Topic 2 - motion and forces

what is a vector

a vector has magnitude and direction

what is a scalar

a scalar has just magnitude

examples of scalar quantities

speed, distance, time, mass, energy

examples of vector quantities

velocity, displacement, acceleration, force, momentum

what is velocity

speed in a stated direction

equation for speed

speed (m/s) = distance (m) / time (s)

displacement (distance) time graphs

• gradient is velocity

• sharper gradient means faster speed

  • negative gradient is returning back to starting point

• horizontal line means stationary

• 0 distance means that it is back to starting point

• area under line = nothing

• curved line means the velocity is changing acceleration)

velocitytime graphs

• gradient is acceleration

• sharper gradient means greater acceleration

  • negative gradient is deceleration

• horizontal line, constant speed

• 0 velocity means that it is stationary

• area under line = distance travelled

• curved line means that the acceleration is changing

what is average speed

• this is for when the speed changed during the motion

• use overall distances and timings to work out average speed

equation for acceleration

acceleration (m/s²) = change in velocity (m/s)/time taken (s)

a = (v-u)/t

equation for final velocity² - initial velocity²

final velocity² (m/s²) - initial velocity² (m/s²) = 2 x acceleration (m/s²) x distance (m)

v² - u² = 2 x a x X

method to determine constant speeds

• measure distance travelled

• use stopwatch for time taken

• use speed = distance/time

method to determine average speed

• work out total distance travelled

• find the time taken for the whole journey

• use speed = distance/time

method to determine speed using light gates

• set up two, one at start and one at end

• measure distance between them

• as soon as the object passes through the first, it will measure the time taken to reach the second

• then use speed = distance/time

  • this is more accurate as it removes reaction time and human error with a stopwatch

typical speed for wind

5 - 7ms^-1

typical speed for sound

340ms^-1

typical speed for walking

5km/h = ~ 1.4ms^-1

typical speed for running

~6 miles per hour = ~3ms^-1

typical speed for cycling

15km/h = ~4ms^-1

typical speed for bus

14km/h

typical speed for train

125miles/h

typical speed for plane

900km/h

what is acceleration due to gravity

g = 10m/s²

Newtons first law

an object has a constant velocity unless acted on by a resultant force

• if a resultant force acts on the object it will accelerate

  • acceleration is change in velocity over time

  • so the velocity will change

  • so the direction or speed of the object will change (or both)

• if the resultant force is zero

  • no acceleration

  • so moving at constant velocity (so same speed and direction)

  • or the object is at rest (no speed)

Newtons second law

force = mass x acceleration

f = ma

where force is in Newtons, N, mass in kg and acceleration in ms^-2

equation for weight

weight (N) = mass (kg) x gravitational field strength (N/kg)

how is weight measured

using a force meter, or weighing scales and is used to work out mass of unknown object

describe the relationship between the weight of a body and the gravitational field strength

the greater the gravitational field strength, the greater the weight

Core Practical: Investigate the relationship between force, mass and acceleration by varying the masses added to trolleys equipment needed

• trolley

• 10 × 0.1kg masses

• string

• pulley

• ramp

• light gates

• clamps and clam stands to hold light gates

• data logger

• balance to measure the mass of trolley

• piece of card to put on top of trolley

Core Practical: Investigate the relationship between force, mass and acceleration by varying the masses added to trolleys method

1. set up the equipment as shown in the diagram

2. use the balance to measure the mass of the trolley (w no extra masses added)

3. start with one 0.1kg mass hanging on the end of the string and no masses on the trolley

4. release the trolley from rest and record the time it takes to travel between the light gates (which will be shown on the data logger) as well as the velocity of the trolley at each light gate (also on data logger)

5. add one 0.1kg mass to the trolley and repeat

6. continue adding masses to the trolley until all of the masses are used up (or a reasonable number have been used in order to get comprehensive results), recording the time taken and the velocity at both gates each time

7. calculate the acceleration for each recorded value using a = v-u/t

8. plot a graph of acceleration against mass, which should give a smooth curve showing an inverse relationship between the two variables

9. plot a graph of acceleration against 1/mass, which should give a straight line

