Mechanics | Relativity Answers

A spaceship is receding from the earth at a speed of 0.3c. A light on the spaceship
emits light of wavelength lamda = 4500Å which appears blue to a passenger on the
spaceship. What colour would the light appear to a person on earth?

A block of mass 1 kg is attached to a spring of force constant k=25/4N/m.It is
pulled 0.3 m from its equilibrium position and released from rest. This spring‐block
apparatus is submerged in a viscous fluid medium which exerts a damping force of
– 4 v (where v is the instantaneous velocity of the block). Determine of the position x(t)
of the block at time t.

What do you understand by the normal modes of a coupled oscillator? If a coupled
system has many normal modes, do all normal modes have the same frequency? In a
solid, the speed of elastic longitudinal wave is 1.35 m/s If the Young’s modulus of
elasticity of the solid is 2*10^11 N/m^2 , calculate its mass density

Titan, a satellite of Saturn, has a mean orbital radius of 1.22 × 109 m. The orbital period
of Titan is 15.95 days. Hyperion, another satellite of Saturn, orbits at a mean radius of
1.48 × 109 m. Estimate the orbital period of Hyperion.

A 2 kilogram mass accelerates for 5 seconds persecond squared for 3 seconds. What is the impluse on the mass?

The amplitude of an oscillator is 8 cm and it completes 100 oscillations in 80s.
i) Calculate its time period and angular frequency. ii) If the initial phase is p/4, write
expressions for its displacement and velocity. iii) Calculate the values of maximum
velocity and acceleration

Given two vectors A⃗ =4.00i^+7.00j^ and B⃗ =5.00i^−2.00j^ , find the vector product A⃗ ×B⃗ (expressed in unit vectors).
Express your answer in terms of the unit vectors i^, j^, and k^. Use the 'unit vector' button to denote unit vectors in your answer.

An ambulance siren has frequency 250 Hz. The ambulance is headed towards an
accident site with a speed of 90 km/h. Two police officers on separate motor
cycles head for the same accident site: one follows the ambulance with a speed of
80 km/h. and the other approaches the accident site from the other direction with a
speed of 80 km/h. What frequency does ambulance siren has for each of the police
officers? Take the speed of sound equal to 340 m/s
.

A harmonic wave on a rope is described by
y(x,t) = (4.0mm) sin [2π/0.82m ((10ms-1 ) t+x)]

i) Calculate the wavelength and time period of the wave. ii) Determine the
displacement and acceleration of the element of the rope located at x = 0.58 m at
time, t = 41.0 s

A racecar is traveling at 85.0m/s. How far does the car travel in 30.0s?