Question

How long does it take a child on a swing to complete one swing if her center of gravity is (4.00 m) below the pivot?

a) (1.00 s)
b) (1.57 s)
c) (2.00 s)
d) (2.51 s)

Answer 1

The period of a child's swing with a 4.00 m long pendulum is approximately 4.008 seconds, utilizing the simple pendulum period formula T = 2π√(L/g). However, none of the provided options match this value, indicating a possible error in the options.

Step-by-step explanation:

The question is asking us to calculate the period of a child's swing when her center of gravity is 4.00 meters below the pivot. To find the period of the swing (T), we can use the formula for the period of a simple pendulum:

T = 2π√(L/g)

Where L is the length of the pendulum (4.00 m in this case) and g is the acceleration due to gravity (approximately 9.81 m/s²). Using this formula, we can compute as follows:

T = 2π√(4.00 m / 9.81 m/s²)

T = 2π√(0.4079 s²)

T = 2π√(0.6387 s)

T = 2 * 3.1416 * 0.6387 s

T = 4.008 s approximately

However, none of the provided options (1.00 s, 1.57 s, 2.00 s, 2.51 s) match the calculated value. As such, it appears there may be an error in the options provided. For a pendulum with a length of 4.00 m, the period is expected to be around 4.008 seconds, assuming no air resistance or other forms of friction.