Physics, 07.07.2019 21:30 figueroajorge8291

Dee is on a swing in the playground. the chains are 2.5 m long, and the tension in each chain is 450 n when dee is 55 cm above the lowest point of her swing. tension is a vector directed along the chain, measured in newtons, abbreviated n. what are the horizontal and vertical components of the tension at this point in the swing

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Answer from: joel4676

Refer to the diagram shown below.

From the geometry, obtain
x = 2.5 - 0.55 = 1.95 m
cos θ = 1.95/2.5 = 0.78
θ = cos⁻¹ 0.78 = 38.74°

From the free body diagram, the tension in the chain is 450 N.
F is the centripetal force,
W is Dee's weight.

The components of the tension are
Horizontal component = 450 sin(38.74°) = 281.6 N, acting left.
Vertical component = 450 cos(38.74°) = 351.0 N, acting upward.

Answers:
Horizontal: 281.6, acting left.
Vertical: 351.0 N, acting upward.
Dee is on a swing in the playground. the chains are 2.5 m long, and the tension in each chain is 450

Dee is on a swing in the playground. the chains are 2.5 m long, and the tension in each chain is 450

Answer from: machapman6594

The horizontal and vertical components of the tension at the given point in the swing are 281.6 N and 351 N respectively.

Given data:

The length of chain is, L = 2.5 m.

The magnitude of tension on each chain is, T = 450 N.

Distance above the lowest point is, d = 55 cm = 0.55 m.

In problem, first we need to obtain the angle of inclination made by string horizontally.

So, the angle inclined by the string with horizontal is given as,

$cos \theta =\dfrac{L-d}{L}\\\\cos \theta =\dfrac{2.5-0.55}{2.5}\\\\\theta = cos^{-1}(\dfrac{1.95}{2.5})\\\\\theta=38.74^{\circ}$

Now, the horizontal component of tension force acting on the string is,

$T_{H}=T \times cos \theta\\T_{H}=450 \times cos 38.74\\T_{H}=281.6 \;\rm N$

And, the vertical component of tension force acting on the string is,

$T_{V}=T \times sin \theta\\T_{V}=450 \times sin 38.74\\T_{V}=351 \;\rm N$

Thus, the horizontal and vertical components of the tension at this point in the swing are 281.6 N and 351 N respectively.

Learn more about the component of forces here:

link

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Dee is on a swing in the playground. the chains are 2.5 m long, and the tension in each chain is 450...

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