Gr 12 Physics: MOMENTUM & IMPULSE
Exercises
Exercise 1: Momentum, Change in momentum
1.1
A soccer ball of mass 420 g is kicked at 20 m.s-1 towards the goal post. Calculate the momentum of the ball.
(8,40 kg.m.s-1)
1.2
A cricket ball of mass 160 g is bowled at 40 m.s-1 towards a batsman. Calculate the momentum of the cricket
ball.
(6,4 kg.m.s-1 towards the batsman)
1.3
The fastest recorded delivery for a cricket ball is 161,3 km.h-1, bowled by Shoaib Akhtar of Pakistan during a
match against England in the 2003 Cricket World Cup, held in South Africa. Calculate the ball’s momentum if
it has a mass of 160 g.
(7,17 kg.m.s-1 towards the batsman)
1.4
A tennis ball of mass 58 g strikes a wall perpendicularly with a velocity of 10 m.s-1.It rebounds at a velocity of
8 m.s-1.
a.
b.
1.5
(1,04 kg.m.s-1 away from the wall)
A rubber ball of mass 0,8 kg is dropped and strikes the floor with an initial velocity of 6 m.s-1. It bounces back
with a final velocity of 4 m.s-1.
a.
b.
1.6
Calculate the change in the momentum of the tennis ball.
Draw a momentum vector diagram.
Calculate the change in the momentum of the rubber ball caused by the floor.
Draw a momentum vector diagram.
(8,0 kg.m.s-1 upwards)
A regulation squash ball weighs 24 g. In a squash match, a ball bounces off the back wall in the direction of the
front wall at 1 m.s-1 before Aleks hits it with a racquet. After being struck towards the front wall the ball is
moving at 20 m.s-1. Calculate the change in momentum.
(0,46 kg.m.s-1 towards the front wall)
Exercise 2: N ll in terms of momentum, Impulse
2.1
A 150 N resultant force acts on a 300 kg trailer. Calculate how long it takes this force to change the trailer’s
velocity from 2 m.s-1 to 6 m.s-1 in the same direction. Assume that the force acts to the right, which is the
direction of motion of the trailer.
(8 s)
2.2
A cricket ball weighing 156 g is moving at 54 km.h-1 towards a batsman. It is hit by the batsman back towards
the bowler at 36 km.h-1. Calculate:
a.
b.
2.3
A 25g tennis ball moves toward a tennis player at 30 m.s-1. The player returns the ball exerting a force on it for
0,1 s sending it over the net to his opponent at 50 m.s-1.
a.
b.
2.4
the ball’s impulse,
( 3,9 kgm.s-1 ; towards the bowler)
the average force exerted by the bat if the ball is in contact with the bat for 0,13 s.
(30 N ; towards the bowler)
Calculate the change in the tennis ball’s momentum.
Calculate the average force which the player exerts on the ball.
(2 kg.m.s-1; away from player)
(20 N; onto the ball)
A cricket player bowls his ball of 100 g at 130 km.h-1 and the wicket keeper catches it.
a.
b.
c.
d.
Calculate the momentum of the ball before the wicket keeper catches it. (3,61 kg.m.s-1; towards keeper)
Calculate the impulse on the ball as the wicket keeper brings it to a stop.
(3,61 kg.m.s-1; on ball)
It takes 0,9 s from when the ball enters the wicket keepers gloves to when it comes to a complete stop.
Calculate the force which the keeper exerts on the ball to bring it to a stop.
(4,01 N ; on ball)
Explain, in terms of impulse and momentum, why the wicket keepers draws his hands back when
catching a fast ball.
Exercise 3: Conservation of momentum
3.1
A small boy of mass 40 kg is riding on a 5kg skateboard along a straight level pavement at a speed of 4 m.s-1. As
he approaches an obstacle, he jumps off the back of the skateboard, which continues with a velocity 16 times
that with which the boy leaves the skateboard.
a.
b.
c.
