Answer:
175.3 N
Explanation:
The motion of the ball is a uniform circular motion, therefore the net force on it must be equal to the centripetal force.
There are two forces acting on the ball at the lowest point of motion:
- The tension in the string, T , upward
- The weight of the ball, [tex]mg[/tex], downward
The net force (centripetal force) has the same direction as the tension (upward, towards the centre of the circular path), so we can write:
[tex]T-mg=m\frac{v^2}{r}[/tex]
where the term on the right is the expression for the centripetal force, and where:
T is the tension in the string
[tex]mg=100 N[/tex] is the weight of the ball
[tex]m=\frac{mg}{g}=\frac{100}{9.8}=10.2 kg[/tex] is the mass of the ball
v = 5.7 m/s is the speed of the ball at the lowest point
r = 4.4 m is the length of the rope, so the radius of the circle
Solving for T, we find the tension in the string:
[tex]T=mg+m\frac{v^2}{r}=(100)+(10.2)\frac{5.7^2}{4.4}=175.3 N[/tex]
