Answer:
1) a = 17.3 m/s²
2) Fnet = 37.5 N
3) T = 16.2 N
Explanation:
1)
- When the bucket is at the top of the circle, there are two forces acting on it: the tension force (T) which pulls from the bucket, so it is directed downward, and the force due to gravity, that also points downward, so both forces add:
- [tex]F_{net} = T + m*g (1)[/tex]
- According to Newton's 2nd Law, this net force must be equal to the mass of the bucket, times the acceleration.
- Now, due to the bucket is moving around a circle, there must be a force that keeps the bucket following a circular trajectory, that is the centripetal force, and always aims toward the center of the circle.
- This force is not a new type of force, it's always the net force that aims toward the center.
- At the top of the circle, because as the tension force as gravity point downward, the centripetal force, is just this net force.
- It can be showed that the centripetal force can be written as follows:
[tex]F_{c} = m*a_{c} = m*\frac{v^{2}}{r} (2)[/tex]
- Since we have already said that a = ac (At the top of the circle), we can solve (1) for a, simplifying and replacing v and r by their values, as follows:
[tex]a = a_{c} = \frac{v^{2} }{r} = \frac{(4.42m/s)^{2} }{1.13m} = 17.3 m/s2 (3)[/tex]
2)
- Once we got the value of a, applying Newton's 2nd law, we can find easily the net force on the bucket at the top of the circle, as follows:
[tex]F_{net} = m*a = 2.17 kg * 17.3 m/s2 = 37.5 N (4)[/tex]
3)
- We have already said, that at the top of the circle, the net force is just the sum of the tension T and the force of gravity, as follows:
[tex]F_{net} = T + m*g = 37.5 N (5)[/tex]
- Replacing m and g by their values, we can solve (4) for T:
[tex]T = 37.5 N - m*g = 37.5 N - (2.17kg*98m/s2) \\ = 37.5 N - 21.3 N = 16.2 N (6)[/tex]
