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M1 maths as level
Hey any help would be great this question has me completly confused.
Particles A and B, of mass 2m and m respectively, are attached to the ends of a light inextensible string. THe string asses over a small pully fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclinded at 30 to the horizontal. THe string is in the same vertical plance as a line or greatest slope of the inclined planes. The coefficient of friction between A and the table is u. The particle A is released from rest and begins to move.
By writing down an equation of motion for each particle.
a) show that, while both particles move with the string taut, each paticle has an acceleration of magnitude 1/6(1-4u)g.
When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that u=0.2
b) find, in terms of h, the total distance moved by A.
For the model described above,
c) state two physical factors, APART from air resistace, which could be taken into account to make the model more realistic,
Particles A and B, of mass 2m and m respectively, are attached to the ends of a light inextensible string. THe string asses over a small pully fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclinded at 30 to the horizontal. THe string is in the same vertical plance as a line or greatest slope of the inclined planes. The coefficient of friction between A and the table is u. The particle A is released from rest and begins to move.
By writing down an equation of motion for each particle.
a) show that, while both particles move with the string taut, each paticle has an acceleration of magnitude 1/6(1-4u)g.
When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that u=0.2
b) find, in terms of h, the total distance moved by A.
For the model described above,
c) state two physical factors, APART from air resistace, which could be taken into account to make the model more realistic,
droid
Hey any help would be great this question has me completly confused.
Particles A and B, of mass 2m and m respectively, are attached to the ends of a light inextensible string. THe string asses over a small pully fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclinded at 30 to the horizontal. THe string is in the same vertical plance as a line or greatest slope of the inclined planes. The coefficient of friction between A and the table is u. The particle A is released from rest and begins to move.
By writing down an equation of motion for each particle.
a) show that, while both particles move with the string taut, each paticle has an acceleration of magnitude 1/6(1-4u)g.
When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that u=0.2
b) find, in terms of h, the total distance moved by A.
For the model described above,
c) state two physical factors, APART from air resistace, which could be taken into account to make the model more realistic,
Particles A and B, of mass 2m and m respectively, are attached to the ends of a light inextensible string. THe string asses over a small pully fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclinded at 30 to the horizontal. THe string is in the same vertical plance as a line or greatest slope of the inclined planes. The coefficient of friction between A and the table is u. The particle A is released from rest and begins to move.
By writing down an equation of motion for each particle.
a) show that, while both particles move with the string taut, each paticle has an acceleration of magnitude 1/6(1-4u)g.
When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that u=0.2
b) find, in terms of h, the total distance moved by A.
For the model described above,
c) state two physical factors, APART from air resistace, which could be taken into account to make the model more realistic,
I tried that question yesterday and couldnt do it either
droid
Hey any help would be great this question has me completly confused.
Particles A and B, of mass 2m and m respectively, are attached to the ends of a light inextensible string. THe string asses over a small pully fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclinded at 30 to the horizontal. THe string is in the same vertical plance as a line or greatest slope of the inclined planes. The coefficient of friction between A and the table is u. The particle A is released from rest and begins to move.
By writing down an equation of motion for each particle.
a) show that, while both particles move with the string taut, each paticle has an acceleration of magnitude 1/6(1-4u)g.
When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that u=0.2
b) find, in terms of h, the total distance moved by A.
For the model described above,
c) state two physical factors, APART from air resistace, which could be taken into account to make the model more realistic,
Particles A and B, of mass 2m and m respectively, are attached to the ends of a light inextensible string. THe string asses over a small pully fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclinded at 30 to the horizontal. THe string is in the same vertical plance as a line or greatest slope of the inclined planes. The coefficient of friction between A and the table is u. The particle A is released from rest and begins to move.
By writing down an equation of motion for each particle.
a) show that, while both particles move with the string taut, each paticle has an acceleration of magnitude 1/6(1-4u)g.
When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that u=0.2
b) find, in terms of h, the total distance moved by A.
For the model described above,
c) state two physical factors, APART from air resistace, which could be taken into account to make the model more realistic,
well C) is easy - add friction to the slope, and make the string elastic.
i'm still thinkign about the other two...
this is what i've worked out
if you resolve equations of motion for both A and B, you have for B
mgsin30 - T = ma and for A
T - 2mgu = 2ma.
rearrange both equations with T as subject:
T = mgsin30 - ma = 2ma + 2mgu
3ma = mgsin30 - 2mgu
3a = 1/2 g - 2gu
= 1/2 (g - 4gu)
so a = 1/6g (1 - 4gu)
Part A completed.
if you resolve equations of motion for both A and B, you have for B
mgsin30 - T = ma and for A
T - 2mgu = 2ma.
rearrange both equations with T as subject:
T = mgsin30 - ma = 2ma + 2mgu
3ma = mgsin30 - 2mgu
3a = 1/2 g - 2gu
= 1/2 (g - 4gu)
so a = 1/6g (1 - 4gu)
Part A completed.
part B. using suvat equations to get a final velocity of A just before the string breaks:
v^2 = u^2 + 2as.
u = 0, so v = square root (1/3(1-4u)gh).
so v = root (1/3 (1/5)gh) = root (1/15)gh
use this as the new u, with the new acceleration being -2gu = -.4g.
so 0^2 = (1/15)gh - .4gs
so 4gs = 2/3 gh
and 4s = 2/3 h
so distance moved after string breaking = 1/6 h
total distance = 7/6 h. is that correct?
v^2 = u^2 + 2as.
u = 0, so v = square root (1/3(1-4u)gh).
so v = root (1/3 (1/5)gh) = root (1/15)gh
use this as the new u, with the new acceleration being -2gu = -.4g.
so 0^2 = (1/15)gh - .4gs
so 4gs = 2/3 gh
and 4s = 2/3 h
so distance moved after string breaking = 1/6 h
total distance = 7/6 h. is that correct?
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