Tension - Revision history

Hanran14: /* Simple */

2019-10-19T18:37:29Z

Simple

← Older revision		Revision as of 14:37, 19 October 2019
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	::[[File:TSimpleFBD.jpeg\|200px]]		::[[File:TSimpleFBD.jpeg\|200px]]

	::Now, we will ~~right~~ down the forces acting on the box:		::Now, we will write down the forces acting on the box:

	:::<math>F_g = mg = 2 \times 9.81 = 19.62 \ \text{Newtons}</math>		:::<math>F_g = mg = 2 \times 9.81 = 19.62 \ \text{Newtons}</math>

Laurence12799: /* Difficult */

2019-07-04T00:42:07Z

Difficult

← Older revision		Revision as of 20:42, 3 July 2019
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	::We will start by drawing a free body diagram for each block:		::We will start by drawing a free body diagram for each block:

	:::~~'''INSERT DRAWING'''~~		::[[File:TDifficultFBD1.jpeg\|200px]] [[File:TDifficultFBD2.jpeg\|182px]] [[File:TDifficultFBD3.jpeg\|235px]]

	::Note that since all the strings are held tight, all the blocks will have the same acceleration along the axis perpendicular to inclined planes (<math>a_x</math>)		::Note that since all the strings are held tight, all the blocks will have the same acceleration along the axis perpendicular to inclined planes (<math>a_x</math>)

Laurence12799: /* Difficult */

2019-07-04T00:36:32Z

Difficult

← Older revision		Revision as of 20:36, 3 July 2019
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	===Difficult===		===Difficult===
	[[File:TDifficultSketch.jpeg\|400px\|right]]		[[File:TDifficultSketch.jpeg\|400px\|right\|thumb\|A diagram of the difficult example]]
	A block of mass <math>M_1</math> (block 1) is positioned on a ramp that is in the shape of an inclined plane. The angle between the horizontal and the inclined plane is <math>\theta = 45^\text{o}</math>. Block 1 has a string of negligible mass attached to it. This string loops over a pulley, and then connects to a block of mass <math>M_2</math> (block 2), which is sitting on another inclined plane, whose angle to the horizontal is <math>\phi = 20^\text{o}</math>. Block 2 has another string of negligible mass attached to its opposite side. This string connects to another block of mass <math>M_3</math> (block 3), who is on the same inclined plane as block 2. All strings are held tightly between the blocks.		A block of mass <math>M_1</math> (block 1) is positioned on a ramp that is in the shape of an inclined plane. The angle between the horizontal and the inclined plane is <math>\theta = 45^\text{o}</math>. Block 1 has a string of negligible mass attached to it. This string loops over a pulley, and then connects to a block of mass <math>M_2</math> (block 2), which is sitting on another inclined plane, whose angle to the horizontal is <math>\phi = 20^\text{o}</math>. Block 2 has another string of negligible mass attached to its opposite side. This string connects to another block of mass <math>M_3</math> (block 3), who is on the same inclined plane as block 2. All strings are held tightly between the blocks.

Laurence12799: /* Difficult */

2019-07-04T00:36:06Z

Difficult

← Older revision		Revision as of 20:36, 3 July 2019
Line 248:		Line 248:

	===Difficult===		===Difficult===
	:~~::'''INSERT DRAWING'''~~		[[File:TDifficultSketch.jpeg\|400px\|right]]
	A block of mass <math>M_1</math> (block 1) is positioned on a ramp that is in the shape of an inclined plane. The angle between the horizontal and the inclined plane is <math>\theta = 45^\text{o}</math>. Block 1 has a string of negligible mass attached to it. This string loops over a pulley, and then connects to a block of mass <math>M_2</math> (block 2), which is sitting on another inclined plane, whose angle to the horizontal is <math>\phi = 20^\text{o}</math>. Block 2 has another string of negligible mass attached to its opposite side. This string connects to another block of mass <math>M_3</math> (block 3), who is on the same inclined plane as block 2. All strings are held tightly between the blocks.		A block of mass <math>M_1</math> (block 1) is positioned on a ramp that is in the shape of an inclined plane. The angle between the horizontal and the inclined plane is <math>\theta = 45^\text{o}</math>. Block 1 has a string of negligible mass attached to it. This string loops over a pulley, and then connects to a block of mass <math>M_2</math> (block 2), which is sitting on another inclined plane, whose angle to the horizontal is <math>\phi = 20^\text{o}</math>. Block 2 has another string of negligible mass attached to its opposite side. This string connects to another block of mass <math>M_3</math> (block 3), who is on the same inclined plane as block 2. All strings are held tightly between the blocks.