3.2
d.
State the principle of conservation of linear momentum.
Calculate the mass of mini-bus B.
(5000 kg)
The time from impact until the mini-busses come to rest is 0,04s. A woman with a mass of 70 kg was
sitting on the front seat of mini-bus A with her safety belt fastened. Calculate the average force exerted
by the safety belt on the woman during the accident.
(43750 N; against her)
Many modern cars are equipped with air bags as a safety feature. Explain using physics principles how
airbags contribute to the safety of a person in a car during a collision.
A child, mass 25 kg, at rest in a boat throws a 2 kg package horizontally out of a boat at a speed of 10 m.s–1 The
mass of the boat is 55 kg.
a.
b.
c.
3.4
(180 kgm.s-1)
(1,5 m.s-1)
Two mini busses, A (mass 4000 kg) and B, are travelling in opposite directions towards each other. A is travelling
at 90 km.h-1 (25 m.s-1) in a westerly direction and B is travelling at 72 km.h-1 in the opposite direction. They
collide head-on and come to rest as a unit at the point of impact.
a.
b.
c.
3.3
State the Law of Conservation of Momentum.
Calculate the momentum of the boy and the skateboard before he jumps off.
Calculate the velocity with which the boy leaves the skateboard.
What is the total momentum of the system before he throws the parcel out of the boat?
(0 kgm.s-1)
Calculate the velocity of the boat immediately after the parcel was thrown.
(0,25 m.s-1; backwards)
Name and state the law used in b.
Two skateboarders, Anke and Pia, stand on their skateboards facing each other, 3m apart, on a smooth, level
surface. They are holding the ends of a light rope stretched between them. Anke gives her end a tug and lets go.
She moves towards Pia at a speed of 0,9 m·s-1. Anke’s mass is 50kg and Pia’s is 60 kg.
a.
b.
c.
What is the total momentum of the skateboarders before the rope is tugged?
(0 kg.m.s-1)
Give a statement of the law or principle that will enable you to calculate the speed at which Pia will
move after Anke tugs the rope.
Calculate the speed at which Pia will move after Anke tugs the rope.
(0,75 m.s-1)
Exercise 4: Conservation of momentum; Elastic and inelastic collisions
4.1
Two ice skaters skate on a slippery (frictionless) ice rink. Daniel (mass 60 kg) is skating northwards at
1 m.s-1 and Lauren (mass 50 kg) is skating towards him at 0, 6 m.s-1. They collide inelastically with each other.
Lauren’s velocity after the collision is 0,8 m.s-1, north
a.
b.
4.2
Calculate Daniel’s velocity after the collision.
Calculate the change in kinetic energy during the collision.
(0,17m.s-1, South)
(22,13 J)
A car of mass 1 600 kg, travelling at a speed of 30 m·s-1 to the left, collides head-on with a minibus of mass
3 000 kg, travelling at 20 m·s-1 to the right. The two vehicles move together as a unit in a straight line after the
collision.
a.
b.
Calculate the velocity of the two vehicles after the collision.
Do the necessary calculations to show that the collision was inelastic.
(2,6 m.s-1)
(∆Ek = 1 304 452 J)
4.3
A railway locomotive and carriage, A, of mass 8000 kg, moves at 2 m·s-1 due east. It collides and couples with
another truck B, of mass 5000 kg moving at 0,2 m·s-1 due west.
a.
b.
c.
4.4
Two roller skaters skate on a cement surface. Jason (mass 65 kg) is skating northwards at 5 m.s-1 and Gabi
(mass 55 kg) is skating towards him at 2 m.s-1. They collide with each other, unite and continue to move
together.
a.
b.
4.5
Determine their combined velocity after the collision.
Determine whether the collision was elastic or inelastic
(1,79 m.s-1)
(Inelastic)
A large truck (mass 4000 kg) travelling at 20 m.s-1 collides with a smaller motorcar (mass 1000 kg) from behind
travelling in the same direction. Their bumpers lock on impact and they continue moving forward at 19 m.s-1.
a.
b.
c.
d.
