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[tex]\tt{\huge{\blue{Explanation:}}}[/tex]
The centripetal force exerted on an object is given by
[tex]\boxed{F_{c} = \frac{mv^{2}}{r}}[/tex]
where:
Fc = centripetal force
m = mass
v = velocity
r = radius
[tex]\tt{\huge{\red{Solution:}}}[/tex]
Note: The height of the vertical circular track is equal to the diameter of the track
[tex]r = \dfrac{d}{2}[/tex]
[tex]r = \dfrac{\text{12 m}}{2}[/tex]
r = 6 m
[tex]F_{c} = \dfrac{mv^{2}}{r}[/tex]
[tex]F_{c} = \dfrac{(\text{280 kg})(\text{40 m/s})^{2}}{\text{6 m}}[/tex]
[tex]\boxed{F_{c} = \text{74.666.67 N}}[/tex]
Therefore, the centripetal force of the motorcycle is 74.666.67 N.
[tex]\\[/tex]
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