General Physics 1 Quiz for Federal University Lokoja

Force is defined as mass times acceleration, which can be expressed using the dimensions of mass (m), length (l), and time (t). In the International System of Units (SI), force is measured in newtons (N), where 1 N is equivalent to 1 kg·m/s². Thus, the dimensional formula for force is derived as follows: mass (m) has the dimension of [m], length (l) has the dimension of [l], and acceleration (a) is expressed as [l][t^-2]. Combining these gives the overall dimension of force as [ml1t−2].

Mass is a scalar quantity because it has magnitude but no direction. Unlike force, velocity, and acceleration, which are vector quantities and require both magnitude and direction for their complete description, mass simply quantifies the amount of matter in an object. It is expressed in units such as kilograms or grams and does not change based on the object's position or movement in space.

Gravitational potential energy (PE) is the energy an object possesses due to its position in a gravitational field. The formula PE = mgh expresses this relationship, where 'm' is the mass of the object, 'g' is the acceleration due to gravity, and 'h' is the height above a reference point. This formula indicates that the potential energy increases with greater mass and height, reflecting how much work is required to lift the object against the force of gravity.

Newton's second law establishes the relationship between force, mass, and acceleration. It states that the acceleration of an object is determined by the net force acting on it, meaning that greater forces will result in greater acceleration, while the mass of the object resists this acceleration. This principle can be summarized by the equation F = ma, where F is the net force, m is the mass, and a is the acceleration. Thus, it highlights how force influences motion, making it fundamental to understanding dynamics in physics.

Work is defined as the energy transferred when a force is applied over a distance. In the International System of Units (SI), the unit of work is the joule. One joule is equivalent to the work done when a force of one newton moves an object one meter in the direction of the force. This relationship highlights the connection between force, distance, and energy, making the joule the standard unit for measuring work in physics.

In an elastic collision, both momentum and kinetic energy are conserved. Momentum conservation arises from the principle of conservation of linear momentum, which states that in a closed system, the total momentum before the collision equals the total momentum after. Similarly, in elastic collisions, the total kinetic energy of the system is also conserved, meaning that the sum of the kinetic energies of the colliding objects before the collision equals the sum after. This distinguishes elastic collisions from inelastic ones, where kinetic energy is not conserved.

The moment of inertia of a point mass is calculated using the formula \( I = mr^2 \), where \( m \) is the mass of the object and \( r \) is the distance from the axis of rotation. This formula reflects how the distribution of mass relative to the axis affects rotational inertia; the farther the mass is from the axis, the greater the moment of inertia. Thus, it captures both the mass and its position, indicating that increasing either will increase the resistance to rotational motion.

Escape velocity is the minimum speed needed for an object to break free from a celestial body's gravitational pull without further propulsion. For Earth, this velocity is approximately 11.2 km/s. This value is derived from the gravitational force and the mass of the Earth, taking into account the radius from the center of the Earth to the point of escape. At this speed, an object can overcome Earth's gravity and enter space.

The principle of conservation of momentum states that in a closed system, where no external forces are acting, the total momentum before any interaction (such as a collision) will equal the total momentum after the interaction. This means that the momentum is conserved, regardless of whether the collision is elastic or inelastic. This principle is fundamental in physics, as it applies to various scenarios, including collisions and explosions, ensuring that the total momentum remains unchanged in the absence of external influences.

Angular momentum of a particle is defined as the product of its moment of inertia (I) and its angular velocity (ω). This relationship captures how the distribution of mass (moment of inertia) and the rate of rotation (angular velocity) contribute to the overall rotational motion of the particle. In contrast, the other options represent linear momentum (mv), rotational inertia (mr²), and torque (Fτ), which are not directly related to angular momentum in its standard form. Thus, Iω is the appropriate expression for angular momentum.