4.6
Do a calculation, show that the speed of the coupled trucks after collision is 1,15m·s-1, east.
How would each of the following changes affect the final velocity of the coupled trucks? State whether
the velocity would increase, decrease or remain unchanged if:
i.
the mass of the truck A is increased.
ii.
the speed of truck A is increased.
iii.
the mass of truck B is increased.
By means of a calculation, prove that the coupling of the trucks is an inelastic collision. (∆Ek =7503,75 J)
The speed limit in the area in which this collision took place is 60 km.h-1. Was the truck exceeding the
speed limit before the collision?
Show that the velocity of the motorcar before the collision was 15 m.s-1.
Do the necessary calculations to prove that the collision was an inelastic one.
(∆Ek = 10 000J)
The driver of the motorcar escaped injury due to the crumple zone built into the car. Explain,
using physics principles, how this feature of the car was able to protect the driver during this collision.
Gailynn and Luke are riding bumper cars at the funfair. Luke is moving across the slippery surface in his bumper
car at 2,4 m.s-1 and collides elastically with Gailynn’s car which is at rest. After the collision, Luke continues to
move in the same direction at 0,8 m.s-1 . The mass of Luke and his bumper car is 340 kg.
a.
b.
Calculate the velocity of Gailynn’s car after the collision.
Calculate the mass of Gailynn and her bumper car
(3,2 m.s-1)
(170 kg)
4.7
A rubber ball falls from rest for 1 second before it strikes the floor. If the ball bounces inelastically up off the floor,
it will most likely leave the floor with a speed of:
A
9,7 m.s-1
B
9,8 m.s-1
C
9,9 m.s-1
D
10,0 m.s-1
4.8
A trolley, with a mass of 2 kg, travelling at 5 m.s-1, collides with a stationary trolley with a mass of 4 kg. What is
the magnitude of the total momentum of the trolleys immediately after the collision?
A
0 kg.m.s-1
B
4 kg.m.s-1
C
8 kg.m.s-1
D
10 kg.m.s-1
4.9
Two trolleys, moving in opposite directions on a horizontal surface, collide elastically with each other. Which
combination for (a) the total momentum and (b) the total kinetic energy of the system of two trolleys is correct?
A
(a): decreases
(b): stays the same
B
(a): stays the same
(b): stays the same
C
(a): decreases
(b): increases
D
(a): stays the same
(b): decreases
Exercise 5: Momentum - Graphs
5.1
The graph shows how the momentum of two train
carriages that collide with each other changes with time.
Take east as positive.
p (x 103 kg.m.s-1)
Mass of carriage A = 20 tons; Mass of carriage B = 30 tons
a.
B
At what time did the collision take place? ( 0,4 - 1 s)
Calculate the:
b.
change in momentum of each carriage.
(A: 30 000 kg.m.s-1, W ; B: 30 000 kg.m.s-1, E)
c.
initial velocity of each carriage.
(A: 3 m.s-1, E ; B: 0,5m.s-1, E)
d.
final velocity of each carriage.
(A: 1,5 m.s-1, E ; B: 1,5m.s-1, E)
5.2
e.
Draw a velocity-time graph showing the motion of
both carriages.
f.
Use the graph to determine the force experienced by each carriage.
g.
Which law do your answers to Q f. confirm?
A
(± 50 000 N)
Car A (mass 1 800 kg) travelling south collides head-on with car B (mass 1 600 kg) which is travelling in the
opposite direction. During the collision, the cars connect and move together as a unit and they eventually
come to a standstill.
The graph shows the velocity of car A.
Which time interval represents ...
a.
the collision?
(4 - 5,6 s)
b.
the motion of the cars as one unit.
(5,6 - 10 s)
c.
What is the velocity of car A and B
immediately after the collision?
