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antoniya [11.8K]
3 years ago
14

Dx= 7.14m and Dy = -7.55m What is the direction and magnitude of the vector

Physics
1 answer:
KengaRu [80]3 years ago
5 0

The Magnitude of the Vector is 10.39m and the direction of the vector is - 46.7°.

<u>Explanation:</u>

GIven dx=7.14m and dy= -7.55m,

The Magnitude of the Vector=\sqrt{dy^{2} +dx^{2} }

Magnitude d= \sqrt{(7.14)^{2} +(-7.55)^{2} } .

                  d=\sqrt{50.97+57}

                  d=\sqrt{107.98}

                  d= 10.39m.

Direction Ф = tan^{-1}\frac{dy}{dx}

                      =tan^{-1} \frac{-7.55}{7.14}      

                      = tan^{-1}(-1.06)

                Ф    = - 46.7°.

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A vertical spring has a length of 0.25 m when a 0.175 kg mass hangs from it, and a length of 0.775 m when a 2.075 kg mass hangs
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Answer:

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Explanation:

Using Hooke's law;

F = Ke where F is the weight of the object = mass of the object in kg * acceleration due to gravity in m/s^2 and k if the force constant of the spring in N/m and e is the extension of the spring which original length of the spring - new length after extension in meters

For the first body, m*g = K * (0.25- li)

Where li is the initial length of the spring

0.175*9.81 = k(0.25-li)

1.72 = k(0.25-li) as equation 1

For the second body, m *g = K* ( 0.775-li)

2.075*9.81 = k (0.775-li) equation 2

20.36 = k(0.775-li)

Make li subject of the formula;

li = 0.775 - 20.36/k

Substitute for li in equation 1

1.72 = k(0.25- (0.775 - 20.36/k))

1.72 = k ( 0.25 - 0.775 + 20.36/k)

Open the bracket with k

1.72 = 0.25k - 0.775k + 20.36 (since k cancel k)

Collect the like terms:

1.72 - 20.36 = - 0.525k

- 18.64 = -0.525k

Divide both side by -0.525

-18.64/-0.525 = -0.525/-0.525k

K = 35.5N/m

B) substitute for k in using

li = 0.775 - 20.36/k

li = 0.775 - 20.36/35.5

li = 0.775 - 0.574

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li = 0.201 * 100 centimeters = 20.1cm

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