Chapter 8: Newton’s laws of motion

Contact time and impact time

• objects collide and bounce off each other - in contact for a certain time

• the shorter the impact time, the greater the impact force for the same initial velocities

• if the objects stick together after the collision, the contact time is not equal to the impact time

• impact time is the duration of the impact force

car safety features

• vehicle bumpers - compress and deform elastically in low speed impact - increase impact time, reducing impact force - but will return to original shape

• crumple zone - engine compartment compresses and deforms inelastically in front end impact, impact time increases, reducing impact force - stores a proportion of collision energy internally, not in elastic potential - prevents kinetic energy transferred back after collision and causing another acceleration of car and passengers, therefore another resultant force

• seat belts - in front end impact, restrains passenger from crashing into the vehicle frame when vehicle suddenly stops. the restraining force is much less than what the impact force would be . wearer is stopped more gradually

• collapsible steering wheel - in front end impact, if the driver collides with steering wheel, it collapses, increasing impact time

• airbags - compress - increases the impact time on the person - decreases impact force

why chevron separation does not take into account the distance travelled as a car comes to rest after breaks are applied

• car in front does not stop instantaneously so car behind will have time to bring car to rest

• assumed that the car in front would take the same time / travel same distance during its own breaking (only difference is the reaction time of the driver behind)

drag force and terminal speed

• force of fluid resistance

• depends on surface area of object, speed of object, viscosity of fluid

• as object’s velocity increases, the drag force on it increases - resultant force on object decreases, acceleration of object decreases

• terminal velocity - maximum velocity reached when drag force becomes equal to the force in the direction of motion - remains at this constant velocity until acted on by an external force

• for a falling object, drag force at terminal any terminal velocity = weight

deceleration of object falling

• a mass of gas particles are displaced, experience change in velocity and so momentum

• force = rate of change of momentum ( second law)

• force exerted from object on gas particles in order to accelerate

• by third law, gas particles exert an equal magnitude and opposite direction force on object

• resistive force greater than weight so there is a resultant force upwards, opposing direction of motion

• second law requires acceleration to be in the direction of resultant force so object is decelerating

deceleration of object falling in a denser fluid

• collides with more particles per second by at a given speed

• displaces a greater total mass of particles

• f = m(v-u)/t so a greater rate of change in momentum of particles occurs

• so requires a greater force exerted on particles by object

• an equal magnitude force is exerted on the object in the opposite direction to motion

• (object was already decelerating) so the resultant force on the object increases

• acceleration is in the direction of motion so it must have a greater deceleration

forces on a lift

(taking upwards as positive)

accelerating and ascending / decelerating and descending T-W = ma

S-W = ma

S>W

decelerating and ascending / accelerating and descending T-W = -ma

S-W = -ma

S<W

constant speed and ascending / constant speed and descending

S = W

Effect of continuously losing mass on terminal speed

• initial mass is the same - initial velocity is the same - initial acceleration of the velocity time graph is the same

• a = f/m (no drag initially)

• drag force increases continuously with speed

• the resistive forces at same speed are much lower for losing mass than for a similar lorry of constant mass (drag same but normal reaction force lower so friction lower) - resultant force lower

• acceleration in the middle of the graph is greater

• when mass stops decreasing, the resistive forces can stop decreasing and will begin to increase, reducing the resultant forces

• so a higher velocity must now be reached for the resistive forces = driving force (since it must gain greater proportion of total resistive forces from drag by reaching higher velocity as friction much lower)

• terminal constant velocity higher

motion of an object moving up and falling

• without air resistance - gradient of at vt graph constant at 9.81

• with air resistance, initially steeper gradient since air resistance in same direction as weight when ball moving upwards, giving larger deceleration

• gradient continuously decreases since speed decreases as moving towards max height - air resistance decreases meaning resultant force decreases

• after time axis crossed, ball moving downwards - increasing in speed - air resistance increases - air resistance in opposite direction to weight - resultant force decreases after- gradient continuously decreases

• higher max height reached without air resistance