Homework Answers
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to t...
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to the bob is defined by er,ce where er is the unit vector orientecd away from the origin and e completes the direct orthonormal basis. The pendulum makes an angle 0(t) between the radial direction and the vertical direction e(t) The position vector beinge ind...
# Problem 1 # Suppose a point-mass particle with mass, 'm', moving in a gravitational potential,...
# Problem 1 # Suppose a point-mass particle with mass, 'm', moving in a gravitational potential, 'U(r)', where 'r' is the distance from the center of the potential. A positional vector and momentum vector of a particle are vec r' and "vec p', respectively. (\vec means vector symbol.) Q1) An angular momentum vector vec J' is defined as vec J = \vec r x \vec p. Show that \vec J is conserved in such a gravitational potential U(r) which depends...
A particle undergoes uniform circular motion. This means that it moves in a circle of radius...
A particle undergoes uniform circular motion. This means that it moves in a circle of radius R about the origin at a constant speed. The position vector of this motion can be written Here, analogous to the simple harmonic motion problem of HW 1, ω is the angular frequency and has units of rad/s 1/s and can also be written in terms of the period of the motion as 2π (a) Show that the particle resides a distance R away...
How do I calculate vg? Example 3.4 In the quick return mechanism shown in Fig. 3.24,...
How do I calculate vg?
Example 3.4 In the quick return mechanism shown in Fig. 3.24, the distance between the fixed centres CB = 90 mm, crank BA = 180 mm, CD = 180 mm, and the rod DE = 360 mm with its centre of mass, G, 90 mm from D. IF AB rotates at 120 rev/min clockwise, find graphically for the given position the linear velocity of G and the angular velocity of DE. If the rod DE...
EXAMPLE 16.5 The large window in Fig. 16-10 is opened using a hydraulic cylinder AB. If...
EXAMPLE 16.5 The large window in Fig. 16-10 is opened using a hydraulic cylinder AB. If the cylinder extends at a constant rate of 0.5 m/s, determine the angular velocity and angular acceleration of the window at the instant 0 30° 1 m SOLUTION Position Coordinate Equation. The angular motion of the window can be obtained using the coordinate 0, whereas the extension or motion along the hydraulic cylinder is defined using a coordinate s, which measures its length from...
32. mier, used for complete mixing of chemical solutions, is depicted in Main arm M is pinned to ...
32. mier, used for complete mixing of chemical solutions, is depicted in Main arm M is pinned to newtonian reference frame N at point A, and to secon The n, unit vectors are fixed in N; the m unit vectors, in M, and the $, unit vectors has length . Mixing point C is constrained to move along secondary arm S at nt B. in S. The m e r) from B You plan to determine the acceleration of point...
1. The cantilever beam AB of length L shown in Fig.(a carries a uniformly distributed load of int...
1. The cantilever beam AB of length L shown in Fig.(a carries a uniformly distributed load of intensity wo, which includes the weight of the beam. Equation of the elastic curve is given by the following differential equation Af _irer where M is the bending moment of the beam. it is also given that of the beam and I modulus of Inertia. where E- Modulus of the elasticity v is the deflection of the beam. Compute the maximum displacement of...
3. When using a reference constituted by the principal axes of a birefringent crystal, the electric field component...
3. When using a reference constituted by the principal axes of a birefringent crystal, the electric field components of a plane wave (E. E E) = E(7,1)= Ë, e(k.F - ct) propagating in the direction (siny, 0, cosu), satisfy the following set of equations, 2 -Cos') E Sin'P CosY E 0 wave.k 21 -1) E = 0 wave & 2 ne Sin y) E, 0 SINY Cos'Y E + n where is the angle between the wave-vector k and the...
1. Show that the Lagrangians L(t,q, y) and Īct, 4, ) = L(1,4,0) + f/10, 9)...
1. Show that the Lagrangians L(t,q, y) and Īct, 4, ) = L(1,4,0) + f/10, 9) yield the same Euler-Lagrange equations. Here q e R and f(t,q) is an arbitrary function. 2 Lagrangian mechanics In mechanics, the space where the motion of a system lies is called the configuration space, which is usually an n-dimensional manifold Q. Motion of a system is defined as a curve q : R + Qon Q. Conventionally, we use a rather than 1 to...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to the bob is defined by er,ce where er is the unit vector orientecd away from the origin and e completes the direct orthonormal basis. The pendulum makes an angle 0(t) between the radial direction and the vertical direction e(t) The position vector beinge ind...