(8,75 m.s-1, S)
Calculate ...
d.
the momentum of car A before the
collision.
(36 000 kg.m.s-1, S)
e.
the impulse experienced by car B.
(20 250 kg.m.s-1, S)
f.
the velocity of car B before the collision.
(3,91 m.s-1 , N)
g.
Use the graph to calculate the acceleration of car A during the collision.
(7,03 m.s-2, N)
h.
Calculate the force experienced by car A during the collision.
(12 654 N, N)
i.
Explain the gradient of the line representing the motion of the cars after the collision.
5.3
Two vehicles are involved in a head-on collision. Vehicle A (mass 1 000 kg) was initially travelling at 20 m·s-1, east
and vehicle B was initially travelling at 15 m·s-1 towards A. The velocities of the vehicles from the moment they
collided are represented in the velocity-time graph below.
Using information from the graph answer the following questions:
a.
b.
c.
d.
e.
5.4
Determine how long the collision between the two vehicles lasted.
Determine the final velocities of each vehicle.
State the Law of Conservation of Momentum.
Calculate the mass of vehicle B.
Prove that this collision is an inelastic collision.
(0,25 s)
(A: 10 m.s-1, E; B: 5 m.s-1, E)
(500 kg)
(ΔEk = 200 000 J)
Ball X (mass 0,06 kg) is initially rolling east at 4 m.s-1. The given graph represents the velocity of ball X versus time.
4
2
v
(m.s-1)
0
2
4
6
8
t(s)
-5
a.
b.
c.
d.
What is the net force acting on ball X between 0 and 2 s?
(0 N)
Use the graph and Newton’s second law of motion in terms of momentum to support your answer to a.
Calculate the magnitude of the impulse that ball X experiences which causes its velocity to change
between t = 2 s and t = 4 s.
(0,12 kgm.s-1, W)
At t = 6 s, ball X collides with ball Y (mass 0,07 kg) which was moving at 5 m.s-1; west. Use information
from the graph and the relevant momentum principle to calculate the velocity of ball Y after the
collision.
(1 m.s-1, E)
Gr. 12 Fisika: MOMENTUM & IMPULS
Oefeninge
Oefening 1: Momentum, Verandering in momentum
1.1
’n Sokkerbal met massa 420 g word teen 20 m·s−1 geskop na die doelhok. Bereken die momentum van die bal.
(8,40 kg.m.s-1)
1.2
‘n Krieketbal met massa 160 g word teen 40 m·s−1 geboul na die kolwer. Bereken die momentum van die
krieketbal.
(6,4 kg.m.s-1, na die kolwer toe)
1.3
Die vinnigste aangetekende aflewering vir ’n krieketbal is 161,3 km·h−1. Dit is deur Shoaib Akhtar van Pakistan
geboul in ’n wedstryd teen Engeland, tydens die Krieket-Wêreldbekertoernooi van 2003 in Suid-Afrika. Bereken
die bal se momentum indien dit ’n massa van 160 g het.
(7,17 kg.m.s-1 , na die kolwer toe)
1.4
’n Tennisbal met ’n massa van 58 g tref ’n muur loodreg met ’n snelheid van 10 m·s−1. Dit spring terug met ’n
snelheid van 8 m·s−1.
a.
b.
Bereken die verandering in die momentum van die tennisbal.
teken ‘n momentum vektordiagram.
(1,04 kg.m.s-1 weg van die muur af)
1.5
’n Rubberbal met ’n massa van 0,8 kg word laat val en tref die vloer met ’n beginsnelheid van 6 m·s−1. Dit spring
terug met ’n eindsnelheid van 4 m·s−1.
a.
Bereken die bal se momentumverandering wat deur die vloer veroorsaak is.
(8,0 kg.m.s-1 opwaarts)
b.
teken ‘n momentum vektordiagram.
