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a) Check the correctness of the following equation using the principle of dimensional homogeneity. (2 Marks)...
a) A container holds Oxygen molecules at constant pressure. Mass of an Oxygen molecule is 5.31...
a) A container holds Oxygen molecules at constant pressure. Mass of an Oxygen molecule is 5.31 X 10-23 g. Calculate the number of Oxygen molecules if the total mass of Oxygen is 53.1 kg. (2 Marks) b) Find the Dimensional Formula of d in the following equation. (2 Marks) I=c(v/t)+d Va (I=Impulse, t= time, v=velocity, a-acceleration) c) Check the correctness of the following equation using the prnciple of dimensional homogeneity. ( 3 Marks) s=ut + 1/2 (at)2
If a is acceleration, v is velocity, x is position, and t is time, then check the validity (wrong or correct) of the following equations using dimensional analysis: a) t2 = 2x/a b) t = x/v c) a = v/x d) v = a/t ALSO , The term 1/2 PV^2 rv2 occu
If a is acceleration, v is velocity, x is position, and t is time, then check the validity (wrong or correct) of the following equations using dimensional analysis: a) t2 = 2x/a b) t = x/v c) a = v/x d) v = a/t ALSO , The term 1/2 PV^2 rv2 occurs in Bernoulli’s equation in Chapter 15, with P being the density of a fluid and v its speed. Find the dimensions of 1/2 PV^2 Thank you in advance...
The principle of filtration is based on the so-called Hagen-Poiseuille Equation (1c). (1c) 4 ao! where...
The principle of filtration is based on the so-called Hagen-Poiseuille Equation (1c). (1c) 4 ao! where V = the volume of filtrate collected (m) t = filtration time (s) A = filter area (m²) P = total pressure across the system (Pa) m = weight of cake per unit volume of filtrate (kg m u = filtrate viscosity (Pas) a = cake-specific resistance r=resistance of the filter ) In a typical filtration experiment, a plot of t/V vs V is...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same in...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...
c) The equation below describes the position r of a block attached to a spring at...
c) The equation below describes the position r of a block attached to a spring at time t: x(t)-x,n cos (wt + ?) i. (2 marks) Explain in words the physical meaning of the variables xm, ? and ?. ii. (2 marks) Derive an expression for the velocity of the block. iii. (2 marks) The spring constant of your oscillator is 400 N/m. At some time the position, velocity and acceleration of the block are r-0.100 m, v- 13.6 m/s...
2. (i)Describe with neat sketches the meanings of streamlines, pathlines and streaklines. (6 marks) (Gi) Derive the equation of the streamlines for the following flow field and sketch them. (4 ma...
2. (i)Describe with neat sketches the meanings of streamlines, pathlines and streaklines. (6 marks) (Gi) Derive the equation of the streamlines for the following flow field and sketch them. (4 marks) (iii) A flow field is given as (a) Determine the z-component of velocity assuming the flow field is for an incompressible fluid. (4 marks) (b) Determine the velocity and acceleration at the point (1,2,3) at time t-1. (6 marks) Assume that the z-component of velocity at z-0 is zero....
I need to rescale (4) from the first page to the equation on the second page. 2.[60pts.] A bead of mass m is constrained to slide along a straight rigid horizontal wire. A spring with natural len...
I
need to rescale (4) from the first page to the equation on the
second page.
2.[60pts.] A bead of mass m is constrained to slide along a straight rigid horizontal wire. A spring with natural length Lo and spring constant k is attached to the bead and to a support point a distance h from the wire. See Figure 1. Let z(t) denote the position of the bead on the wire at time t. (Note that x is measured...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite square well -a < x < a is given by 2 sin2 V inside the well and zero outside. Find the probability that a measurement of energy yields the eigenvalue En. (Hint: use data on page 6.) [6] Useful Data and Formulas = 1.60 x 10-19 C Elementary charge e h/2T=1.05 x 10-34 Js Planck's constant 3.00 x 108 m s-1 Speed of light...
Find part C < Homework for MO2.5 Principle of Linear Impulse and Momentum 3 of 21...
Find
part C
< Homework for MO2.5 Principle of Linear Impulse and Momentum 3 of 21 Review Learning Goal: To use the principle of linear impulse and momentum to relate a force on an object to the resulting velocity of the object at different times. The equation of motion for a particle of mass m can be written as Part A F = ma= m dv By rearranging the terms and integrating, this equation A jetliner of mass 8.54 104...
