Newton used the concept of momentum to explain the results of collisions Momentum = mass x velocity p = m v Units : p (kg m/s) = m (kg) x (m/s) Note since velocity is a vector quantity, (both magnitude and direction) then momentum is also a vector quantity.
Momentum = mass x velocity
p = m v
p (kg m/s) = m (kg) x (m/s)
Note since velocity is a vector quantity, (both magnitude and direction) then momentum is also a vector quantity
When objects collide, assuming that there are no external forces, then momentum is always conserved.... Definition :
Mass 75 kg
Mass 125 kg
Velocity ??? m/s
Mass 50 kg
When objects hit each other the resulting collision can be considered to be either elastic or inelastic. Momentum and total energy are always conserved in both cases.
momentum conserved, kinetic energy conserved, total energy conserved
momentum conserved, kinetic energy NOT conserved, total energy conserved
In an Inelastic collision some of the kinetic energy is converted to other forms of energy (often heat & Sound)
Two trolleys on an air track are fitted with repelling magnets. The masses are 0.1kg and 0.15kg respectively. When they are released the lighter trolley moves to the left at 0.24m/s. What is the velocity of the heavier trolley
A ball of 0.6kg moving at 5m/s collides with a larger stationary ball of mass 2kg. The smaller ball rebounds in the opposite direction at 2.4m/s
Calculate the velocity of the larger ball
Is the Collision elastic or inelastic. Explain your answer
An object of constant mass m is acted upon by a constant force F which results in a change of velocity from u to v
From the 2nd law F = (mv – mu )/t
Rearranging : Ft = mv – mu
Area under graph “Ft” = change of momentum
A train of mass 24,000kg moving at a velocity of 15m/s is stopped by a braking force of 6000N. Calculate :
The velocity of a car of mass 600kg was reduced from a speed of 15m/s by a constant force of 400N which acted for 20s and then by a constant force of 20N for a further 20s.
During the Y11 course of study, it was discussed how many car safety features such as seatbelts, crumple zones and air bags increase safety by making the crash “last longer”
We have seen that momentum is a vector quantity since it’s related to velocity which is a vector quantity. direction is important and therefore we need a “sign” convention to take this into account.
If we consider a ball with mass m hitting a wall and rebounding normally, (i.e. at 90°):
Towards the wall we take as positive
Away from the wall we take as negative
Initial velocity = +u
Initial momentum = +mu
Final velocity = -u
Final momentum = -mu
Initial velocity = +u
Initial momentum = +mu
A squash ball is released from rest above a flat surface. Describe how the energy changes is i) it rebounds to the same height, ii) It rebounds to a lesser height
If the ball is released from a height of 1.20m and rebounds to a height of 0.9m show that 25% of the kinetic energy is lost upon impact
A shell of mass 2kg is fired at a speed of 140m/s from a gun with mass 800kg. Calculate the recoil velocity of the gun
Repeat the last molecule question. This time the molecule strikes the surface at 60° to the normal and rebounds at 60° to the normal.
The angle in radians is defined as the arc length / the radius
For a whole circle, (360°) the arc length is the circumference, (2r)
360° is 2 radians
Common values :
45° = /4 radians
90° = /2 radians
180° = radians
Note. In S.I. Units we use “rad”
How many degrees is 1 radian?
Angular velocity, for circular motion, has counterparts which can be compared with linear speed s=d/t.
Time (t) remains unchanged, but linear distance (d) is replaced with angular displacement measured in radians.
Angular displacement is the number of radians moved
Consider an object moving along the arc of a circle from A to P at a constant speed for time t:
Definition : The rate of change of angular displacement with time
“The angle, (in radians) an object rotates through per second”
= / t
Where is the angle turned through in radians, (rad), yields units for of rad/s
This is all very comparable with normal linear speed, (or velocity) where we talk about distance/time
The period T of the rotational motion is the time taken for one complete revolution (2 radians).
Considering the diagram below, we can see that the linear distance travelled is the arc length
Linear speed (v) = arc length (AP) / t
v = r /t
Substituting... ( = / t)
v = r
A cyclist travels at a speed of 12m/s on a bike with wheels which have a radius of 40cm. Calculate:
If an object is moving in a circle with a constant speed, it’s velocity is constantly changing....
Because the direction is constantly changing....
If the velocity is constantly changing then by definition the object is accelerating
If the object is accelerating, then an unbalanced force must exist
In exactly the same way as we can connect force f and acceleration a using Newton’s 2nd law of motion, we can arrive at the centripetal force which is keeping the object moving in a circle
The wheel of the London Eye has a diameter of 130m and takes 30mins for 1 revolution. Calculate:
An object of mass 0.15kg moves around a circular path which has a radius of 0.42m once every 5s at a steady rate. Calculate:
During the last lesson we saw that an object moving in a circle has a constantly changing velocity, it is therefore experiencing acceleration and hence a force towards the centre of rotation.
We called this the centripetal force: The force required to keep the object moving in a circle. In reality this force is provided by another force, e.g. The tension in a string, friction or the force of gravity.
At the top of the hill, the support force S, is in the opposite direction to the weight (mg). It is the resultant between these two forces which keep the car moving in a circle
A car with mass 1200kg passes over a bridge with a radius of curvature of 15m at a speed of 10 m/s. Calculate:
A car is racing on a track banked at 25°to the horizontal on a bend with radius of curvature of 350m
A car on a big dipper starts from rest and descends though 45m into a dip which has a radius of curvature of 78m. Assuming that air resistance & friction are negligible. Calculate:
A swing at a fair has a length of 32m. A passenger of mass 69kg falls from the position where the swing is horizontal. Calculate:
A wall of death ride at the fairground has a radius of 12m and rotates once every 6s. Calculate: