3. Other Forces - Revision history

Ian at 13:48, 18 March 2009

Ian — Wed, 18 Mar 2009 13:48:08 GMT

←Older revision		Revision as of 13:48, 18 March 2009
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	Considering the 12 kg mass, which		Considering the 12 kg mass, which
	is also in equilibrium gives,		is also in equilibrium gives,
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		+	[[Image:TF3.3c.GIF]]


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	Now consider the block on the plane, which is also in equilibrium.		Now consider the block on the plane, which is also in equilibrium.
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		+
		+	[[Image:TF3.3d.GIF]]

	Vertically:		Vertically:
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-		+	[[Image:TF3.4a.GIF]]


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		+	[[Image:TF3.4b.GIF]]

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		+	<math>{{R}_{1}}={{W}_{1}}</math>

		+	[[Image:TF3.4c.GIF]]

-
-
-
-
-
-
-	<math>{{R}_{1}}={{W}_{1}}</math>

	<math>\begin{align}		<math>\begin{align}
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	'''Solution'''		'''Solution'''
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		+	[[Image:TF3.5.GIF]]
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	In this case		In this case

Ian at 13:26, 18 March 2009

Ian — Wed, 18 Mar 2009 13:26:38 GMT

←Older revision		Revision as of 13:26, 18 March 2009
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	on the crate the forces will be		on the crate the forces will be
	as shown in the diagram.		as shown in the diagram.
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		+	[[Image:TF3.2b.GIF]]

	In this case F will take the value that		In this case F will take the value that
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	(c) The forces are now as shown in		(c) The forces are now as shown in
	the diagram.		the diagram.
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		+	[[Image:TF3.2c.GIF]]

	A force of 400 N would be needed to		A force of 400 N would be needed to
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	'''[[Example 3.3]]'''		'''[[Example 3.3]]'''
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		+

	The diagram shows a block that is at rest on a horizontal plane. Two light ropes, attached to the block pass over pulleys and are also attached to masses as shown in the diagram. Find the tension in each rope and the friction between the block and the plane and an inequality that the coefficient of friction must satisfy.		The diagram shows a block that is at rest on a horizontal plane. Two light ropes, attached to the block pass over pulleys and are also attached to masses as shown in the diagram. Find the tension in each rope and the friction between the block and the plane and an inequality that the coefficient of friction must satisfy.
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		+	[[Image:TF3.3a.GIF]]


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	is in equilibrium gives,		is in equilibrium gives,

		+	[[Image:TF3.3b.GIF]]

	<math>{{T}_{1}}=78.4\text{ N}</math>		<math>{{T}_{1}}=78.4\text{ N}</math>

Ian at 12:48, 18 March 2009

Ian — Wed, 18 Mar 2009 12:48:47 GMT

←Older revision		Revision as of 12:48, 18 March 2009
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	In all of the cases described above, the		In all of the cases described above, the
	same vertical forces act on the crate.		same vertical forces act on the crate.
		+
		+	[[Image:TF3.2a.GIF]]

	So in all of these cases R = 490, since		So in all of these cases R = 490, since

Ian: New page: Tensions exist in ropes and act along rope towards the centre. Tensions and thrusts exist in rods. Friction exists where rough surfaces are in contact. $F\le \mu R$ The ...

Ian — Mon, 16 Mar 2009 11:41:09 GMT

New page: Tensions exist in ropes and act along rope towards the centre. Tensions and thrusts exist in rods. Friction exists where rough surfaces are in contact. <math>F\le \mu R</math> The ...

New page

Tensions exist in ropes and act along rope towards the centre.

Tensions and thrusts exist in rods.

Friction exists where rough surfaces are in contact.

<math>F\le \mu R</math>

The coefficient of friction is ..
The normal reaction force is R.

'''[[Example 3.1]]'''

Draw a diagram to show the forces acting on a ladder leaning against a wall.

'''Solution'''

Note it has been assumed that the wall is vertical and the ground horizontal

[[Image:TF3.1.gif]]

'''[[Example 3.2]]'''

The coefficient of friction between a crate, of mass 50 kg, and the floor is 0.7. Find the magnitude of the friction force acting on the crate if it is on a horizontal surface and;
(a) no horizontal force acts on the crate,
(b) a horizontal force of 80 N acts on the crate,
(c) A horizontal force of 400 N acts on the crate.