1.6
Die voorgeskrewe massa van ’n muurbalballetjie is 24 g. Tydens ’n potjie muurbal wip die balletjie terug vanaf
die agterste muur na die voorste muur teen 1 m·s−1 voordat Aleks dit met sy raket slaan. Dit beweeg teen
20 m·s−1 nadat dit geslaan is. Bereken die die momentumverandering? (0,46 kg.m.s-1 na die voorste muur toe)
Oefening 2: N ll in terme van momentum, Impuls
2.1
’n 150 N resulterende krag werk in op ’n 300 kg sleepwa. Bereken hoe lank dit hierdie krag neem om die
sleepwa se snelheid van 2 m·s−1 na 6 m·s−1 in die rigting van beweging te verander. Neem aan dat die kragte na
regs inwerk, wat die rigting van die sleepwa se beweging is.
(8 s)
2.2
’n Krieketbal met ’n mass van 156 g weeg beweeg teen 54 km·h−1 na ’n kolwer. Dit word deur die kolwer na die
bouler teruggeslaan teen 36 km·h−1. Bereken:
a.
b.
2.3
‘n 25g-tennisbal beweeg na ‘n tennisspeler toe teen 30 m.s-1.Die speler slaan die bal en oefen ‘n krag op die bal
vir 0,1s uit en stuur dit terug oor die net teen 50m.s-1.
a.
b.
2.4
die bal se impuls,
(3,9 kgm.s-1; na die bouler toe)
die gemiddelde krag wat uitgeoefen word deur die kolf as die bal in kontak daarmee is vir 0,13 s.
(30 N; na die bouler toe)
Bereken die verandering in die tennisbal se momentum.
Bereken die gemiddelde krag wat die speler op die bal uitoefen.
(2 kg.m.s-1, weg van die speler af)
(20 N; op die bal)
‘n Krieketspeler boul sy 100g-bal teen 130km.h-1 en die paaltjiewagter vang die bal.
a.
b.
c.
d.
Bereken die momentum van die bal voor die paaltjiewagter dit vang.. (3,61 kg.m.s-1, na die wagter toe)
Bereken die impuls van die bal voordat die paaltjiewagter dit tot stilstand bring. (3,61 kg.m.s-1, op bal)
Dit neem 0,9 s van wanneer die bal die paaltjiewagter se hande tref totdat hy dit tot stilstand bring.
Bereken die krag wat hy op die bal uitoefen om dit tot stilstand te bring.
(4,01 N ; op bal)
Verduidelik, in terme van impuls en momentum, hoekom die paaltjiewagter sy hande terug trek
wanneer hy ‘n vinnige bal moet vang.
Oefening 3: Behoud van momentum
3.1
‘n Seuntjie met ‘n massa van 40 kg ry op ‘n 5kg-skaatsplank langs ‘n gelyke, reguit voetpadjie teen 4 m.s-1.
Wanneer hy ‘n versperring in die pad sien, spring hy van die agterkant van die skaatsplank af. Die skaatsplank
hou aan om te beweeg teen ‘n spoed sestien keer dié waarmee die seun die skaatsplank verlaat het.
a.
b.
c.
3.2
d.
Gee die stelling van die beginsel van behoud van lineêre momentum
Bereken die massa van minibus B.
(5000 kg)
Die tyd van impak totdat die minibusse tot stilstand gekom het, was 0,04s. ‘n Vrou (massa: 70 kg) het op
die voorste sitplek van minibus A met haar veiligheidsgordel vasgemaak, gesit. Bereken die gemiddelde
krag wat die veiligheidsgordel tydens die ongeluk op die vrou, uit geoefen het.
(43750N; teen haar)
Baie moderne motors het lugsakke as veiligheidsmaatreël. Verduidelik, met die gebruik van fisiese
beginsels, hoe die lugsakke tydens ‘n botsing ‘n persoon in die motor se veiligheid verseker.
