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M1 Questions
Any help, along with workin, would be greatly appreciated.
Many Thanks in advance.
Adam
1. Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 3ms-1 and the speed of B is 2ms-1. The speed of A immediately after the collision is 1.5ms-1. The direction of motion of A is unchanged as a result of the collision.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
b) The tension in the tow bar.
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
Many Thanks in advance.
Adam
1. Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 3ms-1 and the speed of B is 2ms-1. The speed of A immediately after the collision is 1.5ms-1. The direction of motion of A is unchanged as a result of the collision.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
b) The tension in the tow bar.
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
Scroll to see replies
adk
Any help, along with workin, would be greatly appreciated.
Many Thanks in advance.
Adam
1. Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 3ms-1 and the speed of B is 2ms-1. The speed of A immediately after the collision is 1.5ms-1. The direction of motion of A is unchanged as a result of the collision.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
b) The tension in the tow bar.
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
Many Thanks in advance.
Adam
1. Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 3ms-1 and the speed of B is 2ms-1. The speed of A immediately after the collision is 1.5ms-1. The direction of motion of A is unchanged as a result of the collision.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
b) The tension in the tow bar.
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
1a) m1u1 + m2u2 = m2v1 + m2v2
b) Ft = mv-mu
2a) F = ma
b) F = ma
adk
Thanks, but could do actually do it. I think I have the wrong answers!
Cheers.
Cheers.
What are you having problems with? The first one is exceedingly simple, literally a case of sticking the numbers into that equation. Are you sure you have the minus signs in the right places? Remember you need to take direction into account.
adk
Any help, along with workin, would be greatly appreciated.
Many Thanks in advance.
Adam
1. Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 3ms-1 and the speed of B is 2ms-1. The speed of A immediately after the collision is 1.5ms-1. The direction of motion of A is unchanged as a result of the collision.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
Many Thanks in advance.
Adam
1. Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 3ms-1 and the speed of B is 2ms-1. The speed of A immediately after the collision is 1.5ms-1. The direction of motion of A is unchanged as a result of the collision.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
a. CLM: m1u1 + m2u2 = m1v1 + m2v2
v2 = (m1u1 + m2u2 - m1v1)/m2
Taking A's velocity as positive: u1 = 3, m1 = 0.5, v1 = 1.5, m2 = 0.2, u2 = -2
v2 = (0.5*3 + 0.3*-2 - 0.5*1.5)/0.2
v2 = 6.75 ms^-1
b. Impulse = change in momentum
= m1v1 - m1u1
= 0.5(3 - 1.5)
= 0.75 Ns.
adk
1. Two small balls A and B have masses 0.5kg and 0.2kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 3ms-1 and the speed of B is 2ms-1. The speed of A immediately after the collision is 1.5ms-1. The direction of motion of A is unchanged as a result of the collision.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
b) The tension in the tow bar.
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
By modelling the balls as particles, find:
a) The speed of B immediately after the collision.
b) The magnitude of the impulse exerted on B in the collision.
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
b) The tension in the tow bar.
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
1. momentum before = (0.5*3)+(0.2*-2)
=(1.5)+(-0.4)
=1.1
momentum after = (0.5*1.5)+(0.2V)
=0.75+(0.2V)
momentum before = momentum after
1.1=0.75+0.2V
0.35=0.2V
V=1.75ms^-1
impulse = change in momentum
momentum of A after collision-momentum of A before collision
=0.75-1.5
=-0.75 on A
so 0.75 on B
2.resultant force =a*m
(2320-800-240)=(2000+1200)*a
1280=3200a
a=0.4ms^-2
resultant force on car = mass on car*acceleration of car
(2320-800-T)=0.4*2000
1520-T=800
T=-720N
a) The speed of B immediately after the collision.
m1u1 + m2u2 = m1v1 + m2v2
v2 = (m1u1 + m2u2 - m1v1)/m2 = (0.5*3 + 0.2*-2 - 0.5*1.5)/0.2 = 1.75ms^-1
b) The magnitude of the impulse exerted on B in the collision.
I = m(v-u) = 0.2(1.75--2) = 0.75Ns
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
F=ma
2320 - T - 800 = 2000*a
T - 240 = 1200a
2320 - 800 - 240 = 2000*a + 1200*a
1280 = 3200a
a = 0.4ms^-2
b) The tension in the tow bar.
