Question

You have two identical strings of the same length. At the lowest point in their paths, Ball A moves three times as fast as Ball B. Which ball will swing to a higher point, and how much higher will it go?

A) Ball A will swing to a higher point, three times higher.
B) Ball B will swing to a higher point, three times higher.
C) Ball A and Ball B will swing to the same height.
D) The relationship between their speeds and heights is not provided.

Answer 1

Ball A, moving three times faster than Ball B at the bottom of the swing, will swing to a higher point because its kinetic energy is nine times greater. However, Ball A will not reach a height three times greater than Ball B since the relationship between height and velocity is quadratic, not linear.

Step-by-step explanation:

The potential energy of a swinging ball is converted into kinetic energy at the lowest point of its swing, and then back into potential energy as it rises to the highest point of its swing. Given that Ball A moves three times as fast as Ball B at the lowest point, the kinetic energy of Ball A is greater. The kinetic energy is proportional to the square of the velocity (K = 0.5 * m * v2), so if Ball A's velocity is three times greater, its kinetic energy will be nine times greater. This increased kinetic energy will convert back into potential energy, allowing Ball A to reach a higher point.

However, the relationship between final heights is not linear with respect to velocity. Since the potential energy related to height (PE = m * g * h) must equal the kinetic energy at the lowest point, we can determine that Ball A will swing higher, but not three times higher.

The accurate choice is A) Ball A will swing to a higher point, but the amount higher is not three times; it is determined by the square of the velocity ratio.