# Problem 1 # Suppose a point-mass particle with mass, 'm', moving in a gravitational potential, 'U(r)', where 'r' is the distance from the center of the potential. A positional vector and momentum vector of a particle are vec r' and "vec p', respectively. (\vec means vector symbol.) Q1) An angular momentum vector vec J' is defined as vec J = \vec r x \vec p. Show that \vec J is conserved in such a gravitational potential U(r) which depends...
A particle undergoes uniform circular motion. This means that it moves in a circle of radius R about the origin at a constant speed. The position vector of this motion can be written Here, analogous to the simple harmonic motion problem of HW 1, ω is the angular frequency and has units of rad/s 1/s and can also be written in terms of the period of the motion as 2π (a) Show that the particle resides a distance R away...
How do I calculate vg?
Example 3.4 In the quick return mechanism shown in Fig. 3.24, the distance between the fixed centres CB = 90 mm, crank BA = 180 mm, CD = 180 mm, and the rod DE = 360 mm with its centre of mass, G, 90 mm from D. IF AB rotates at 120 rev/min clockwise, find graphically for the given position the linear velocity of G and the angular velocity of DE. If the rod DE...
EXAMPLE 16.5 The large window in Fig. 16-10 is opened using a hydraulic cylinder AB. If the cylinder extends at a constant rate of 0.5 m/s, determine the angular velocity and angular acceleration of the window at the instant 0 30° 1 m SOLUTION Position Coordinate Equation. The angular motion of the window can be obtained using the coordinate 0, whereas the extension or motion along the hydraulic cylinder is defined using a coordinate s, which measures its length from...
32. mier, used for complete mixing of chemical solutions, is depicted in Main arm M is pinned to newtonian reference frame N at point A, and to secon The n, unit vectors are fixed in N; the m unit vectors, in M, and the $, unit vectors has length . Mixing point C is constrained to move along secondary arm S at nt B. in S. The m e r) from B You plan to determine the acceleration of point...
1. The cantilever beam AB of length L shown in Fig.(a carries a uniformly distributed load of intensity wo, which includes the weight of the beam. Equation of the elastic curve is given by the following differential equation Af _irer where M is the bending moment of the beam. it is also given that of the beam and I modulus of Inertia. where E- Modulus of the elasticity v is the deflection of the beam. Compute the maximum displacement of...
3. When using a reference constituted by the principal axes of a birefringent crystal, the electric field components of a plane wave (E. E E) = E(7,1)= Ë, e(k.F - ct) propagating in the direction (siny, 0, cosu), satisfy the following set of equations, 2 -Cos') E Sin'P CosY E 0 wave.k 21 -1) E = 0 wave & 2 ne Sin y) E, 0 SINY Cos'Y E + n where is the angle between the wave-vector k and the...
1. Show that the Lagrangians L(t,q, y) and Īct, 4, ) = L(1,4,0) + f/10, 9) yield the same Euler-Lagrange equations. Here q e R and f(t,q) is an arbitrary function. 2 Lagrangian mechanics In mechanics, the space where the motion of a system lies is called the configuration space, which is usually an n-dimensional manifold Q. Motion of a system is defined as a curve q : R + Qon Q. Conventionally, we use a rather than 1 to...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
Most questions answered within 3 hours.
-
can the neoclassical and endogenous growth model help us to
explain the lack of growth in...
asked 13 minutes ago -
This section aims to convince the client of the importance and
benefits, and outline some potential...
asked 22 minutes ago -
Match each class operation with its most likely category type.
1. SelectCamera( ); 2. ComputeArea( );...
asked 21 minutes ago -
Show all work and calculations.
Find the ΔH for the target reaction below, given the following...
asked 23 minutes ago -
Assume the user always enters the correct values for a. Next,
your program should compute and...
asked 35 minutes ago -
you created an application named
QuartsToGallonsInteractive that accepts a number of quarts
from a user and...
asked 40 minutes ago -
The Friendly Sausage Factory (FSF) can produce hot dogs at a
rate of 5,000 per day....
asked 41 minutes ago -
What is the component concentration ratio,
[BrO−]/[HBrO], of a buffer that has a pH of 8.02?...
asked 44 minutes ago -
A simple random sample of 49 8th graders at a large suburban
middle school indicated that...
asked 1 hour ago -
1. The following test data apply to a 208-V, 6-pole,
Y-connected, three-phase induction motor:
- No-load...
asked 1 hour ago -
1. If Ksp = 6.4 x 10-9 for magnesium fluoride, what
is the concentration of Mg2+...
asked 57 minutes ago -
9. Given the length an athlete throws a hammer is a
normal random variable with mean 60...
asked 1 hour ago