All Flashcards
What are the differences between distance and displacement?
Distance: Total path length (scalar) | Displacement: Change in position (vector)
What is the difference between average speed and average velocity?
Average Speed: Total distance traveled divided by time (scalar) | Average Velocity: Change in position divided by time (vector)
Compare horizontal and vertical motion in projectile motion.
Horizontal (x) motion: Constant velocity (no acceleration) | Vertical (y) motion: Constant acceleration due to gravity (g)
How often does the kinetic energy of a body in simple harmonic motion become zero if it has a frequency of 20 Hz?
In simple harmonic motion, kinetic energy is zero at the points of maximum displacement. Since this occurs twice per cycle, for a frequency of 20 Hz, kinetic energy is zero 40 times per second.
When do energy losses occur in simple harmonic motion?
Energy losses occur when there is resistance, such as air resistance or friction. True simple harmonic motion does not have energy losses.
How do greenhouse gases exhibit simple harmonic motion characteristics?
Greenhouse gas molecules absorb and re-emit electromagnetic radiation, vibrating in a manner akin to simple harmonic oscillators. Their vibrational energy exchange resembles the energy oscillations in SHM.
How is simple harmonic motion related to waves in physics?
Simple harmonic motion (SHM) and wave motion are intimately related. A rotating vector, or phasor, can represent SHM, mirroring a wave particle's motion. The concepts share common terms like amplitude, frequency, and period, illustrating the wave-particle duality in physics.
When does a pendulum have maximum potential energy during its oscillation?
At the oscillation extremes when its speed is zero and it's momentarily stationary, a pendulum's potential energy is at its maximum.
What is the equation for velocity in simple harmonic motion (SHM)?
v = -ωx0 sin(ωt), where v is velocity, ω is angular frequency, x0 is amplitude, and t is time.
What is the equation for acceleration in simple harmonic motion?
a = -ω^2 x. In SHM, acceleration is directly proportional to, and in the opposite direction of, the displacement x and is given by the negative square of the angular frequency (ω) times the displacement.
What does the ± sign signify in the equation for velocity (v = ±ω√(x0^2 − x^2)) in Simple Harmonic Motion?
The ± sign indicates the velocity's direction can vary, showing the object may move in one of two opposite directions at a particular displacement (x) from its equilibrium position.
How is the frequency of oscillation calculated for an object hanging from a vertical spring?
Frequency f = 1/T, with the period T given by T = 2π√(m/k), where m is mass and k is the spring constant.
How do you calculate the speed of an object in simple harmonic motion at a specific displacement?
The speed (v) at a given displacement (x) can be calculated using the formula v = ω√(A² - x²), where ω is the angular frequency and A is the amplitude of the motion.
How do you calculate the maximum force in a mass-spring system undergoing simple harmonic motion?
The maximum force (Fmax) in a mass-spring system is given by Fmax = mω²x0, where m is the mass, ω is the angular frequency, and x0 is the amplitude of oscillation.
Define the amplitude in the context of simple harmonic motion.
Amplitude in simple harmonic motion is the maximum extent of displacement from the midpoint or equilibrium position.
When is the kinetic energy at its maximum in simple harmonic motion?
The kinetic energy is at its maximum when the mass is at the equilibrium position, moving at its fastest speed. There are two kinetic-energy maxima per oscillation.
Explain how simple harmonic motion is related to uniform circular motion.
Simple harmonic motion can be visualized as the projection of uniform circular motion onto one axis. If an object rotates uniformly in a horizontal circle and this motion is viewed from the side, the up-and-down motion maps out simple harmonic motion.
How are the coordinates x and y linked to the circle's radius r and angle θ with the x-axis in simple harmonic motion?
The horizontal coordinate x and the vertical coordinate y can be derived from the circle's radius r and angle θ by using trigonometric functions: x = r cos(θ) and y = r sin(θ).
What are the equations for the x-projection of point P moving in a circle (in terms of r, ω, and t)?
x = r cos(ωt) and y = r sin(ωt) represent the x and y projections, respectively, where r is the radius, ω is the angular frequency, and t is time.
State the equations for displacement in simple harmonic motion starting from extremes and from the center.
For SHM starting at extremes, x = x0 cos(ωt). For motion starting at the center, x = x0 sin(ωt), where x0 is maximum displacement, ω is angular frequency, and t is time.
How is angular frequency (ω) calculated from the period of oscillation?
ω = 2π / T, where T is the period.
How is the maximum velocity of an object in simple harmonic motion related to angular frequency and amplitude?
The maximum velocity (vmax) in simple harmonic motion is calculated using the formula vmax = ω * A, where ω is the angular frequency, and A is the amplitude.
How do you calculate the maximum acceleration of an object in simple harmonic motion using angular frequency and amplitude?
The maximum acceleration (amax) in simple harmonic motion is given by the formula: amax = ω^2 * A, where ω is the angular frequency and A is the amplitude.