‘n Kind (massa 25 kg) wat stil sit in ‘n boot, gooi ‘n 2kg- pakkie horisontaal teen ‘n spoed van 10 m.s–1 uit die
boot. Die massa van die boot is 55 kg.
a.
b.
c.
3.4
(180 kgm.s-1)
(1,5 m.s-1)
Twee minibusse, A (massa 4000 kg) en B, reis in teenoorgestelde rigtings na mekaar toe. A reis teen 90 km.h-1
(25 m.s-1) in ‘n westelike rigting en B reis teen 72 km.h-1 in die teenoorgestelde riging. Hulle bots kop- aan- kop
en kom as ‘n eenheid by die punt van impak tot rus.
a.
b.
c.
3.3
Gee ‘n die wet van behoud van momentum.
Bereken die momentum van die seun en die skaatsplank voordat hy afspring.
Bereken die snlelheid waarmme die seun die skaatsplank verlaat.
Wat is die totale momentum van die sisteem voordat hy die pakkie uit die boot gooi?
(0 kgm.s-1)
Bereken die snelheid van die boot onmiddellik nadat hy die pakkie uitgegooi het. (0,25 m.s-1, agtertoe)
Noem en gee die wet wat in b. gebruik word.
Twee skaatsplankryers, Anke en Pia, staan op hulle skaatsplanke, 3m uitmekaar, op ‘n gladde, gelyk oppervlakte
en kyk na mekaar. Hulle hou vas aan ‘n ligte tou wat tussen hulle gespan is. Anke trek die tou en laat los. Sy
beweeg in die rigting van Pia teen ‘n spoed van 0,9 m·s1. Anke se massa is 50kg en Pia s’n is 60 kg.
a.
b.
c.
Wat is die totale momentum van die skaatplankryers voordat die tou getrek is?
(0 kg.m.s-1)
Gee ‘n stelling van die wet of beginsel wat jy kan gebruik om die spoed waarteen Pia sal beweeg nadat
Anke die tou getrek het, te bereken.
Bereken die spoed waarteen Pia sal beweeg nadat Anke die tou getrek het.
(0,75 m.s-1)
Oefening 4: Behoud van momentum; Elastiese en onelastiese botsings
4.1
Twee ysskaatsers skaats op ‘n gladde (wrywinglose) skaatsbaan. Daniel (massa 60 kg) beweeg noord teen
1 m.s-1 en Lauren (massa 50 kg) beweeg na hom toe teen 0,6 m.s-1. Hulle bots onelasties. Lauren se snelheid
na die botsing is 0,8 m.s-1, noord
a.
b.
4.2
Bereken Daniel’s se snelheid na die botsing.
Bereken die verlies aan kinetiese energie tydens die botsing.
(0,17 m.s-1; suid)
(22,13 J)
‘n Motor met massa 1 600 kg, teen ‘n spoed van 30 m·s-1 na links en bots kop-aan-kop met ‘n minibus met
massa 3 000 kg, wat teen 20 m·s-1 na regs beweeg. Die twee voertuie beweeg saam as ‘n eenheid in ‘n reguit
lyn na die botsing.
a.
b.
Bereken die snelheid van die twee voertuie na die botsing.
Doen die nodig berekening om te toon dat die botsing oneleasties was.
(2,6 m.s-1)
(∆Ek = 1 304 452 J)
4.3
‘n Treintrok en wa, A, massa 8000 kg, beweeg reg oos teen 2 m·s-1. Dit bots en koppel aan ’n ander trok , B,
massa 5000 kg wat reg wes teen 0,2 m·s-1 beweeg
a.
b.
c.
4.4
Twee rolskaatsers skaats op ‘n sement oppervlak. Jason (massa 65 kg) skaats noordwaarts teen 5 m.s-1 en
Gabi (massa 55 kg) skaats na hom toe teen 2 m.s-1. Hulle bots met mekaar, verenig en beweeg dan voort saam.
a.
b.
4.5
Bepaal hulle gesamentlike snelheid na die botsing.
