Jimmy M.

asked • 04/02/22

Physics Questions


  1. A force of 120. N [E30.0N] and 80.0 N [E40S] act on an object.

a.   Draw a vector diagram of the two original vectors


b.   Find the resultant of the two vectors. (Trig or Component method)


c.   What would a third force need to be to make the net force zero?


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Jimmy M.

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04/02/22

Julius N.

Force 1 F1=120N [E30N] (30° North of East) Force 2 F2​=80.0N [E40S] (40° South of East) a. Vector Diagram To draw a vector diagram, follow these steps: Choose a reference point (like the origin). Draw Force1: From the origin, draw a line30° from the eastward axis (x-axis) moving upwards (north). This represents F1F1​. Draw Force2: From the same origin, draw a line going towards the east and then downwards at40° from the eastward (x-axis) moving downwards (south). This represents F2F2​. Label both vectors. The angle between them should be visually represented in your drawing, with both vectors originating from the same point. b. Finding the Resultant of the Two Vectors Using the Component Method: Resolve each vector into components: For F1F1​: F1x=120.0cos⁡(30∘)F1x​=120.0cos(30∘) F1y=120.0sin⁡(30∘)F1y​=120.0sin(30∘) For F2F2​: F2x=80.0cos⁡(0∘)=80.0F2x​=80.0cos(0∘)=80.0 F2y=−80.0sin⁡(40∘)F2y​=−80.0sin(40∘) (negative because it's south) Calculating the components: F1x=120.0×0.866≈103.92 NF1x​=120.0×0.866≈103.92N F1y=120.0×0.5=60.0 NF1y​=120.0×0.5=60.0N F2x=80.0F2x​=80.0 N - F2y=−80.0×0.643≈−51.44 NF2y​=−80.0×0.643≈−51.44N Resultant Components: Resultant in x-direction Rx=F1x+F2x=103.92+80=183.92 NRx​=F1x​+F2x​=103.92+80=183.92N Resultant in y-direction Ry=F1y+F2y=60.0−51.44≈8.56 NRy​=F1y​+F2y​=60.0−51.44≈8.56N Magnitude of Resultant Vector: R=Rx2+Ry2=(183.92)2+(8.56)2≈33829.38+73.18≈33895.37≈183.16 NR=Rx2​+Ry2​​=(183.92)2+(8.56)2​≈33829.38+73.18​≈33895.37​≈183.16N Direction of the Resultant: θ=tan⁡−1(RyRx)=tan⁡−1(8.56183.92)≈2.68∘ North of Eastθ=tan−1(Rx​Ry​​)=tan−1(183.928.56​)≈2.68∘North of East c. Third Force to Make Net Force ZeroTo find the third force F3F3​ needed to make the net force zero, it must equal the negative of the resultant vector: Magnitude of F3F3​: - The magnitude should be 183.16 N183.16N. Direction of F3F3​: It should point in the exact opposite direction of the resultant vector. Therefore, it will be: F3=183.16 NF3​=183.16N [E180.0° -2.68°] = [E180.0° +2.68°] = [E177.32°] (which means2.68° South of West). Summary- Vector Diagram: Draw F1F1​ and F2F2​ from a common point with the correct angles. Resultant Force: Approximately 183.16 N183.16N directed 2.68∘2.68∘ North of East. Third Force: Approximately 183.16 N183.16N directed 177.32∘177.32∘ [E177.32°] (2.68° South of West) to make the net force zero.
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10/29/24

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Arsen H. answered • 2d

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