QuestionMay 7, 2025

A child on a spinning playground ride is 0.36 m from the center of the ride The centripetal force on the child is 19 N. What is the mass of the child if the child has a tangential speed of 0.54m/s 3.7 kg 13 kg 23 kg 79 kg

A child on a spinning playground ride is 0.36 m from the center of the ride The centripetal force on the child is 19 N. What is the mass of the child if the child has a tangential speed of 0.54m/s 3.7 kg 13 kg 23 kg 79 kg
A child on a spinning playground ride is 0.36 m from the center of the ride The centripetal force on the child is 19 N. What is the mass of the child if the child has a tangential speed of 0.54m/s 3.7 kg 13 kg 23 kg 79 kg

Solution
4.4(345 votes)

Answer

23 kg Explanation 1. Use the centripetal force formula The formula for centripetal force is F_c = \frac{mv^2}{r}. Rearrange to solve for mass m: m = \frac{F_c \cdot r}{v^2}. 2. Substitute values into the formula Given: F_c = 19 \, \text{N}, r = 0.36 \, \text{m}, and v = 0.54 \, \text{m/s}. Substitute: m = \frac{19 \cdot 0.36}{(0.54)^2} = \frac{6.84}{0.2916} \approx 23.45 \, \text{kg}. 3. Match the closest option The closest option is **23 kg**.

Explanation

1. Use the centripetal force formula<br /> The formula for centripetal force is $F_c = \frac{mv^2}{r}$. Rearrange to solve for mass $m$: <br />$m = \frac{F_c \cdot r}{v^2}$.<br /><br />2. Substitute values into the formula<br /> Given: $F_c = 19 \, \text{N}$, $r = 0.36 \, \text{m}$, and $v = 0.54 \, \text{m/s}$. <br />Substitute: <br />$m = \frac{19 \cdot 0.36}{(0.54)^2} = \frac{6.84}{0.2916} \approx 23.45 \, \text{kg}$.<br /><br />3. Match the closest option<br /> The closest option is **23 kg**.
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