Bepaal of die botsing elasties of onelasties was
(1,79 m.s-1)
(Onelasties)
‘n Swaar trok (massa 4000 kg) wat teen 20 m.s-1 ry, bots van agteraf met ‘n kleiner motor (met massa 1000 kg)
wat in dieselfde rigting beweeg. Hulle buffers haak vas op impak en hulle hou aan om te beweeg teen 19 m.s-1.
a.
b.
c.
d.
4.6
Met die gebruik van ‘n geskikte berekening, toon aan dat die spoed van die gekoppelde trokke na die
botsing 1,15 m·s-1, oos is.
Hoe sal die finale snelheid van die gekoppelde trokke deur elk van die volgende veranderings beïnvloed
word? Dui aan of die snelheid sou toeneem, afneem of onveranderd sou bly as:
i.
die massa van trok A neem toe.
ii.
die spoed van trok A neem toe.
iii.
die massa van trok B neem toe. .
Gebruik die nodige berekeninge om te bewys dat die koppeling van die trokke ‘n onelastiese botsing is
(∆Ek =7503.75 J)
Die spoedbeperking in die area waar die botsing plaas giving het is 60 km.h-1. Het die trok die
spoedbeperking voor die botsing oorskry?
Toon dat die snelheid van die motor voor die botsing 15 m.s-1 was.
Doen die nodige berekeninge om te bewys dat die botsing onelasties was.
(∆Ek = 10 000J)
As gevolg van die vervrommelingsone,het die bestuurder geen beserings opgedoen nie. Verduidelik met
die gebruik van fisika beginsels hoe hierdie sone die bestuurder tydens die botsing beskerm het.
Gailynn en Luke ry stampkarre by ‘n pretpark. Luke, in sy stampkar, beweeg oor die gladde baan teen 2,4 m.s-1
en bots elasties met Gailynn se stampkar wat in rus was. Na die botsing beweeg Luke steeds in dieselfde rigting
teen 0,8 m.s-1. Die massa van Luke en sy stampkar is 340 kg.
a.
b.
Bereken die snelheid van Gailynn se kar na die botsing.
Bereken die massa van Gailynn en haar stampkar.
(3,2 m.s-1)
(170 kg)
4.7
‘n Rubberbal val vanuit rus vir 1 sekonde voordat dit die vloer tref. As die bal onelstiese vanaf die vloer bons, sal
dit heel waarskynlik die vloer met ‘n spoed van … verlaat.
A
9,7 m.s-1
B
9,8 m.s-1
C
9,9 m.s-1
D
10,0 m.s-1
4.8
'n Trollie, met 'n massa van 2 kg, wat teen 5 m.s-1 beweeg, bots met 'n stilstaande trollie met 'n massa van 4 kg.
Wat is die grootte van die totale momentum van die trollies onmiddellik na die botsing?
A
0 kg.m.s-1
B
4 kg.m.s-1
C
8 kg.m.s-1
D
10 kg.m.s-1
4.9
Twee trollies, wat in teenoorgestelde rigtings op 'n horisontale oppervlak beweeg, bots elasties met mekaar.
Watter kombinasie vir (a) die totale momentum en (b) die totale kinetiese energie van die stelsel van twee trollies
is korrek?
A
(a): neem af
(b): bly dieselfde
B
(a): bly dieselfde
(b): bly dieselfde
C
(a): neem af
(b): neem toe
D
(a): bly dieselfde
(b): neem af
Oefening 5: Momentum - Grafieke
5.1
Die grafiek wys hoe die momentum van twee treintrokke
wat mekaar bots, verander met tyd.
Neem oos as positief.
p (x 103 kg.m.s-1)
Massa van trok A = 20 ton; Massa van trok B = 30 ton
a.
