Forces on a Slope with Friction 20Nov09

1
Forces on a Slope with Friction 20-Nov-09
2
F
F is the force created by friction
2kg
X
Force X to push up the slope so that the particle
is on the point of moving
200
? 0.2
2g cos20
Xsin20
Xcos20
200
2g
F ?2gcos20 ? Xsin20
200
NB Friction acts against direction of movement
2g sin20
Xcos20 2gsin20 F Xcos20 2gsin20 ?2gcos20
?Xsin20 0.94X 6.70 3.68 0.07X 0.87X
10.38 ? X 11.9 Newtons
3
F
F is the force created by friction
2kg
X
Force X to stop the particle sliding down the
slope
200
? 0.2
2g cos20
Xsin20
Xcos20
200
2g
F ?2gcos20 ? Xsin20
200
NB Friction acts against direction of movement
2g sin20
Xcos20 F 2gsin20 ? Xcos20 2gsin20 -
F Xcos20 2gsin20 (?2gcos20 ?Xsin20) 0.94X
6.70 - 3.68 - 0.07X 1.01X 3.02 ? X 3 Newtons
4
250
Force X to push up the slope so that the particle
is on the point of moving
X
F
Xcos25
F is the force created by friction
2kg
450
? 0.2
2g cos20
Xsin25
NB Friction acts against direction of movement
200
2g
F ?2gcos20 ? Xcos25
200
2g sin20
Xsin25 2gsin20 F ? Xcos20 2gsin20 -
F Xsin25 2gsin20 ?2gcos20 ?Xcos25 0.42X
6.70 3.68 0.18X 0.24X 10.38 ? X 43.3
Newtons
5
250
X
F
Force X to stop the particle sliding down the
slope
Xcos25
F is the force created by friction
2kg
450
? 0.2
2g cos20
Xsin25
200
NB Friction acts against direction of movement
2g
F ?2gcos20 ? Xcos25
200
2g sin20
Xsin25 F 2gsin20 Xsin25 2gsin20 (?2gcos20
?Xcos25) 0.42X 6.70 - 3.68 - 0.18X 0.6X
3.02 ? X 5 Newtons
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M1 Jan 06
A parcel of weight 10 N lies on a rough plane
inclined at an angle of 30? to the horizontal.
A horizontal force of magnitude P Newtons acts on
the parcel, as shown in Figure 2. The parcel is
in equilibrium and on the point of slipping up
the plane. The normal reaction of the plane on
the parcel is 18 N. The coefficient of friction
between the parcel and the plane is ?.
Find (a) the value of P,
(4) (b) the value of ?.
(5) The horizontal force is removed. (c) Determi
ne whether or not the parcel moves.
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Pcos30
F
Psin30
Friction force F ? ?Pcos30
10cos30
10N
10sin30
The normal reaction of the plane is 18 ? 18
10cos30 Psin30 ? 18 8.66 0.5P ? P 18.7 N
Since the block is on the point of moving Pcos30
10sin30 ?10cos30 18.7 (?sin30) 16.2 5
8.6? 9.4? ? 18? 11.2 ? ? 0.62