Understanding Pendulums, Fluid Pressure, and Molecular Forces

Understanding Pendulums

State the following terms:

• Pendulum
• Simple pendulum
• Conical pendulum

Ans: A tiny mass (assumed to be a point object and called a bob) connected to a long, flexible, massless, inextensible string, and suspended to a rigid support is called a pendulum.

If a tiny mass (assumed to be a point object and called a bob) connected to a long, flexible, massless, inextensible string, and suspended to a rigid support is made to oscillate in a single vertical plane, it is said to be a simple pendulum.

A tiny mass (assumed to be a point object and called a bob) connected to a long, flexible, massless, inextensible string, and suspended to a rigid support revolves in such a way that the string moves along the surface of a right circular cone of vertical axis and the point object performs a uniform horizontal circular motion. Such a system is called a conical pendulum.

Sphere of Death

1). This is a popular show in a circus. During this, a two-wheeler rider (or riders) undergo rounds inside a hollow sphere. 2) Starting with small horizontal circles, they eventually perform revolutions along vertical circles. 3) The dynamics of this vertical circular motion is the same as that of the point mass tied to the string, except that the force due to tension T is replaced by the normal reaction force N. 4). The linear speed is more for larger circles but angular speed (frequency) is more for smaller circles (while starting or stopping). This is as per the theory of a conical pendulum.

Defining Fluid Pressure

1). The normal force (F) exerted by a fluid at rest per unit surface area (A) of contact is called the pressure (P) of the fluid. P = F/A. 2). Pressure is a scalar quantity. Unit: Nm^-2 or Pascal (Pa) in the S.I. system 3). Pressure is also measured in the following units:

• 1 bar = 10⁵ Nm^-2
• 1 hectopascal (hPa) = 100 Pa
• 1 torr = 1 mm of mercury column

Dimensions: [L^-1M¹T^-2]

Molecular Attraction and Sphere of Influence

Define the following terms:

i.) Range of molecular attraction

ii.) Sphere of influence

Ans:

1). Range of molecular attraction: The maximum distance from a molecule up to which the molecular force is effective is called the range of molecular attraction.

ii.) Sphere of influence: An imaginary sphere with a molecule at its center and a radius equal to the molecular range is called the sphere of influence of the molecule. The intermolecular force is effective only within the sphere of influence.