Laurence12799: /* Simple */

2019-07-04T00:33:32Z

Simple

← Older revision		Revision as of 20:33, 3 July 2019
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	===Simple===		===Simple===
	[[File:TSimpleSketch.jpeg\| 400px\|right]]		[[File:TSimpleSketch.jpeg\| 400px\|right\|thumb\|A diagram for the simple example]]

	A <math>2 \ \text{kg}</math> toy box is being dragged by a child. To do so, the child is pulling on a rope that is tied to the toy box. This rope makes an angle of <math>\theta = 60^\text{o}</math> with the horizontal. There is a frictional force between the box and the floor with a coefficient of kinetic friction <math>\mu_k = 0.2</math>. With the x-axis as the horizontal shown in the image, and the y-axis as the vertical shown in the image, the toy box gains an acceleration of:		A <math>2 \ \text{kg}</math> toy box is being dragged by a child. To do so, the child is pulling on a rope that is tied to the toy box. This rope makes an angle of <math>\theta = 60^\text{o}</math> with the horizontal. There is a frictional force between the box and the floor with a coefficient of kinetic friction <math>\mu_k = 0.2</math>. With the x-axis as the horizontal shown in the image, and the y-axis as the vertical shown in the image, the toy box gains an acceleration of:

Laurence12799: /* Middling */

2019-07-04T00:32:09Z

Middling

← Older revision		Revision as of 20:32, 3 July 2019
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	===Middling===		===Middling===
	[[File:TMiddlingSketch.jpeg\|300px\|right]]		[[File:TMiddlingSketch.jpeg\|300px\|right\|thumb\|A diagram for the middling example]]
	A box with mass <math>m</math> hangs in a static state from two ropes. One rope is attached to the ceiling with an angle <math>\theta = 30^\text{o}</math> to the horizontal. The other rope, which pulls the box to the left, is along the horizontal (to the left of the box) and attached to a wall. Refer to the diagram for any confusion.		A box with mass <math>m</math> hangs in a static state from two ropes. One rope is attached to the ceiling with an angle <math>\theta = 30^\text{o}</math> to the horizontal. The other rope, which pulls the box to the left, is along the horizontal (to the left of the box) and attached to a wall. Refer to the diagram for any confusion.

Laurence12799: /* Middling */

2019-07-04T00:31:27Z

Middling

← Older revision		Revision as of 20:31, 3 July 2019
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	===Middling===		===Middling===
			[[File:TMiddlingSketch.jpeg\|300px\|right]]
	A box with mass <math>m</math> hangs in a static state from two ropes. One rope is attached to the ceiling with an angle <math>\theta = 30^\text{o}</math> to the horizontal. The other rope, which pulls the box to the left, is along the horizontal (to the left of the box) and attached to a wall. Refer to the diagram for any confusion.		A box with mass <math>m</math> hangs in a static state from two ropes. One rope is attached to the ceiling with an angle <math>\theta = 30^\text{o}</math> to the horizontal. The other rope, which pulls the box to the left, is along the horizontal (to the left of the box) and attached to a wall. Refer to the diagram for any confusion.

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	::First, as always, we should draw a free body diagram:		::First, as always, we should draw a free body diagram:

	:::~~'''INSERT DRAWING'''~~		::[[File:TMiddlingFBD.jpeg\|200px]]

	::Referring to the free body diagram, we see the main forces acting on the box are:		::Referring to the free body diagram, we see the main forces acting on the box are:

Laurence12799: /* Simple */

2019-07-04T00:26:29Z

Simple

← Older revision		Revision as of 20:26, 3 July 2019
Line 143:		Line 143:
	::First, we start by drawing a free body diagram for the toy box. The main forces acting on the box are the gravitational force, normal force, frictional force, and tension force.		::First, we start by drawing a free body diagram for the toy box. The main forces acting on the box are the gravitational force, normal force, frictional force, and tension force.

	[[File:TSimpleFBD.jpeg\|200px~~\|left~~]]		::[[File:TSimpleFBD.jpeg\|200px]]

	::Now, we will right down the forces acting on the box:		::Now, we will right down the forces acting on the box:

Laurence12799: /* Simple */

2019-07-04T00:26:03Z

Simple

← Older revision		Revision as of 20:26, 3 July 2019
Line 143:		Line 143:
	::First, we start by drawing a free body diagram for the toy box. The main forces acting on the box are the gravitational force, normal force, frictional force, and tension force.		::First, we start by drawing a free body diagram for the toy box. The main forces acting on the box are the gravitational force, normal force, frictional force, and tension force.

	:~~::'''INSERT FREE BODY DIAGRAM HERE'''~~		[[File:TSimpleFBD.jpeg\|200px\|left]]

	::Now, we will right down the forces acting on the box:		::Now, we will right down the forces acting on the box:

Laurence12799: /* Simple */

2019-07-04T00:23:40Z

Simple

← Older revision		Revision as of 20:23, 3 July 2019
Line 133:		Line 133:

	===Simple===		===Simple===
	[[File:TSimpleSketch.jpeg\| ~~300px~~\|right]]		[[File:TSimpleSketch.jpeg\| 400px\|right]]

	A <math>2 \ \text{kg}</math> toy box is being dragged by a child. To do so, the child is pulling on a rope that is tied to the toy box. This rope makes an angle of <math>\theta = 60^\text{o}</math> with the horizontal. There is a frictional force between the box and the floor with a coefficient of kinetic friction <math>\mu_k = 0.2</math>. With the x-axis as the horizontal shown in the image, and the y-axis as the vertical shown in the image, the toy box gains an acceleration of:		A <math>2 \ \text{kg}</math> toy box is being dragged by a child. To do so, the child is pulling on a rope that is tied to the toy box. This rope makes an angle of <math>\theta = 60^\text{o}</math> with the horizontal. There is a frictional force between the box and the floor with a coefficient of kinetic friction <math>\mu_k = 0.2</math>. With the x-axis as the horizontal shown in the image, and the y-axis as the vertical shown in the image, the toy box gains an acceleration of: