Work, Energy, and Power Quiz

The scalar product of two vectors A and B, denoted as A.B, is defined as the product of their magnitudes and the cosine of the angle between them. It is represented as A.B = AB cos θ, where θ is the angle between vectors A and B.

The dot product of two vectors can be calculated by multiplying the corresponding components of the vectors and adding the results.

The scalar product provides a measure of how much two vectors are aligned with each other. A larger dot product (A.B) indicates a smaller angle between them, implying more alignment.

The result of the dot product of two vectors is a scalar quantity. This means it only has magnitude and no direction.

The dot product of two perpendicular vectors is zero. Since cos(90°) = 0, the entire dot product becomes zero.

The change in an object's kinetic energy is equal to the total work done on the object by the net force.

The force acting on an object, multiplied by the distance the object moves in the direction of the force.

A force acting at an angle to the direction of motion does less work than a force acting parallel to the motion.

Work done by a force is zero when the displacement of the object is zero, even if the force is large.

Work is done on an object when a force causes the object to move, and work is done by an object when the object exerts a force that causes another object to move.

The work done by the spring force in a complete cycle (returning to the starting position) is zero.

The spring force depends only on the displacement from the equilibrium position (Fs = -kx), and work done by the spring force is independent of the path, only depending on the start and end positions.

The potential energy of a spring is proportional to the square of the displacement from its equilibrium position (V(x) = (kx^2)/2).

In a spring-mass system, the total mechanical energy (potential + kinetic) remains constant. As the potential energy increases, the kinetic energy decreases, and vice-versa.

In a collision, the kinetic energy of the colliding object is transformed into potential energy stored in the spring. The maximum compression of the spring occurs when all kinetic energy is converted to potential energy.

The spring force is inversely proportional to the displacement from its equilibrium position, meaning as displacement increases, the force decreases, and vice versa.

Work done by a spring force is calculated as -1/2 * k * xm^2, where k is the spring constant, and xm is the displacement from its equilibrium position.

The potential energy stored in a spring is directly proportional to the square of the displacement from its equilibrium position.

The work done by a spring force only depends on the initial and final positions, not the path taken.

The total mechanical energy of a system remains constant even if the potential and kinetic energies change. This principle is demonstrated by the conservative nature of the spring force.