Question No.2 (CLO 21 10 marks) ) In the circuit shown the input v(O) is a...
Question No.2 (CLO 21 10 marks) ) In the circuit shown the input v(O) is a step voltage of sv and the output is the voltage across the capacitor vot) a. Find the output voltage in Laplace domain. Find the output voltage as a function of time (assume the initial voltage across the capacitor is zero). Sketch the output voltage. Find the time constant and settling time. . c. (b) Given the following system G (s)-=-: i Find the differential...
a) A container holds Oxygen molecules at constant pressure. Mass of an Oxygen molecule is 5.31 X 10-23 g. Calculate the number of Oxygen molecules if the total mass of Oxygen is 53.1 kg. (2 Marks) b) Find the Dimensional Formula of d in the following equation. (2 Marks) I=c(v/t)+d Va (I=Impulse, t= time, v=velocity, a-acceleration) c) Check the correctness of the following equation using the prnciple of dimensional homogeneity. ( 3 Marks) s=ut + 1/2 (at)2
The principle of filtration is based on the so-called Hagen-Poiseuille Equation (1c). (1c) 4 ao! where V = the volume of filtrate collected (m) t = filtration time (s) A = filter area (m²) P = total pressure across the system (Pa) m = weight of cake per unit volume of filtrate (kg m u = filtrate viscosity (Pas) a = cake-specific resistance r=resistance of the filter ) In a typical filtration experiment, a plot of t/V vs V is...
Problem 36 bclow presents a model describing the drag of a fluid medium that is released from rest at time t 0 (same initial conditions). Using Newton's Second Law, you build a model of the form particle moving through a (governing equation (initial velocity) mi mg-F drag '0 (0)(0)a (t) is the particle's position, m is the mass of the particle, g is the acceleration due to gravity, and Fa is the magnitude of the drag force. You account for...
c) The equation below describes the position r of a block attached to a spring at time t: x(t)-x,n cos (wt + ?) i. (2 marks) Explain in words the physical meaning of the variables xm, ? and ?. ii. (2 marks) Derive an expression for the velocity of the block. iii. (2 marks) The spring constant of your oscillator is 400 N/m. At some time the position, velocity and acceleration of the block are r-0.100 m, v- 13.6 m/s...
2. (i)Describe with neat sketches the meanings of streamlines, pathlines and streaklines. (6 marks) (Gi) Derive the equation of the streamlines for the following flow field and sketch them. (4 marks) (iii) A flow field is given as (a) Determine the z-component of velocity assuming the flow field is for an incompressible fluid. (4 marks) (b) Determine the velocity and acceleration at the point (1,2,3) at time t-1. (6 marks) Assume that the z-component of velocity at z-0 is zero....
I
need to rescale (4) from the first page to the equation on the
second page.
2.[60pts.] A bead of mass m is constrained to slide along a straight rigid horizontal wire. A spring with natural length Lo and spring constant k is attached to the bead and to a support point a distance h from the wire. See Figure 1. Let z(t) denote the position of the bead on the wire at time t. (Note that x is measured...
3 At a given time, the normalised wave function for a particle in a one-dimensional infinite square well -a < x < a is given by 2 sin2 V inside the well and zero outside. Find the probability that a measurement of energy yields the eigenvalue En. (Hint: use data on page 6.) [6] Useful Data and Formulas = 1.60 x 10-19 C Elementary charge e h/2T=1.05 x 10-34 Js Planck's constant 3.00 x 108 m s-1 Speed of light...
Find
part C
< Homework for MO2.5 Principle of Linear Impulse and Momentum 3 of 21 Review Learning Goal: To use the principle of linear impulse and momentum to relate a force on an object to the resulting velocity of the object at different times. The equation of motion for a particle of mass m can be written as Part A F = ma= m dv By rearranging the terms and integrating, this equation A jetliner of mass 8.54 104...
Question No.2 (CLO 21 10 marks) ) In the circuit shown the input v(O) is a step voltage of sv and the output is the voltage across the capacitor vot) a. Find the output voltage in Laplace domain. Find the output voltage as a function of time (assume the initial voltage across the capacitor is zero). Sketch the output voltage. Find the time constant and settling time. . c. (b) Given the following system G (s)-=-: i Find the differential...
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