Question

A Newton's cradle consists of several pendulum bobs made of steel balls that collide elastically to transfer energy and momentum to each other. If each of the two balls in the setup above has a length of 0.1 m, and the left ball is displaced 0.05 m from the resting position, how long will it take the left ball to collide with the right ball?

(a) π/20=0.157 s
(b) π/10=0.314 s
(c) π√2/10=0.444 s (
(d) π/5= 0.628 s

Answer 1

The time it takes for the left ball in a Newton's cradle to collide with the right ball can be calculated using the formula for the period of a simple pendulum. Using the length of the pendulum and the displacement of the left ball, we can determine the period and find the answer to the question. The correct answer is option (a) π/20 = 0.157 s.

Step-by-step explanation:

The time it takes for the left ball in a Newton's cradle to collide with the right ball can be determined using the formula for the period of a simple pendulum, which is given by:

T = 2π√(l/g)

where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. In this case, the length of each ball in the setup is 0.1 m, and the left ball is displaced 0.05 m from the resting position.

Using the formula, we can calculate the period:

T = 2π√((0.1 + 0.05)/g)

Since the acceleration due to gravity is approximately 9.8 m/s², we can plug in this value and solve for the period:

T = 2π√((0.15)/9.8) ≈ 0.157 s

Therefore, the correct answer is option (a) π/20 = 0.157 s.