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 - give way in low speed impact - increase impact time, reducing impact force

• crumple zone - engine compartment gives way in front end impact, impact time increases, reducing impact 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 - increases the impact time on the person - decreases impact force

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

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 than for a similar lorry of constant mass - 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

• 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