a child on a spinning playground ride is 0.36 m from the center of the ride. the centripetal force on the…
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 0.54 m/s?\no 3.7 kg\no 13 kg\no 23 kg\no 79 kg
Answer
Explanation:
Step1: Recall centripetal - force formula
The centripetal - force formula is $F = \frac{mv^{2}}{r}$, where $F$ is the centripetal force, $m$ is the mass, $v$ is the tangential speed, and $r$ is the radius. We need to solve for $m$.
Step2: Rearrange the formula for $m$
Rearranging $F=\frac{mv^{2}}{r}$ gives $m=\frac{Fr}{v^{2}}$.
Step3: Substitute the given values
We are given that $F = 19\ N$, $r = 0.36\ m$, and $v = 0.54\ m/s$. Substituting these values into the formula $m=\frac{Fr}{v^{2}}$, we get $m=\frac{19\times0.36}{(0.54)^{2}}$. First, calculate the numerator: $19\times0.36 = 6.84$. Then, calculate the denominator: $(0.54)^{2}=0.2916$. Now, divide: $m=\frac{6.84}{0.2916}\approx23\ kg$.
Answer:
23 kg