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Answer :
Final answer:
To calculate the child’s speed at the lowest point, we used the total tension in the swing chains and equated it with the sum of gravitational force and centripetal force. After performing the calculation, we found that the child’s speed is approximately 3.04 m/s.
Explanation:
The question involves a calculation based on principles of physics, specifically centripetal force and kinetic energy. To find the child’s speed at the lowest point of the swing, we first recognize that the total tension in the chains is the sum of the force due to gravity and the centripetal force necessary to keep the child moving in a circular path.
At the lowest point, the tension in each chain (T) must support the child’s weight (W = m*g, where m = mass of the child and g = acceleration due to gravity) plus provide the centripetal force (Fc) to keep the child moving in a circle. This condition can be expressed as 2T = W + Fc. Since Fc = m*v²/r, where v is the speed of the child and r is the radius of swing, we can solve for v.
Substituting and rearranging the terms, we get v = √[(2T/m) - g]*r. Plugging in the given values, 2*159 N for 2T, 27 kg for m, 9.8 m/s² for g, and 4 m for r, we can calculate the child’s speed at the lowest point. After calculating, we find that the speed (v) is approximately 3.04 m/s.
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