Physics Answers

An object of mass m and initial position ⃗r₀ and initial velocity ⃗v₀ is moving under the action of the gravitational force near to earth surface at some latitude λ. Neglect the effects of both the air resistance and wind.

a) Choose your latitude and describe your system in detail.

b) Name all the forces acting on the object and sketch the free-body diagram (FBD) due to the dominant forces only.

c) Write the equation of motion (EOM) for the object and its general solutions.

d) Use relevant octave script to plot the position (trajectory) of the object when it is released from initial height z’₀ = h₀ and describe the motion.

e) Use the same script to plot the position of the object when it is launched with initial velocity ⃗v₀ at initial position ⃗r₀ and describe the motion.

A metal cylinder of mass 4kg vibrates harmonically with an amplitude of 0.25m and period of 2second. Calculate 1)Frequency 2)its maximum speed and speed when y=0.15m

A skydiver steps out of a perfectly good airplane. How far did the skydiver

fall in 5 sec? What was the skydiver’s velocity after 5 sec? Create

position-time, velocity-time, and acceleration-time curves for the first five

sec of the fall. (Assume no other influences are acting on the skydiver,

acceleration due to gravity is –10 m/s2, and start at time 0 with 0.25-sec

increments for the plots.)

A ski jumper takes off from a horizontal ramp 5 meters in the air. The ramp is directly next to a steep drop of 70 meters. The skier lands 146 meters away from the base of the ramp. What was the skier’s original horizontal velocity?

Two storage tanks with a tapering circular cross-sectional area are used to intermittently supply a water-soluble binder fluid to a mixer, in an ibuprofen tablet manufacturing process. The noninteracting tanks are arranged in series, as shown in Figure Q1. The effluent volumetric flowrates (m3hr−1 ) are related to the fluid height in each tank by the following linear relationships: 𝑓1 (𝑡) = 𝐶v1 × ℎ1 𝑓2 (𝑡) = 𝐶v2 × ℎ2 Where 𝐶v1and 𝐶v2 are the valve discharge coefficients of the first and second valves respectively. The inlet volumetric flowrate is 𝑓𝑖 . The relevant parameters of the system are as follows: 𝐷1 = Top diameter of the first tank = 0.915m 𝑥1 = Base diameter of the first tank = 0.305m 𝑦1 = Vertical height of the first tank = 10𝑥1 Figure Q1: Non-interacting tanks in series 𝐷2 = Top diameter of the second tank = 0.725 𝐷1 𝑥2 = Base diameter of the second tank = 0.725 𝑥1 𝑦2 = Vertical height of the second tank = 10𝑥2 𝐶v1 = Valve discharge coefficient = 0.366 m3 . m−1 . hr−1 𝐶v2 = Valve discharge coefficient = 0.183 m3 . m−1 . hr−1 1.) Develop a linearised dynamic model for the system. 2.) Obtain the transfer function (in deviation variable form) between the liquid level in the second tank and the volumetric flowrate into the first tank. 3.) If the initial steady state height in tank 1 is ℎ̅ 1 = 1.83m and that in tank 2 is and ℎ̅ 2 = 1.11m. Plot the open loop time response of the process for a unit step change in the inlet flowrate for the following valve discharge coefficients values: 𝐶v2 ∈ {0.01, 0.10, 1.00}. Assume all other parameters remain as originally defined. Explain the plots you obtained. 4.) If the initial steady state height in tank 1 is ℎ̅ 1 = 1.83m and that in tank 2 is and ℎ̅ 2 = 1.11m, fit a proportional controller to the system and plot the closed loop time response of the process for a unit step change in the inlet flowrate. Vary the value of the controller proportional gain, 𝐾C three times. Assume that all other parameters remain as originally defined. Explain the plots you obtained. 5.) Using the same steady state conditions as in (4) and the original valve discharge coefficients, replace the proportional controller in (4) with a proportional-integral controller. Fix the controller proportional gain, 𝐾C and vary the integral gain, 𝐾I three times. Plot all three responses and discuss the significance of your results. 6.) A sensor-transmitter modelled by the following first order transfer function: 𝐺m(𝑠) = 0.4 5𝑠 + 1 is fitted to a closed loop. Replace the proportional integral controller with a proportional integral derivative (PID) controller and tune it using the continuous cycling ZieglerNichols method.

The length of the object is 18.2+or-0.01cm Estimate the percentage error this measurement

Find A X B when A = 2i-3j-k and B = i + 4j -2k

You’re involved in the design of a mission carrying humans to the surface of the 

planet Mars, which has a radius 3.37x106m and a mass of 6.42x1023 kg. The 

earth weight of the Mar’s lander is 39,200 N. Calculate its weight and the 

acceleration due to Mar’s gravity at 6.0 x 106 m above the surface of Mars.

You’re involved in the design of a mission carrying humans to the surface of the 

planet Mars, which has a radius 3.37x106m and a mass of 6.42x1023 kg. The 

earth weight of the Mar’s lander is 39,200 N. Calculate its weight and the 

acceleration due to Mar’s gravity at 6.0 x 106 m above the surface of Mars.

A plane mirror and a concave mirror of radius of curvature 60 cm are placed facing each other with a point object at the centre of them, if the image formed by first reflection at the spherical mirror and then at the plane mirror coincides with the object then the separation between two mirrors will be