A 35.0 kg girl swings on a swingset. At the bottom of the swing’s path, she feels as though she weighs 435 N. What is the value of the tension in the swing’s ropes at the bottom of the swing’s path?
Question
A 35.0 kg girl swings on a swingset. At the bottom of the swing’s path, she feels as though she weighs 435 N. What is the value of the tension in the swing’s ropes at the bottom of the swing’s path?
Solution
To solve this problem, we need to understand that the feeling of "weight" the girl experiences is actually the net force acting on her. This net force is the result of both the gravitational force pulling her downwards and the tension in the swing's ropes pulling her upwards.
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First, let's calculate the gravitational force acting on the girl. This is given by the equation F = m*g, where m is the mass and g is the acceleration due to gravity. On Earth, g is approximately 9.8 m/s². So, the gravitational force is F = 35.0 kg * 9.8 m/s² = 343 N.
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The net force the girl feels at the bottom of the swing is 435 N. This is the result of the gravitational force and the tension in the ropes. Since these forces are in opposite directions, we can say that the net force is the tension in the ropes minus the gravitational force.
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Therefore, we can set up the following equation to solve for the tension (T): 435 N = T - 343 N.
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Solving for T, we get T = 435 N + 343 N = 778 N.
So, the tension in the swing's ropes at the bottom of the swing's path is 778 N.
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