CLOZE Simple Statics 1 A weight of 80 N hangs at the end of a cord knotted to two other cords making angles of 45 degrees and 60 degrees with the horizontal.  The other ends of these two cords are tied to fixed supports.  Calculate the tension in all three cords.

Tension in Cord 1: {#1}

 Tension in Cord 2:  {#2}

Tension in Cord 3:  {#3}


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3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mn>41</mn><mo>.</mo><mn>42</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mn>58</mn><mo>.</mo><mn>57</mn></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-8)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> CLOZE Simple Statics 2 A weight of 80 N hangs at the end of a cord knotted to two other cords making angles of 30 degrees and 60 degrees with the horizontal.  The other ends of these two cords are tied to fixed supports.  Calculate the tension in all three cords.



Tension in Cord 1: {#1}

 Tension in Cord 2:  {#2}

Tension in Cord 3:  {#3}


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3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mn>34</mn><mo>.</mo><mn>6</mn></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-8)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> CLOZE Simple Statics 3 A tightrope walker of mass #M kilograms moves to the center of the wire, which deflects at an angle of #A degrees with the horizontal on each side.  Calculate the tension in the wire in Newtons.


Tension in Wire: {#1}



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1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>(</mo><mi>M</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>sin</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>*</mo><mi>A</mi><mo>/</mo><mn>180</mn><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">15</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> CLOZE Simple Statics 4 A tightrope walker of mass #M kilograms moves to the center of the wire, which deflects at an angle of #A degrees with the horizontal on each side.  Calculate the tension in the wire in Newtons.


Tension in Wire: {#1}



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1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mo>(</mo><mi>M</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>sin</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>*</mo><mi>A</mi><mo>/</mo><mn>180</mn><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">15</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> CLOZE Simple Statics 5 A child weighing #W Newtons sits on a swing attached to an overhead support by a chain of negligible weight.  The child is drawn aside and held in equilibrium by a horizontal force of #F Newtons.  Calculate the angle that the supporting chain makes with the vertical and the tension in the chain.


Tension in the Chain: {#1}

Angle of Chain with Vertical in Degrees:  {#2}



]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>F</mi><mo>/</mo><mi>W</mi><mo>)</mo><mo>*</mo><mn>180</mn><mo>/</mo><mn>3</mn><mo>.</mo><mn>1415</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>F</mi><mo>/</mo><mi>sin</mi><mo>(</mo><mi>A</mi><mo>*</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>/</mo><mn>180</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">5</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> CLOZE Simple Statics 6 Calculate the tension in the cords shown below in the diagram, which support a weight of #C Newtons.

Angle A:  #A Degrees

Angle B:  #B Degrees

Weight C:  #C Newtons



Tension in Cord 1 in Newtons: {#1}

Tension in Cord 2 in Newtons: {#2}

Tension in Cord 3 in Newtons: {#3}



]]> 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3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>55</mn><mo>,</mo><mn>75</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>55</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>C</mi><mo>/</mo><mo>(</mo><mi>sin</mi><mo>(</mo><mi>A</mi><mo>*</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>/</mo><mn>180</mn><mo>)</mo><mo>*</mo><mi>tan</mi><mo>(</mo><mi>B</mi><mo>*</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>/</mo><mn>180</mn><mo>)</mo><mo>-</mo><mi>cos</mi><mo>(</mo><mi>A</mi><mo>*</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>/</mo><mn>180</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mo>=</mo><mo>(</mo><mi>T</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>A</mi><mo>*</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>/</mo><mn>180</mn><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>cos</mi><mo>(</mo><mi>B</mi><mo>*</mo><mn>3</mn><mo>.</mo><mn>1415</mn><mo>/</mo><mn>180</mn><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">5</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> CLOZE Simple Statics 7 To pull an automobile from a ditch a rope #A m long is tied to the automobile and a post that is #B m away.  A force of #C Newtons is applied to the center of the rope as shown in the diagram.  Calculate the tension in the rope.

Distance A:  #A meters

Distance B:  #B meters

Force C:  #C Newtons


Tension in the Rope:: {#1}


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1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>3000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mo>(</mo><mi>B</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>/</mo><mo>(</mo><mi>A</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>C</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>Q</mi><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">5</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question>