Quiz

Figure 4.5 Schematic representation of an elastic head-on collision between two particles: (a) before collision and (b) after collision.

Find v1f and v2f.

Quick Quiz 1 A block of mass m is projected across a horizontal surface with an initial speed v. It slides until it stops due to the friction force between the block and the surface. The same block is now projected across the horizontal surface with an initial speed 2v. When the block has come to rest, how does the distance from the projection point compare to that in the first case? (a) It is the same. (b) It is twice as large. (c) It is four times as large. (d) The relationship cannot be determined.

Quick Quiz 2 A car and a large truck traveling at the same speed make a head-on collision and stick together. Which vehicle experiences the larger change in the magnitude of momentum? (a) the car (b) the truck (c) The change in the magnitude of momentum is the same for both. (d) impossible to determine.

Course of lectures «Contemporary Physics: Part1»

Lecture №6

Oscillatory Motion.

Wave Motion.

Periodic motion is motion of an object that regularly repeats—the object returns to a given position after a fixed time interval. With a little thought, we can identify several types of periodic motion in everyday life. Your car returns to the driveway each afternoon. You return to the dinner table each night to eat. A bumped chandelier swings back and forth, returning to the same position at a regular rate. The Earth returns to the same position in its orbit around the Sun each year, resulting in the variation among the four seasons. The Moon returns to the same relationship with the Earth and the Sun, resulting in a full Moon approximately once a month.

A special kindof periodic motion occurs in mechanical systems when the force acting on an object is proportional to the position of the object relative to some equilibrium position. If this force is always directed toward the equilibrium position, the motion is called simple harmonic motion.

Motion of an Object

Attached to a Spring

Figure 4.16 A block attached to a spring moving on a frictionless surface. (a) When the block is displaced to the right of equilibrium (x > 0), the force exerted by the spring acts to the left. (b) When the block is at its equilibrium position (x = 0), the force exerted by the spring is zero. (c) When the block is displaced to the left of equilibrium (x < 0), the force exerted by the spring acts to the right.

Hooke’s law, a restoring force

(4.25) (4.26)

Motion of an Object

Attached to a Spring

(4.27)

Simple harmonic motion. An object moves with simple harmonic motion whenever its acceleration is proportional to its position and is oppositely directed to the displacement from equilibrium.

Mathematical Representation

of Simple Harmonic Motion

(4.28)

(4.29)

(4.30)

Mathematical Representation

of Simple Harmonic Motion

(4.31)

(4.32)

(4.33)

(4.34)

Mathematical Representation

of Simple Harmonic Motion

A, called the amplitude of the motion, is simply the maximum value of the position of the particle in either the positive or negative x direction. The constant ω is called the angular frequency, and has units of rad/s.

(4.35)