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 t
he 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
1 answer:
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.
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.
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