M1 Connected particles questions - will rep

Hi please help with the following:

1) A car of mass 1000kg exerts a driving force of 2.2kN when pulling a caravan of mass 500kg along a horizontal road. The car and caravan increase speed from rest to 4ms^-1 while travelling 16m. Given that teh resistances on the car and caravan are proportional to their masses find these resistances and the tension in the tow bar.

2)Two particles P and Q of masses 3kg and 6 kg respectively are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley. The system is released from rest with both masses a distance of 2m above a horizontal floor. Find how long it takes for particle Q to hit the floor.
I've done this bit - 1.11s and its right according to teh book
But then it says assuming particle P does not reach the pulley find its greatest height above hte floor.

3) Two partciles P and Q of masses 7kg and 2kg respectively are connected by a light inextensible string. Particle P rests on a smooth tablr. The string passes over a smooth pulley fixed at the edge of the table and Q is hanging freely. The system is released from rest. Find the accleration of P.

Thanks all in advance for your help and effort and i do appreciate the time spent!

Regards, Asad

Reply 1

Malik

12

asadtamimi

Hi please help with the following:

1) A car of mass 1000kg exerts a driving force of 2.2kN when pulling a caravan of mass 500kg along a horizontal road. The car and caravan increase speed from rest to 4ms^-1 while travelling 16m. Given that teh resistances on the car and caravan are proportional to their masses find these resistances and the tension in the tow bar.

v²=u²+2as
a=(v²-u²)/2s
a= 4²/(2x16) = 16/32= 0.5

Using F=ma;

Car:
2200–T–1000k= 1000×0.5
T+1000k= 1700 (1)

Caravan:
T–500k = 500 × 0.5
T–500k = 250 (2)

(1)-(2) => 1500k=1450 .:. k=29/30

Sub k into (2)

T=250+500(29/30)
T=733 ^1/3N

Reply 2

Malik

12

asadtamimi

2)Two particles P and Q of masses 3kg and 6 kg respectively are attached to the ends of a light inextensible string. The string passes over a smooth fixed pulley. The system is released from rest with both masses a distance of 2m above a horizontal floor. Find how long it takes for particle Q to hit the floor.
I've done this bit - 1.11s and its right according to teh book
But then it says assuming particle P does not reach the pulley find its greatest height above hte floor.

Jumping straight to the second part then.

Speed of Q
v²=u²+2as
...=0+ 4(g/3)
v=2√(g/3)
.:. speed of P up the plane must be the same.

P:
v²=u²+2as
where u=2√(g/3) v=0 a=-g
0=(4g/3) - 2gs
s= (4g/3)/2g = 2/3 m

P already starts 2m above, then moves further 2m. And finally goes an extra 2/3m after Q reaches floor.

Height=2+2+2/3
.........=4 ^2/3 m

Reply 3

Malik

12

asadtamimi

3) Two partciles P and Q of masses 7kg and 2kg respectively are connected by a light inextensible string. Particle P rests on a smooth tablr. The string passes over a smooth pulley fixed at the edge of the table and Q is hanging freely. The system is released from rest. Find the accleration of P.

Using F=ma:
For P:
T=7a (1)
For Q:
2g-T=2a (2)
(1)+(2)=> 2g=9a .:. a=2g/9

Reply 4

asadtamimi

OP

13

Malik

v²=u²+2as
a=(v²-u²)/2s
a= 4²/(2x16) = 16/32= 0.5

Using F=ma;

Car:
2200–T–1000k= 1000×0.5
T+1000k= 1700 (1)

Caravan:
T–500k = 500 × 0.5
T–500k = 250 (2)

(1)-(2) => 1500k=1450 .:. k=29/30

Sub k into (2)

T=250+500(29/30)
T=733 ^1/3N

Thanks a lot but for this question - the back of the book contain 3 answers - 966 2/3, 483 1/2 and 733 1/3 how come?

Reply 5

Malik

12

asadtamimi

Thanks a lot but for this question - the back of the book contain 3 answers - 966 2/3, 483 1/2 and 733 1/3 how come?

Sorry didnt read question fully it wants to know the two resistances and the tension. The 733 is the tension.

Resistance for Car= 1000k= 1000(29/30)= 966 2/3 N
Resistance for van= 500k =500(29/30)= 483 1/3 N

Reply 6

asadtamimi

OP

13

Excellent - thanks a lot - are these the sort of stuff that tend to come up in exams?

Reply 7

Malik

12

They do like to chuck around the word porpotional a lot just to make sure you understand.

In the second question if the pully was on the end of a rough slope then it would be more like exam question.

The third question is a bit of a joke though.