Classical Mechanics Answers

A many-particle system

A system of four(4) free particles each has a mass m_i and initial position r_i and initial velocity v_i .

a) Describe your own four-particle system in detail.

b) Determine the position R_cm and velocity V_cm of the centre of mass of the system.

c) Determine the total linear momentum P_tot and the linear momentum P_cm of the centre of mass of the system.

d)Determine the total angular momentum L_tot and the linear momentum P_cm of the centre of mass of the system.

e) Discuss briefly about your answers in part b), c) and d).

There are many comets in our solar system. A comet is located at a distance r_c = 16 AU from the sun moving at a speed v_c = 0.26vE where v_E is the average speed of Earth orbital motion. At that particular instant the position vector r_c makes an angle ϕ = 68^o with velocity vector v_c .

a) Determine eccentricity ε of the orbit.

b) If the semi-major axis of the orbit a = 13.7 AU, write the equation of the orbit for the comet.

c) Determine the period of the comet. Can you identify the most probable name for the comet?

What is the equation of coriolis theorem

1.  a beam LO weighing 50N rests against a wall, the lower part of the beam extending 15 m from the base of the wall. Calculate the minimum value of the force F that can be applied to keep the beam in equilibrium. The coefficient of friction at L and O is 0.30. Height from the bottom of the ground up to the top of the ladder is 30m. F is not at the middle of the ladder. The componenets acting on the top the ladder are R_L and N_L. The componenets acting on the top the ladder are R₀ and N₀. The distance of force F from the ground is 10m.

box of mass m is placed at the centre of a flat truck bed while the truck is moving at constant velocity V_O . The truck bed has a length of L and its surface has a sliding friction coefficient μ. The truck then accelerates with a constant acceleration A_O for a few seconds. Assume the origin O’ of the moving coordinate system coincides with the centre of the box and it is aligned perfectly vertically with the origin O of the static coordinate system on the road at the exact instant when the truck starts to accelerate and accidentally opens up its back doors. (assume the box as a particle and g = 10 ms^-2)

a) Describe your system in detail and sketch the free-body diagrams (FBD) of the box when it is sliding and falling off the truck.

b) Write the equation of motion (EOM) of the box and its general solutions inside and outside of the truck.

c) Use relevant octave script provided to solve and plot the velocity and position of the box as a function of time.

d) Describe in detail the motion of the box based on the plots in part c)

i) Describe a Foucault pendulum.

ii) Choose your latitude λ on Earth and write the equation of motion (EOM) for the pendulum.

iii) Use relevant octave script to plot the oscillations both in static and rotating coordinate systems. iv)Discuss when and how, in the actual experiment with pendulum in your lab, you would see the phenomena you see in part iii)

A system of four(4) free particles each has a mass m_i and initial position r_i and initial velocity v_i .

i) Describe your own four-particle system in detail.

ii) Determine the position R_cm and velocity V_cm of the centre of mass of the system.

iii) Determine the total linear momentum P_tot and the linear momentum P_cm of the centre of mass of the system.

iv) Determine the total angular momentum L_tot and the linear momentum P_cm of the centre of mass of the system.

v) Discuss briefly about your answers in part ii), iii), iv)

show that [x, e^iap/h]= -ae^iae/h

Find the maximum height reached by an object projected vertically upwards with an initial velocity of 40 meters per second and find the time taken for that

Can you explain fluid.