting on it in either direction so it is either at rest or moving at a constant velocity (uniform motion), according to newtons first law
How can you show that an object is in equilibrium
- Add the horizontal components and then the vertical components. They would each add to 0
- If there are 3 forces acting on an object, you can draw a scale diagram and if the diagram is a closed triangle, the object is in equilibrium
Formula for a moment
Moment of a force (Nm) = Force (N) x perpendicular distance from the pivot to the line of action of the force (m)
What is the principle of moments
For an object to be in equilibrium, the sum of the clockwise moments about a point must equal the sum of the anticlockwise moments about that same point
Define a couple
A pair of coplanar forces which are equal in magnitude, but act in opposite directions,
so there no is no resultant linear force but there is a moment
How would you calculate the moment produced by a couple
One of the forces x perpendicular distance between the lines of action of the forces
What is the difference between mass and weight
mass is a measure of the amount of matter in an object (kg)
Weight is the force experienced by a mass due to a gravitational field
W=mg
Define centre of mass
A point on an object that you can consider its whole weight to act through. The object always balances around this point, but sometimes the centre of mass is outside the object e.g. a ring
How can you find the centre of mass of a regular shaped object
Where the lines of symmetry cross, at its centre
How can you find the centre of mass of an irregular object
1) hang the object from a point, e.g. one of its corners
2) Draw a vertical line downwards from the point of suspension, use a plumb line to make sure its vertical. This is done because the centre of mass is directly below the point of suspension, so somewhere on that vertical line
3) Draw another vertical line down from another point
4) See where the lines intersect, this is the centre of mass
When does an object topple over when you push it
When the centre of mass has a line of action which lies outside the objects base
Because pushing an object (e.g. a bus) to its side, creates a moment about the wheel and the centre of mass needs to create another moment about the wheel to bring it back to equilibrium.
Why does an object topple over when its centre of mass has a line of action outside its base
When you push the object about a pivot, clockwise, and let go, then if the line of action is above the base, the centre of mass creates an anticlockwise moment, since its acting down and to the left of the pivot, so there is a net anticlockwise moment and the bus is still stable
If the line of action is outside the base, then the weight is acting down and to the right of the pivot so it produces a net clockwise moment and the bus topples to the right
What is the difference between speed and velocity
Speed is how fast something is moving, regardless of direction
Velocity is the rate of change of an objects displacement, which is its speed in a given direction
v=∆s/∆t
Define displacement
How far an object has travelled from its starting point in a given direction
Define acceleration
The rate of change of an objects velocity a=∆v/∆t
How can you find the average velocity from a displacement-time graph
Calculate the final displacement - the initial displacement
Divide this by the change in time
How could you find the instantaneous velocity at a point on a displacement time graph
Draw a tangent to the curve at that point and find its gradient
How is acceleration shown on a displacement time graph
Acceleration is a change in the gradient of the graph ie curved line
A quicker change in gradient means a greater acceleration
A decreasing gradient means deceleration
Displacement is found from the area under the graph
How do you find acceleration and displacement from a velocity time graph
For acceleration: The gradient
Uniform acceleration is s a straight line, with a steeper gradient meaning a greater acceleration
A curved graph shows increasing or decreasing acceleration
For displacement:
Find the area under the graph
A ball is dropped from rest and bounces.
How would you show this on a velocity-time graph
- The velocity starts at 0 and becomes negative as the speed is increasing downwards. The gradient is constant.
- The ball hits the floor and changes direction, so its velocity instantly becomes positive
- The velocity then decreases at a constant rate, but in the positive direction because the ball is moving up
- The velocity becomes 0 at the top of the bounce
- Then it repeats
What is the area under an acceleration time graph
- The change in velocity
- If a is 0, the object is moving at a constant velocity
If an objects acceleration is decreasing, when is the maximum velocity
When the acceleration is 0, as below this the object starts decelerating and the velocity decreases
What are the 5 SUVAT equations
v=u+at
s=ut+1/2at^2
v^2 = u^2+2as
s=((v+u)/2)t
s=vt-1/2at^2
what is an object in free fall
The only force acting on the object is weight. Its acceleration is g (9.81 ms^-2)
What is the acceleration of the horizontal and vertical components of u in projectile motion
horizontal acceleration is 0
vertical acceleration is -9.8
When is a projectile at its max height and
If it it starts from the ground, when does it land
max height when its velocity is 0
hits the ground when s=0
What is Newtons first law
The velocity of an object will not change unless a resultant force acts on it
What is Newtons second law
The acceleration of an object is proportional to the resultant force experienced by the object.
