Answer:
The magnitude of the child's centripetal acceleration is 2.53 [tex]\frac{m}{s^{2} }[/tex]
Explanation:
Centripetal acceleration is calculated with the following formula:
[tex]a_{c} =w^{2} *r[/tex]
[tex]a_{c}[/tex]= Centripetal acceleration ([tex]\frac{m}{s^{2} }[/tex])
w= speed angular ([tex]\frac{rad}{s}[/tex])
r= radius of the curve(m)
Calculation of the angular velocity of the child
[tex]w=\frac{1 revolution}{8.04s}[/tex] equation (1)
[tex]1revolution=2*\pi[/tex], then, in the equation(1):
[tex]w=\frac{2*\pi }{8.04}[/tex]
[tex]w=0.78\frac{rad}{s}[/tex]
Calculation of the child's centripetal acceleration
We replaced [tex]w=0.78\frac{rad}{s}[/tex]and [tex]r=4.17m[/tex]in the equation (1)
[tex]a_{c} =0.78^{2} *4.17[/tex]
[tex]a_{c} =0.6084*4.17[/tex]
[tex]a_{c} =2.53\frac{rad}{s^{2} }[/tex]
Answer: The magnitude of the child's centripetal acceleration is [tex]2.53\frac{m}{s^{2} }[/tex]
