4.1 force, energy, and momentum

• Scalars 

  Scalar quantities have a magnitude but no direction

  • Density
  • Potential difference
  • Frequency
  • Wavelength
  • Power
  • Pressure
  • Speed
  • Mass
  • Time
  • Distance
  • energy
• Vectors 

  Vector quantities have both magnitude and direction

  • Displacement 
  • Velocity
  • Acceleration
  • Force
  • Impulse
  • Momentum
  • Current
  • Electric/magnetic field
  • Weight 
• Resolving vectors - every force has a horizontal and vertical component

  • horizontal force = Fcosx
  • vertical force = Fsinx

  
• Equilibrium - all forces are balanced, resultant force is 0

  • All horizontal forces balance
  • All vertical forces balance

  At a constant speed or no movement, equilibrium means no change to the condition when forces are equal - newton's first law

  • scale diagram produces a closed triangle
• Moments - the turning effect of a force (Nm)

  • Moment of a force about a point
  • Also called a torque (τ)
  • = F x d
  • Moment = force x perpendicular distance from point to line of action from force 
• Couples - two forces equal in magnitude but opposite in direction

  • Coplanar forces - acting on the same ‘plane’
  • Have different lines of action
  • No resultant force
  • Moment of a couple = force x perpendicular distance between lines of action of forces
• Principle of moments - in equilibrium, the sum of clockwise moments is equal to the sum of anti-clockwise moments
• Centre of mass/gravity - the point in an object where its entire weight appears to act

  • In a uniform regular solid this is at its centre
  • Weight of uniform regular solid x distance from centre of mass to pivot point = weight of object x distance from pivot
• Displacement (s) - vector quantity shortest distance to travel between two points

  • Overall distance travelled - includes direction

  Speed - scalar quantity, rate of change of distance

  Velocity (v) - rate of change of displacement

  • v = s / t
  • velocity = displacement / time

  Acceleration - the rate of change of velocity

  • a = v / t
  • acceleration = velocity / time
  • The gradient of a displacement-time graph
• Instantaneous velocity 

  • The velocity of an object at a specific point in time
  • The gradient of a displacement-time graph

  Average velocity 

  • The velocity of an object over a particular time frame
  • final displacement-time taken

  Uniform acceleration 

  • When acceleration is constant
  • Gradient of 0

  
• Graphs 

  Displacement-time graph

  • Gradient shows velocity

  Velocity-time graph 

  • Gradient shows acceleration
  • Area shows displacement

  Acceleration-time graph 

  • Area shows velocity

  e.g. bouncing ball graphs

  
• SUVAT equations

  $v=$$u+$$at$

  $s=$$1/2(u+v)t$

  $s=$$ut+$$1/2at^2$

  $s=$$vt-1/2at^2$

  $v^2=$$u^2+$$2as$

  Acceleration due to gravity

  • Vertically upwards = -9.81ms-2
  • Vertically downwards = 9.81ms-2
• Horizontal and vertical components

  • The projectile has a horizontal component
  • The projectile has a vertical component
  • Resolve separately where acceleration is constant 
  • Both are affected by air resistance
• Friction  

  • Force opposing the motion of an object
  • e.g. Drag, air resistance
  • Frictional forces convert kinetic energy into other energy forms - e.g. heat and sound 
  • The magnitude of air resistance increases as speed increases

  Lift 

  • Upward force
  • Acts objects travelling in a fluid
  • Caused by object creating change in the direction of fluid flow
  • Acts perpendicular to the direction of fluid flow

  Terminal speed (terminal velocity)  

  • When frictional forces and driving forces are equal
  • No resultant force
  • No acceleration
  • constant speed
• Newtons laws

  • Newton’s 1st law - an object will remain at rest or a constant velocity until it experiences a resultant force
  • No resultant force
  • No acceleration
  • Newton’s 2nd law - the acceleration of an object is proportional to the resultant force experienced by the object
  • F = m x a
  • Change in acceleration - change in speed, direction, magnitude 
  • Newton’s 3rd law - for every force on an object, the object exerts an equal and opposite force
  • All forces exist in pairs
  • Equal in size
  • Opposite in direction
  • Acting on different objects 
• Momentum

  • momentum = mass x velocity
  • Always conserved 
  • Total momentum before = total momentum after
  • Force is the rate of change of momentum
  • F = (mv) / t     F x t = (mv) 
  • F is a constant

  Impulse 

  • change in momentum
  • F x t
  • The area under a force-time graph
  • Used in crumple zones, seat belts, and airbags - increase the impact time
  • Causes force exerted to decrease - minimise injury
• Elastic and inelastic collisions

  • Elastic - both momentum and kinetic energy are conserved
  • Inelastic - only momentum is conserved
  • Kinetic energy is converted into other forms - explosions
  • If objects stick together after the collision, it's inelastic

  
• Work done 

  • force causing a motion x distance travelled in the direction of the force
  • W = F x s x cos(x)
  • Measure of energy transfer
  • Rate of doing work = rate of energy transfer 
  • The area under a force-displacement graph

  Power  

  • Rate of energy transfer
  • P = W / t  = (F x s) / t  = F x v
• Efficiency 

  • Measure how efficiently a system transfers energy
  • efficiency = useful output power / input power
  • percentage efficiency = (useful output power / input power) x 100
• Principle of conservation of energy

  • Energy cannot be created or destroyed 
  • Transferred from one form to another
  • The total energy in a closed system is constant
  • Total energy in = total energy out

  Change in gravitational potential

  • PE = mgh

  Kinetic energy

  • KE = 1/2 x m x v^2
  • Work is done against resistive forces - the initial kinetic energy given isn't equal to the maximum gravitational potential
• Core practical (3) - determination of gravity

  Aims

  • The overall aim of the experiment is to calculate the value of the acceleration due to gravity, g
  • This is done by measuring the time it takes for a ball-bearing to fall a certain distance. The acceleration is then calculated using an equation of motion

  Test Variables

  • Independent variable = height, h
  • Dependent variable = time, t
  • Control variables = Same steel ball–bearing, same electromagnet, distance between ball-bearing and top of the glass tube
  • Resolution of measuring equipment:
  • Metre ruler = 1 mm
  • Timer = 0.01 s

  
• Method

  1. Set up the apparatus by attaching the electromagnet to the top of a tall clamp stand. Do not switch on the current till everything is set up
  2. Place the glass tube directly underneath the electromagnet, leaving space for the ball-bearing. Make sure it faces directly downwards and not at an angle
  3. Attach both light gates around the glass tube at a starting distance of around 10 cm
  4. Measure this distance between the two light gates as the height, h with a metre ruler
  5. Place the cushion directly underneath the end of the glass tube to catch the ball-bearing when it falls through

  
• 6. Switch the current on the electromagnet and place the ball-bearing directly underneath so it is attracted to it

  7. Turn the current to the electromagnet off. The ball should drop

  8. When the ball drops through the first light gate, the timer starts

  9. When the ball drops through the second light gate, the timer stops

  10. Read the time on the timer and record this as time, t

  11. Increase h (eg. by 5 cm) and repeat the experiment. At least 5 – 10 values for h should be used

  12. Repeat this method at least 3 times for each value of h and calculate an average t for each
• Analysing results

  • Comparing this to the equation of a straight line: y = mx + c
  • y = 2h/t
  • x = t
  • Gradient, m = a = g 
  • y-intercept = 2u