resultant force = mass x acceleration
This also means mass and acceleration are inversely proportional (except for an object in free fall)
What is Newtons third law
Each force has an equal and opposite reaction force
This means if object A exerts a force on object B, object B exerts an equal but opposite force on object A of the same type e.g. both gravitational or electrical
If a book lies on a table, so gravity pulls down on the book and the table pushes upwards on the book, which Newton law is shown
It is not Newtons third law because:
- Both forces are acting on the book so they cancel each other out. An action-reaction pair does not cancel because the forces are acting on different bodies
- Newtons third law is with 2 bodies. Here there are 3 objects involved, the earth, the book and the table. The gravity is caused by the earth so the reaction force to it would be the force of the book on the earth, not the table on the book
Therefore, it shows Newtons first law (the book is at constant speed because there is no resultant force)
What is a frictional/drag force
A force which opposes the motion of an object by converting the kinetic energy into other forms, such as heat and sound. It can never cause an acceleration.
What are the different types of frictional/drag forces
Dry friction, which is between solid surfaces
Fluid friction, in which air or water resists motion (commonly known as drag, air resistance or fluid resistance)
What factors affect the magnitude of the fluid frictional force
Increased viscosity (thickness) of the fluid increases the size of force
Increased area of the object passing through the fluid increases resistive force
As the speed of the object increases it experiences a greater frictional force
This is because these factors increase how frequent collisions with fluid particles are
What causes lift
When an object moves through a fluid, it forces the fluid downward, causing the fluid to change direction. This causes an equal and opposite reaction force (lift), which pushes the fluid back upwards on to the object (newtons third law)
The lift is always perpendicular to the fluid flow, and is opposite the weight
What causes terminal (maximum) speed
If you apply a constant driving force on a stationary object, it will accelerate
As it accelerates, its speed increases, so the frictional forces acting increase, which reduces the resultant force.
Eventually, the frictional forces will equal the constant driving force, so there will be no resultant force so no acceleration.
This is the terminal speed of the object
What are the 2 ways of increasing an objects maximum (terminal) speed
- Increase the driving force e.g. increase engine size
- Decrease frictional force
e.g. make the body more streamlined
Explain the motion of a skydiver until he lands
1) He will leave the plane and begin to accelerate due to his weight
2) the air resistance will increase until it equals his weight, this is his terminal speed
3) Before reaching the ground, he will open his parachute which has a large area so immediately increases air resistance. The air resistance is now bigger than his weight, so he slows down
4) As the speed decreases, air resistance decreases as well, so eventually there will be no resultant force, causing a new terminal velocity, which is at a lower speed.
How does air resistance affect projectile motion
The maximum height is reached earlier and both vertical and horizontal distance travelled decreases
What does a skydivers journey look like on a velocity time graph
Velocity increases from rest but the gradient is decreasing as the acceleration is decreasing as air resistance is increasing
The gradient keeps decreasing until the velocity is now constant (gradient is 0). This is the first terminal speed.
Then, the velocity quickly decreases when the skydiver opens his parachute. However the gradient is still increasing (even though its negative) because as his speed decreases, air resistance decreases
This happens until the gradient is 0 again and a new lower terminal velocity is reached
What is the formula for momentum
momentum (kgms^-1) = mass (kg) x velocity(ms^-1)
so p=mv
Describe the principle of conservation of momentum
The total momentum before a collision is equal to the total momentum after a collision, provided no external force acts
What do you need to do before doing momentum calculations
Set a positive and negative direction as momentum is a vector quantity. Therefore if you have 2 velocities in different directions, one of them has to be positive and one has to be negative
How would you calculate the recoil of a 4 kg gun, given the velocity and mass of the bullet fired is 0.005 kg and 200ms^-. What type of collision is this?
