Question

A “Newton’s Cradle” is a toy consisting of a series of balls suspended on strings, as shown in the drawing. It is a fine example of elastic collisions. Design a Newton’s Cradle subject to the following conditions: ? The leftmost ball has a mass of 0.2kg. The rest have a mass of 0.1kg. ? You want the rightmost ball to rise to a final height of exactly 0.5m. ? You can choose the following: • The starting height of the leftmost ball. • How many balls rise on the right-hand side after the collision.

Answer 1

The kinetic energy is conserved in every collision.

So, for the right-most ball to rise up by 0.5m, the change from kinetic energy to potential energy will be:

U = mg(0.5)

from conservation of energy, this would have been the kinetic energy of the 0.2 kg ball just before striking the other balls.

therefore, initial height to which the 0.2kg ball must be raised should be:

h = (0.1)g(0.5)/(0.2 x g) = 0.25 m.

with this, only the last ball rises. Alternatively, if the 0.2kg ball is raised to 0.5m (twice the initial height) instead, the number of balls rising to 0.5m will then be 2.