Answer:
A) r = 20.0 m
B) T = 41.6 s
C) = 6.1 m/s²
Explanation:
A)
- The centripetal acceleration is the one that explains that even though the cyclist is moving at a constant speed, his velocity is changing the direction all the time, keeping him around a circle.
- This acceleration can be expressed as follows:
[tex]a_{c} =\frac{v^{2}}{r} = \frac{(10.0m/s)^{2}}{r} = 5.00 m/s2 (1)[/tex]
[tex]r = \frac{v^{2}}{a_{c} } = \frac{(10.0m/s)^{2}}{5.00m/s2} = 20.0 m (2)[/tex]
B)
- We can apply the definition of linear velocity, remembering that the period is the time needed to complete an entire circle (T).
- The arc around a circumference (the distance traveled) , is just 2*π*r, so applying the definition of linear velocity, we can write the following expression:
[tex]v = \frac{\Delta s}{\Delta t} = \frac{2*\pi*r}{T} (3)[/tex]
[tex]T = \frac{\Delta s}{v} = \frac{2*\pi*r}{v} = \frac{2*\pi*265m}{40.0m/s} =41.6 s (4)[/tex]
C)
- The centripetal acceleration of the car from B) can be found as follows:
[tex]a_{c} =\frac{v^{2}}{r} = \frac{(40.0m/s)^{2}}{265m} = 6.1 m/s2 (5)[/tex]
