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Mechanics: dynamics of a particle moving in a straight line/plane
Hi, I'm in a bit of a rut with mechanics - could any of you help me with these questions?
1) a particle rests in limiting equilibrium on a plane inclined at 30° to the horizontal. Determine the acceleration with which the particle will slide down the plane when the angle of inclination is increased to 40°.
2) a particle of mass 2 kg rests in limiting equilibrium on a plane inclined at 25° to the horizontal. The angle of inclination is decreased to 20° and a force of magnitude 20N is applied up a line of greatest slope. Find the particle's acceleration. (I managed to get the acceleration but was lost from that point on...) When the particle has been moving for 2 seconds the force is removed. Determine the further distance the particle will move up the plane.
Thank you so much if you can help, I've been spending ages and I feel like I'm getting nowhere
1) a particle rests in limiting equilibrium on a plane inclined at 30° to the horizontal. Determine the acceleration with which the particle will slide down the plane when the angle of inclination is increased to 40°.
2) a particle of mass 2 kg rests in limiting equilibrium on a plane inclined at 25° to the horizontal. The angle of inclination is decreased to 20° and a force of magnitude 20N is applied up a line of greatest slope. Find the particle's acceleration. (I managed to get the acceleration but was lost from that point on...) When the particle has been moving for 2 seconds the force is removed. Determine the further distance the particle will move up the plane.
Thank you so much if you can help, I've been spending ages and I feel like I'm getting nowhere
yapster
Hi, I'm in a bit of a rut with mechanics - could any of you help me with these questions?
1) a particle rests in limiting equilibrium on a plane inclined at 30° to the horizontal. Determine the acceleration with which the particle will slide down the plane when the angle of inclination is increased to 40°.
1) a particle rests in limiting equilibrium on a plane inclined at 30° to the horizontal. Determine the acceleration with which the particle will slide down the plane when the angle of inclination is increased to 40°.
Resolving perpendicular => R=mg cos 30
Resolving parallel => Friction(F)= mg sin 30
limiting equilibriam=> F=uR (where u=mue)
u=F/R = mgsin30/mgcos30 = tan30
Now angle increase to 40:
Resolving Perpendicular => R=mgcos40
F=uR we know u=tan30 and R=mgcos40
.:. F=tan30(mgcos40)
Resolving motion parallel using F=ma:
mgsin40 - mgtan30cos40 =ma
gsin40-gtan30cos40=a
g(sin40-tan30cos40)=a
a=1.965
Sorry but just cant be arsed to do the second one.
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