B
Op watter tydstipvind die botsing plaas? ( 0,4 - 1 s)
Bereken die:
b.
verandering in momentum van elke trok
(A: 30 000 kg.m.s-1, W ; B: 30 000 kg.m.s-1, O)
c.
beginsnelheid van elke trok
(A: 3 m.s-1, E ; B: 0,5m.s-1, O)
d.
eindsnelheid van elke trok.
(A: 1,5 m.s-1, E ; B: 1,5m.s-1, O)
5.2
e.
Teken 'n snelheid-tydgrafiek wat die beweging van
beide trokke aandui.
f.
Gebruik die grafiek om die die krag wat elke trok ervaar te bepaal.
g.
Watter wet word deur jou antwoorde vir V f. bevestig?
A
(± 50 000 N)
Motor A (massa 1 800 kg) wat suidwaarts ry, bots kop-aan-kop met motor B (massa 1 600 kg) wat in die
teenoorgestelde rigting ry. Tydens die botsing, haak die motors aan mekaar vas; hulle beweeg as 'n eenheid
saam en kom uiteindelik tot stilstand.
Die grafiek toon die snelheid van motor A.
Watter tydsinterval verteenwoordig ...
a.
die botsing?
(4 - 5,6 s)
b.
die beweging van die motors as ‘n
eenheid.
(5,6 - 10 s)
c.
Wat is die snelheid van motor A en B
onmiddellik na die botsing?
(8,75 m.s-1, S)
Bereken ...
d.
die momentum van motor A voor die
botsing
(36 000 kg.m.s-1, S)
e.
die impuls wat motor B ervaar
(20 250 kg.m.s-1, S)
f.
die snelheid van motor B voor die botsing.
(3,91 m.s-1 , N)
g.
Gebruik die grafiek om die versnelling van motor A tydens die botsing te bereken.
(7,03 m.s-2, N)
h.
Bereken die krag wat motor A tydens die botsing ervaar.
(12 654 N, N)
i.
Verduidelik die gradiënt van die lyn wat die beweging van die motors na die botsing voorstel.
5.3
Twee voertuie is betrokke in ‘n kop-aan-kop botsing. Voertuig A (massa 1 000 kg) het aanvanklik teen 20 m·s-1,
oos beweeg en voertuig B het aanvanklik teen 15 m·s-1 na A toe beweeg. Die snelhede van die voertuie vanaf die
oomblik dat hulle gebots het word in die snelheid-tyd-grafiek hieronder verteenwoordig.
Gebruik die inligting op die grafiek en beantwoord die volgende vrae:
a.
b.
c.
d.
e.
5.4
Bepaal hoe lank die botsing tussen die twee voertuie geduur het.
Bepaal die finale snelhede van elke voertuig.
Gee die stelling van die Wet van Behoud van Momentum.
Bereken die massa van voertuig B.
Bewys dat hierdie botsing ‘n onelstiese botsing is.
(0,25 s)
(A: 10 m.s-1, O; B: 5 m.s-1, O)
(500 kg)
(ΔEk = 200 000 J)
Bal X (massa 0,06 kg) rol aanvanklik oos teen 4 m.s-1. Die gegewe grafiek verteenwoordig die snelheid van bal X
teenoor tyd.
4
2
v
(m.s-1)
0
2
4
6
8
t(s)
-5
a.
b.
c.
d.
Wat is die nettokrag op die bal X tussen 0 en 2 s?
(0 N)
Gebruik die grafiek en Newton se tweede wet van beweging in terme van momentum om jou antwoord
vir a. te ondersteun.
Bereken die grootte van die impuls wat bal X ervaar wat veroorsaak dat sy snelheid tussen t = 2 s en
t = 4 s verander.
(0,12 kgm.s-1, W)
By t = 6 s, bots bal X met bal Y (massa 0,07 kg) wat teen 5 m.s-1 wes beweeg. Gebruik inligting uit die
grafiek en die relevante momentumbeginsel om die snelheid van die bal Y na die botsing te bereken.
(1 m.s-1, O)