'''Solution'''

In all of the cases described above, the
same vertical forces act on the crate.

So in all of these cases R = 490, since
the vertical forces are in equilibrium.

Using the friction inequality gives,
`
<math>\begin{align}
& F\le \mu R \\
& F\le 0.7\times 490 \\
& F\le 343 \\
\end{align}</math>

So the maximum friction force in this situation is 343 N.

(a) If no horizontal force acts on the crate there will be no friction force.

(b) If a horizontal force of 80 N acts
on the crate the forces will be
as shown in the diagram.

In this case F will take the value that
is needed to produce equilibrium,
provided that it is less than 343 N.

In this case F = 80 N, as this produces equilibrium, but is less than the maximum of 343 N.

(c) The forces are now as shown in
the diagram.

A force of 400 N would be needed to
produce equilibrium. As this is greater
than the maximum friction, F takes its
maximum value of 343 N.

F = 343 N

In this case there is a resultant force of 57 N to the right.

'''[[Example 3.3]]'''

The diagram shows a block that is at rest on a horizontal plane. Two light ropes, attached to the block pass over pulleys and are also attached to masses as shown in the diagram. Find the tension in each rope and the friction between the block and the plane and an inequality that the coefficient of friction must satisfy.

'''Solution'''

Considering the 8 kg mass, which
is in equilibrium gives,

<math>{{T}_{1}}=78.4\text{ N}</math>

Considering the 12 kg mass, which
is also in equilibrium gives,

<math>{{T}_{2}}=117.6\text{ N}</math>

Now consider the block on the plane, which is also in equilibrium.

Vertically:

<math>R=196</math>

Horizontally

<math>\begin{align}
& {{T}_{1}}+F={{T}_{2}} \\
& F={{T}_{2}}-{{T}_{1}} \\
\end{align}</math>

Using the values for the two tensions gives,

<math>\begin{align}
& F=117.6-78.4 \\
& =39.2
\end{align}</math>

Using the friction inequlity
<math>F\le \mu R</math>
gives,

<math>\begin{align}
& 39.2\le \mu \times 196 \\
& \mu \ge \frac{39.2}{196}=0.2 \\
\end{align}</math>

'''[[Example 3.4]]'''

Two boxes are placed on top of each other on a horizontal surface as shown in the diagram. The top box has mass 5 kg and the lower box has mass
10 kg. Draw diagrams to show the forces acting on each box and calculate the magnitude of each of these forces.

'''Solution'''

<math>{{R}_{1}}={{W}_{1}}</math>

<math>\begin{align}
& {{R}_{2}}={{R}_{1}}+{{W}_{2}} \\
& ={{W}_{1}}+{{W}_{2}}
\end{align}</math>

'''[[Example 3.5]]'''

A crate has mass 250 kg and rests on a horizontal surface. The coefficient of friction between the crate and the surface is 0.6. A horizontal force of magnitude P N is applied to the crate. What is the resultant force on the box if:
(a) P = 1200 N (b) P = 1700 N

'''Solution'''

In this case
<math>R=W=250\times 9.8=2450\text{ N}</math>
.

Hence using
<math>F\le \mu R</math>
gives,

<math>\begin{align}
& F\le 0.6\times 2450 \\
& F\le 1470\text{ N} \\
\end{align}</math>

(a) In this case
<math>F=1200</math>
and the resultant force is zero.

(b) In this case
<math>F=1470</math>
and the resultant force is 230 N in the direction of P.

3. Other Forces - Revision history

Ian at 13:48, 18 March 2009

Ian at 13:26, 18 March 2009

Ian at 12:48, 18 March 2009

Ian: New page: Tensions exist in ropes and act along rope towards the centre. Tensions and thrusts exist in rods. Friction exists where rough surfaces are in contact. F\le \mu R The ...

Ian: New page: Tensions exist in ropes and act along rope towards the centre. Tensions and thrusts exist in rods. Friction exists where rough surfaces are in contact. $F\le \mu R$ The ...