In the figure, a ball hangs by a very light string. What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A, which is 1.0 m above the bottom of the swing?

A) 2.2 m/s
B) 3.1 m/s
C) 4.4 m/s
D) 4.9 m/s

Question

In the figure, a ball hangs by a very light string. What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A, which is 1.0 m above the bottom of the swing?

A) 2.2 m/s 
B) 3.1 m/s 
C) 4.4 m/s 
D) 4.9 m/s

Quizplus · Accepted Answer

The total mechanical energy of the ball will remain constant throughout the swing, neglecting air resistance. At the bottom of the swing (point B), all of the energy is in the form of kinetic energy, so we can use conservation of energy to find the minimum speed required for the ball to reach point A.
At point A, all of the energy will be in the form of potential energy, so we can write:
$mgh = \frac{1}{2}mv^2$
where $m$ is the mass of the ball, $h$ is the height of point A above point B, and $v$ is the speed of the ball at point B.
Solving for $v$, we get:
$v = \sqrt{2gh} = \sqrt{2\cdot9.81\cdot1} \approx 4.4 	ext{ m/s}$
Therefore, the minimum speed required for the ball to reach point A is 4.4 m/s. The answer is (C).

In the Figure, a Ball Hangs by a Very Light