Two trees are located 6 m apart. A tightrope is stretched between them. A girl i

Question

Two trees are located 6 m apart. A tightrope is stretched between them. A girl is balancing herself on the rope, 2 m away from the tree to the right (and, correspondingly, 4 m away from the tree to the left). The tension in the 2 m-long section of the rope is 3500 N. The rope sags by 15 cm. Angle between the 2 m section of the rope and the horizontal is a) 2.15 degree b) 3.57 degree c)4.29 degree d)7.13 degree X-component of tension in 2 m side? a) 3500 N b) 3490 N c) 1520 N d) 262 N e) 131N Y-component of tension in 2 m side? a) 3500 N b) 3490 N c) 1520 N d) 262 N e) 131N X-component of tension in 4 m side? a) -3500 N b) -3490 N c) -1520 N d) -262 N e) 131N Angle between the 4 m section of the rope and the horizontal? a) 2.15 degree b)3.57 degree c)4.29 degree d)7.13 degree Y-component of tension in 4 m side? a) 3500 N b) 3490N c) 1520N d) 262N e)131 N Weight of the girl? a)131 N b) 262 N c) 393 N d)465 N e)47 kg

Explanation / Answer

here,

the angle between the 2 m section and the horizontal , theta = arctan(0.15/2) = c) 4.29 degree

X - component of tension , Tx = T * cos(theta)

Tx = 3500 * cos(4.29) = 3490 N

so answer is b) 3490 N

Y component of tension , Ty = T * sin(theta)

Ty = 261.8 N = d) 262 N

X component of tension , Tx' = - Tx = - 3490 N

  

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