The string in the figure is 50 cm long.When the ball is released from rest, it swings along the dotted arc.How fast is it going at the lowest point in its swing?
A)2.0 m/s
B)2.2 m/s
C)3.1 m/s
D)4.4 m/s
E)6.0 m/s

Question

The string in the figure is 50 cm long.When the ball is released from rest, it swings along the dotted arc.How fast is it going at the lowest point in its swing? 
A)2.0 m/s 
B)2.2 m/s 
C)3.1 m/s 
D)4.4 m/s 
E)6.0 m/s

Quizplus · Accepted Answer

At the highest point, all of the gravitational potential energy is converted to kinetic energy.
$$mgh=\frac{1}{2}mv^2$$
$$v=\sqrt{2gh}$$
At the lowest point, all of the gravitational potential energy is converted to kinetic energy.
$$\frac{1}{2}mv^2=mgh$$
$$v=\sqrt{2gh}$$
Using $h=0.5(50	ext{ cm})=0.5	ext{ m}$ and $g=9.81	ext{ m/s}^2$, we get:
$$v=\sqrt{2	imes9.81	imes0.5}=3.1	ext{ m/s}$$
Therefore, the answer is C.

The String in the Figure Is 50 Cm Long