T = 1200a + 240 = 720N
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
Assuming the resistances are the same as no coefficient of friction is given, we just need to add that tiny weight downwards to our existing equations:
F=ma
2320 - T - 800 - 100g = 2000*a
T - 240 - 60g = 1200a
2320 - 800 - 240 - 160g = 3200a
-288 = 3200a
a = -0.09ms^-2
Therefore their speed decreases.
m1u1 + m2u2 = m1v1 + m2v2
v2 = (m1u1 + m2u2 - m1v1)/m2 = (0.5*3 + 0.2*-2 - 0.5*1.5)/0.2 = 1.75ms^-1
b) The magnitude of the impulse exerted on B in the collision.
I = m(v-u) = 0.2(1.75--2) = 0.75Ns
2. A breakdown van of mass 2000kg is towing a car of mass 1200kg along a straight horizontal road. The two vehicles are joined by a tow bar which remains parallel to the road. The van and the car experience constant resistances to motion of magnitudes 800N and 240N respectively. There is a constant driving force acting on thevan of 2320N.
Find:
a) The magnitude of the acceleration of the van and car.
F=ma
2320 - T - 800 = 2000*a
T - 240 = 1200a
2320 - 800 - 240 = 2000*a + 1200*a
1280 = 3200a
a = 0.4ms^-2
b) The tension in the tow bar.
T = 1200a + 240 = 720N
The two vehicles come to a hill inclined at an angle of x to the horizontal, where sin x=1/20. The driving force and the resistance to motion are unchanged.
c) Find the magnitude of the acceleration of the van and the car as they move up the hill ans state whether their speed increases or decreases.
Assuming the resistances are the same as no coefficient of friction is given, we just need to add that tiny weight downwards to our existing equations:
F=ma
2320 - T - 800 - 100g = 2000*a
T - 240 - 60g = 1200a
2320 - 800 - 240 - 160g = 3200a
-288 = 3200a
a = -0.09ms^-2
Therefore their speed decreases.
imasillynarb
1a) m1u1 + m2u2 = m2v1 + m2v2
b) Ft = mv-mu
2a) F = ma
b) F = ma
b) Ft = mv-mu
2a) F = ma
b) F = ma
Yes, his textbook has those equations. I don't think stating them again is helpful.
mik1a
Nylex your first answer looks a bit high. I got 1.25ms^-1
I'll check for you mik1a.
Let the direction which ball A is moving in to be defined as the +ve direction, and the direction which ball B is moving is in to be defined as the -ve direction.
Momentum Prior Collision = (3 * 0.5) - (2 * 0.2) = 1.1 kgms-1
Momentum Prior Collision = Momentum After Collision.
Hence: Momentum After Collision = 1.1 = (1.5 * 0.5) + (0.2 * Velocity Of Ball B)
1.1 - (1.5 * 0.5) = 0.2 * (Velocity Of Ball B)
0.35 = 0.2 * (Velocity Of Ball B)
Velocity Of Ball B = 0.35/0.2
Velocity Of Ball B = 1.75 ms^-1
mik1a
Nylex your first answer looks a bit high. I got 1.25ms^-1
You put 1.75 ms^-1 as your answer in the post above, which is correct.
Nylex
a. CLM: m1u1 + m2u2 = m1v1 + m2v2
v2 = (m1u1 + m2u2 - m1v1)/m2
Taking A's velocity as positive: u1 = 3, m1 = 0.5, v1 = 1.5, m2 = 0.2, u2 = -2
v2 = (0.5*3 + 0.3*-2 - 0.5*1.5)/0.2
v2 = 6.75 ms^-1.
v2 = (m1u1 + m2u2 - m1v1)/m2
Taking A's velocity as positive: u1 = 3, m1 = 0.5, v1 = 1.5, m2 = 0.2, u2 = -2
v2 = (0.5*3 + 0.3*-2 - 0.5*1.5)/0.2
v2 = 6.75 ms^-1.
You made a mistake mate, check again.
mik1a
Old age 
You got the answer correct.
You put 1.75 ms^-1.
Nylex got a really high answer.
imasillynarb
Maybe he didnt know what ones to use?
Knowing which formula's to use isn't helpful in this instance. What other formula's are there in the momentum chapter? He has the formula's, just struggling to apply them to the question.
BTW: Nothing is easy unless you can do it. Remember that.
imasillynarb
Yeh ok bono, I think weve established the right answer, Im sure Nylex doesnt care that he did it wrong. End of thread? I think so.
We should have ended it after your first post in this thread.
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