Classical Mechanics Answers

A bullet after penetrating 3cm of a wall loses half of its speed. How far will the bullet penetrate the wall afterwards?

Motion of a planet of mass mp in our solar system is an example of motions under the action of 

central force F

⃗ c due to the sun of mass Ms. 

a)

Is F

⃗ c

a conservative force? Explain your answer.

b)

It is well known that the planet is moving about the sun in a same fixed orbit located on a 

fixed orbital plane. Name two (2) physical principles that dictate why the planet moves the 

way it does. Explain your answers.

c)

The orbit of the planet has an eccentricity ϵ = 0.047 and semi-major axis a = 19.18 AU. Use

the octave script provided to plot the orbit. Mark the perihelion and the aphelion centre of 

the orbit on the plot.

1.

A small box of mass m is located at the middle point of the front end of a flat truck bed while the 

truck is stopped at a traffic light. The truck bed has a length L = 2.2 m , a height H = 1.2 m off 

the the road surface and its surface has a sliding friction coefficient μ = 0.05. The truck then 

accelerates with a constant acceleration AO = 1.1ms

−2

for a few seconds the traffic light turns 

green. 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. (assume the box as a particle and g = 

10 ms-2)

a)

Assume that both the x-axis and x’-axis for both coordinate systems are parallel to the 

length of the truck bed and the motion is observed by a non-inertial observer (NIO) in the 

truck and by an inertial observer (IO) on the roadside.

i)

Sketch the free-body diagrams (FBDs) of the box when it starts sliding according to 

both the NIO and the IO.

ii)

Write the equations of motion (EOMs) of the box and their general solutions.

b)

Use the octave script provided to solve and plot the velocity and position of the box as a 

function of time.

i)

Describe the motion of the box according to the NIO and the IO.

ii)

What are the accelerations of the box according to the two observers?

iii)

Determine the velocities of the box when it hit the back door.

iv)

According to the IO what is the position of the box when it hits the back door?

Motion of a planet of mass mp in our solar system is an example of motions under the action of

central force ⃗F

c due to the sun of mass Ms.

a) Is ⃗Fc a conservative force? Explain your answer.

b) It is well known that the planet is moving about the sun in a same fixed orbit located on a

fixed orbital plane. Name two (2) physical principles that dictate why the planet moves the

way it does. Explain your answers.

c) The orbit of the planet has an eccentricity ϵ = 0.047 and semi-major axis a = 19.18 AU. Use

the octave script provided to plot the orbit. Mark the perihelion and the aphelion centre of

the orbit on the plot.

An object has a rectangular shape with a surface area of 40m2 and 0.1m thick. What is the maximum mass of a polar bear can sit on the floe before sinking? (density of ice is 900kg/m3 and density of seawater is 1025kg/m3)

Linear motion in an accelerating coordinate system

A box of mass m is placed at the centre of a flat truck bed while the truck is moving at

constant velocity V⃗ 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)

Water (specific heat Cv = 4,2 kJ/kg.K) is being heated by a 1500 W heater. What is the rate of change in temperature of 1 kg of the water?

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.