(0.005x200) = (4 x -v)
V = -0.25ms^-1
You put -v because the velocity of the recoil is opposite to the velocity of the bullet
This is an explosion because it is 2 objects coming apart due to a large transfer of potential to kinetic energy for one of the objects
How would you form an equation showing momentum before and after if an object, A, with momentum collides with a stationary object, B, and they move off in the same direction
mAvA + 0 = (mA+mB)v
Object B has a momentum of 0 because its stationary
Their masses add up because they become one particle and you can calculate the velocity they move off together, v.
How would you form an equation showing momentum before and after if an object, A, with momentum collides with a stationary object, B, and they move in opposite directions. (B moves forward, A moves back)
mAmV + 0 = -(mAvA) + mBvB
object A has a negative momentum after the collision as it moves in the opposite direction to initial travel
What is the difference between external and internal forces
External forces act on a structure from the outside e.g. weight and friction
Internal forces are exchanged by particles in the system e.g. tension in a string
Systems with no external forces are described as closed/isolated
Describe and explain the relationship between force and momentum
Force is the rate of change of momentum
F=ma so F=mΔv/Δt so F=Δp/t, where Δp is pfinal - pinitial
Define impulse
impulse (Ns) F(N)xΔt(s)
Therefore impulse is the change in momentum
(mv-mu)
Therefore it is the area under a force time graph
How do vehicle safety features reduce the force of an impact
Crumple zones - the front and back of a car crumple upon impact, which increases the time taken to stop, which increases impact time, decreasing the force on the passengers
Seat belts - They stretch slightly, meaning when the passenger moved forward suddenly, there time taken to stop increases so impact time increases so force on the chest decreases
Air bags - Compresses slowly upon impact so increases time to stop, increases impact time so decreases force. These also stop you from hitting the hard surface in the car, which do not compress
What is the difference between an elastic and inelastic collision giving examples
Elastic - momentum and kinetic energy are conserved so 1/2mv^2 before = 1/2mv^2 after
e.g. when 2 objects move in opposite directions after the collision
Inelastic - momentum is still conserved but kinetic energy is not
e.g. when 2 objects move together after a collision as energy is transferred to bonding energy, heat or sound,
Or during an explosion as kinetic energy increases after the explosion
Define work
The amount of energy transferred from one form to another when a force causes a movement
Work done (J) = force causing the motion (N) x distance moved (m)
where:
The force is in the same direction as the distance moved
The force is constant/ an average
What component of a force at an angle is important for work done
The horizontal component (Fcosx) as this is the component causing work to done, the vertical component is just balancing weight.
W = Fscosx
How can you calculate the work done for a variable force
Plot a graph of force against distance moved and calculate the area under the graph
Define power
The rate of doing work - (the amount of energy transferred from one form to another per second)
P (W) =ΔW (J) /Δt (s)
Derive P=Fv
W=FΔs and P=W/Δt
so P=FΔs/Δt
so P = Fv
where:
The force/component of the force is in the direction of the velocity
The force is constant/ an average
Define efficiency
The ratio of useful power output from a system to its total power input
Efficiency (%) = useful power output/total power input x100
Or it can be written in terms of energy:
Efficiency = useful energy output/total energy input x 100
What is the principle of the conservation of energy
Energy cannot be created or destroyed, it can only be transferred from one form to another. Therefore, the total energy in a closed system remains constant
Describe the energy transfer when someone is jumping on a trampoline
1) Elastic potential energy is caused from the stretched trampoline when he jumps
2) When he jumps this elastic potential energy is immediately converted to KE
3) As he rises, the KE is converted to GPE until he stops as all of his KE has been converted
4) Then he falls, and the GPE is converted to KE
5) As he lands on the trampoline, KE is converted to elastic potential
Why is not all of the KE converted to GPE in real life when you throw a ball up
As the ball rises, it is also doing work against air resistance as well as gravity. This means some of the initial (max) kinetic energy is lost as heat in order to overcome the air resistance so:
Loss in Ek = gain in GPE + work done against friction
Therefore if air resistance is negligible, Loss of Ek = gain in GPE so max Ek =GPE
