Mechanics AS question
Discussion
Ok so i've got a bit of a tricky question to do i'd be greatful for any solutions:
A particle rests in limiting equilibrium on a plan inclined at 30' to the horizontal. Determine the acceleration with which the particle will slide down the plane when the angle is changed to 40'.
Thanks
A particle rests in limiting equilibrium on a plan inclined at 30' to the horizontal. Determine the acceleration with which the particle will slide down the plane when the angle is changed to 40'.
Thanks
Don't know butas no-one has answered so far I'll take a guess, (and it really is a guess).
At 30 degrees it is at rest and gravity is 9.6 m/s2
The remaining angle to 90 degrees are 60
60/90 is 66.66%
Thus 66.66% of 9.6 m/s2 is 6.4 m/s2
Very simplistic and I think entirely wrong but at least I had what I believe is a semi-intelligent stab at it!
At 30 degrees it is at rest and gravity is 9.6 m/s2
The remaining angle to 90 degrees are 60
60/90 is 66.66%
Thus 66.66% of 9.6 m/s2 is 6.4 m/s2
Very simplistic and I think entirely wrong but at least I had what I believe is a semi-intelligent stab at it!
How does a particle rest in limiting equilibrium... unless there's friction. So you need to work out the coefficient of friction then apply that for the change in angle to gravity acting in the direction of the plane.
But it's been about 20 years since I did applied mathematics so I may be talking s
t.
But it's been about 20 years since I did applied mathematics so I may be talking s
t.I think (bearing in mind my A levels were 20 years ago) that the friction force on the point of slipping or slipping is the same (which is complete bks but that's not the point here)
So at 30 degree friction is equal and opposite to the mass * sin30
The difference in force will be mass*(sin40 - sin30)
So the acceleration will be
mass*(sin40 - sin30)/mass = sin40 - sin30
Although a more complete answer would be to calculate the coeficient of friction as the resistive force of the friction will be less at the higher angle.
>> AS has now been mentioned
ks but that's not the point here)So at 30 degree friction is equal and opposite to the mass * sin30
The difference in force will be mass*(sin40 - sin30)
So the acceleration will be
mass*(sin40 - sin30)/mass = sin40 - sin30
Although a more complete answer would be to calculate the coeficient of friction as the resistive force of the friction will be less at the higher angle.
>> AS has now been mentioned
Edited by Incorrigible on Wednesday 25th March 21:34
) A-levels, too.ShadownINja said:
How does a particle rest in limiting equilibrium... unless there's friction. So you need to work out the coefficient of friction then apply that for the change in angle to gravity acting in the direction of the plane.
But there are not any values for any forces / coefficient of friction. If F=ma and F= m g sin 30 than maybe i can cancel out mass or something???Edited by motordave on Wednesday 25th March 21:38
No coeff of F required, no mass of particle required.
Particle at rest therefore F due to friction up the slope is equal to F due to gravity down the slope.
Accel due to gravity down slope = 9.81 * sin30 = 4.9
Now tip slope up to 40 deg.
Accel due to gravity down slope = 9.81 * sin40 = 6.3
Therefore
The particle will accelerate down the 40 deg slope at 1.4ms^-2.
(i.e. what incorrigible said)
If you write out F=ma for the forces along the slope, you'll see that F and m cancel out, leaving you just working with a (which is what I expect the question wants).
HTH
Particle at rest therefore F due to friction up the slope is equal to F due to gravity down the slope.
Accel due to gravity down slope = 9.81 * sin30 = 4.9
Now tip slope up to 40 deg.
Accel due to gravity down slope = 9.81 * sin40 = 6.3
Therefore
The particle will accelerate down the 40 deg slope at 1.4ms^-2.
(i.e. what incorrigible said)
If you write out F=ma for the forces along the slope, you'll see that F and m cancel out, leaving you just working with a (which is what I expect the question wants).
HTH
filski666 said:
since when did accel due to gravity reduce to 9.6m/s^2? - When I was at school it was 9.81 - has something happened to the planet I missed?
If you go to the equator it's only 9.79ms^-2 (I think). That's why the French send their satellites to French Guiana - saves on fuel.
motordave said:
Thanks Incorrigble but 2 things. a) i assume when you say sin40-sin30 you mean 9.8sin40-9.8sin30 and b)my text book says the answer is 1.97 but that gives 1.39ms^-2
If you already know the answer, why the fk are you asking us 
Anyway I think you need to take into account the difference in friction in the 2 angles
Is that enough of a hint.....
Sorry we had to work it out ourselves when I were a lad blah blah all fields etc
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