In the figure,a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight.The string is 2 m long.If the weight is released with zero initial velocity from a horizontal position,its angular momentum (in kg⋅m²/s)at the lowest point of its path relative to the center of the circle is approximately A)40 B)10 C)30 D)20 E)50

Question

Quizplus · Accepted Answer

At the lowest point of its path, the weight will have the maximum speed, which can be calculated using conservation of energy:

Potential energy at top = Kinetic energy at lowest point
mgh = (1/2)mv^2

where m is the mass of the weight, g is the acceleration due to gravity, h is the height of the top position (which is the same as the length of the string), and v is the speed of the weight at the lowest point.

Solving for v, we get:

v = √(2gh)

Substituting the given values, we get:

v = √(2 x 9.8 x 2) = 6.26 m/s

The angular momentum of the weight can be calculated as:

L = mvr

where r is the radius of the circle (which is the same as the length of the string).

Substituting the given values, we get:

L = 1.6 x 6.26 x 2 = 20.03 kg⋅m²/s

Rounding this to the nearest integer, we get 20. Therefore, the best choice is D.

In the Figure,a 1