Core Practical: Investigate the relationship between force, mass and acceleration by varying the masses added to trolleys tips

• counteract friction by raising the ramp slightly so that, when pushed, the trolley will roll to the end of the ramp without stopping

• you must also measure the length of the card attached to the trolley and input that into the data logger so that it can calculate the velocity of the trolley as it passes through the light gates

• the force in the string must be kept constant, so the mass at the end of the string must remain the same

• you may need two sets of light gates: one on each stand to measure the velocity of the trolley at each point, and a set of two to measure the time taken to travel between them

Core Practical: Investigate the relationship between force, mass and acceleration by varying the masses added to trolleys safety precautions

• place something soft below the falling mass at the end of the string to break the fall

• do not stand next to the end of the ramp so as to ensure that you do not get hit by the falling mass or the trolley

• attach the masses to the trolley using something that will keep them in place such as tape or sticky tack so that they do not fall off and cause injury

what is circular motion

object moving in a circle, with a constant speed

• the speed is constant, but direction always changing

• so the velocity is always changing

• so it is acceleration

force in circular motion

• for motion in a circle, there must be a force which supplies this acceleration

• this is called centripetal force, and is directed towards the centre of the circle

what is inertial mass

• this is a measure of how difficult it is to change the velocity of an object (including from rest)

• this is measured by inertial mass = force/acceleration

what is Newtons third law

every action has an equal and opposite reaction force

• a book on a table

  • the weight of the book on the table = the reaction force on the book by the table

• rocket taking off

  • the force of the gases being ejected from the rocket is equal to the force that lifts the rocket from the surface

• collisions

  • two marbles colliding

  • the force exerted by one marble on the other is the same as the force from the other

equation for momentum

momentum (kg m/s) = mass (kg) x velocity (m/s)

p = m x v

momentum in a collision

• momentum is always conserved in a collision (where there are no external forces like friction, air resistance, electrostatic attraction etc)

• in collisions:

  • total momentum before = total momentum after

• so two marbles colliding, each will have momentum before and after the collision

  • remember momentum is a vector

Newtons second law

force = change in momentum/time

f = (mv - mu)/t

what is the average human reaction time

0.25 seconds (250 milliseconds)

what is human reaction time and method to work it out

• there is a delay between human observing an event, and acting

• ruler drop experiment

  • someone else holds a ruler just above your open hand

  • they drop it at a random time

  • record the distance from the bottom of the ruler to the point where it was caught

  • average this, and 1cm is 50ms, 2cm 60ms, and so on

what is the stopping distance of a vehicle made up of

the sum of the thinking distance and the braking distance

what is vehicle stopping distance

• after seeing a hazard

  • before you react, during reaction time you travel X meters

    • thinking distance

  • then you react, causing the car to slow down and stop over Y meters

    • braking distance

affects on thinking distance

• speed

• affected by reaction time

• concentration

• tiredness

• distractions

• influence of drugs/alcohol

affects on braking distance

• speed

• poor road conditions (icy, wet)

• bald tires (low friction)

• worn brake pads

• mass (more passengers)

typical stopping distances

20mph = 6m thinking, 6m braking

30mph = 9m thinking, 14m braking

40mph = 12m thinking, 24 braking

50mph = 15m thinking, 38m braking

60mph = 18m thinking, 55m braking

70mph = 21m thinking, 75m braking

dangers of large decelerations

• when in a crash, there is a large deceleration over a very short time as you stop moving from a high speed

• as force = mass x acceleration, this large decrease means a great force is exerted on the car, and the passengers

• this force can cause injury

now in terms of momentum (large decel)

• before the crash, you have a large momentum (due to high velocity)

• after the crash, you have no momentum (as you are not moving)

• so force = change in momentum/time so a great force is felt

how to estimate the forces felt on a road

• use known values of mass and acceleration to calculate force

• average mass of a car ~1500kg

work done to stop

• the work done to stop a vehicle is equal to the initial KE of the vehicle

  • as all the kinetic energy the car had has to be transferred to friction for it to stop

• braking distance ~&~ (initial velocity)² as work done = KE = Fd = 1/2(mu²)