The m1 and m2 (m1=m2=m) are attached to the ends of a string of
length l. The string is going through a frictionless hole in the
middle of a frictionless table. m1 is given certain initial push
along the x-y plane and perpendicular to the position vector
r. find the Lagrangian L and Lagrange equations of
motion for the system.
Homework Answers
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The m1 and m2 (m1=m2=m) are attached to the ends of a string of
length l....
An Atwood machine consists of two masses m1 and m2 (with m1 > m2) attached to the ends of a light string that passes over a light
An Atwood machine consists of two masses m1 and m2 (with m1 > m2) attached to the ends of a light string that passes over a light, frictionless pulley. When the masses are released, the mass m1 is easily shown to accelerate down with an accelerationSuppose that m1 and m2 are measured as m1=100±1 gram and m2=50±1 gram. Derive a formula of the uncertainty in the expected acceleration in terms of the masses and their uncertainties, and then calculate δα for...
An Atwood machine consists of two masses m1 and m2 (with m1 > m2 ) attached...
An Atwood machine consists of two masses m1 and m2 (with m1 > m2 ) attached to the ends of a light string that passes over a light, frictionless pulley. When the masses are released, the mass m1 is easily shown to accelerate down with an acceleration a = g*(m1+m2)/)m1−m2 Suppose that m and are measured as m1 = 100 +- 1 gram and m2 = 50 +- 1 gram. Derive a formula of uncertainty in the expected acceleration in...
An inextensible massless string of length 2l has mass mand m3 attached to the two ends...
An inextensible massless string of length 2l has mass mand m3 attached to the two ends A and B respectively. A particle of mass m2 is attached to the midpoint of the string at point C. Initially, the three particles are at the vertices of an equilateral triangle as shown in the figure below and the string is taut. Particle 2 is given an impulse J along the bisector of the angle ACB. It is known that the whole set...
QUESTION 5 [25 marks] Two masses mi and m are joined by an inextensible string of...
QUESTION 5 [25 marks] Two masses mi and m are joined by an inextensible string of length I, as shown in Figure 2. The string passes over a massless pulley with frictionless bearings and radius R. The acceleration of gravity g points vertically downwards (a) 13 marks] Write down the Lagrangian, using the position of mass mi as the generalized coordinate m1 (b) 12 marks] Find the Lagrange equation of motion and solve it for 白m2 acceleration of mass mi...
a) Write down the Lagrangian L(x1, x2, 81, 82) for two particles of equal masses, m1...
a) Write down the Lagrangian L(x1, x2, 81, 82) for two particles of equal masses, m1 = m2 = m, confined to the x axis and connected by a spring with potential energy U = kx2 . [Here x is the extension of the spring, x = x1 - x2-1, where l is the spring's unstretched length, and I assume that mass 1 remains to the right of mass 2 at all times.) (b) Rewrite L in terms of the...
Two equal masses, m, are joined by a massless string of length L that passes through...
Two equal masses, m, are joined by a massless string of length L
that passes through a hole in a frictionless horizontal table.
First mass slides on table while the second hangs below the table
and moves up and down in a vertical line.
a.) Assuming the string remains taut, write down the Lagrangian
for the system in terms of the polar coordinates
of the mass on the table.
b.) Find the two Lagrangian equations of motion and interpret
the...
Consider an elastic string of length L whose ends are held fixed. The string is set in motion fro...
Answer needed in form summation from n=1 to infinity:
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity ut(x, 0) = g(x). Let L-12 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) 8x 2 (a) Find the displacement u(x, t) for the given g(x). (Use a to represent an arbitrary constant.)
Consider an elastic string of...
Mass in Cone. Masses A and each of mass m, are attached at the ends of a string that runs through...
Please Solve using angular momentum
Mass in Cone. Masses A and each of mass m, are attached at the ends of a string that runs through the small hole in the center of a cone, for which θ-60° (a) If ball B is hanging a constant distance below the cone and ball A is moving in a horizontal cir- cle with constant speed vo, de- termine, as a function of vo and Neglect friction between A and the cone and...
Use the 1D diffusion equation to find T(x,t): 2. A bar of length L has an...
Use the 1D diffusion equation to find T(x,t):
2. A bar of length L has an initial temperature distribution T(x,0) = a + br ( x = L are the ends of the bar). The ends are insulated. Find T(x,t) for t > 0. 0 and си oFlu сх
2. Atwood's Table with Two Hanging Masses You have table of width L, masses m1, m2,...
2. Atwood's Table with Two Hanging Masses You have table of width L, masses m1, m2, and m3, two frictionless pulleys, and ideal string. Placing m2 on the table, you attach a bit of string to mass m1 the left pulley, to the left side of m2. Similarly, you hang mass m3 from the right side of m2 using the pulley on the right side of the table. The coefficient of friction of the table is mu. The acceleration of...
An inextensible massless string of length 2l has mass mand m3 attached to the two ends A and B respectively. A particle of mass m2 is attached to the midpoint of the string at point C. Initially, the three particles are at the vertices of an equilateral triangle as shown in the figure below and the string is taut. Particle 2 is given an impulse J along the bisector of the angle ACB. It is known that the whole set...
QUESTION 5 [25 marks] Two masses mi and m are joined by an inextensible string of length I, as shown in Figure 2. The string passes over a massless pulley with frictionless bearings and radius R. The acceleration of gravity g points vertically downwards (a) 13 marks] Write down the Lagrangian, using the position of mass mi as the generalized coordinate m1 (b) 12 marks] Find the Lagrange equation of motion and solve it for 白m2 acceleration of mass mi...
a) Write down the Lagrangian L(x1, x2, 81, 82) for two particles of equal masses, m1 = m2 = m, confined to the x axis and connected by a spring with potential energy U = kx2 . [Here x is the extension of the spring, x = x1 - x2-1, where l is the spring's unstretched length, and I assume that mass 1 remains to the right of mass 2 at all times.) (b) Rewrite L in terms of the...
Two equal masses, m, are joined by a massless string of length L
that passes through a hole in a frictionless horizontal table.
First mass slides on table while the second hangs below the table
and moves up and down in a vertical line.
a.) Assuming the string remains taut, write down the Lagrangian
for the system in terms of the polar coordinates
of the mass on the table.
b.) Find the two Lagrangian equations of motion and interpret
the...
Answer needed in form summation from n=1 to infinity:
Consider an elastic string of length L whose ends are held fixed. The string is set in motion from its equilibrium position with an initial velocity ut(x, 0) = g(x). Let L-12 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) 8x 2 (a) Find the displacement u(x, t) for the given g(x). (Use a to represent an arbitrary constant.)
Consider an elastic string of...
Please Solve using angular momentum
Mass in Cone. Masses A and each of mass m, are attached at the ends of a string that runs through the small hole in the center of a cone, for which θ-60° (a) If ball B is hanging a constant distance below the cone and ball A is moving in a horizontal cir- cle with constant speed vo, de- termine, as a function of vo and Neglect friction between A and the cone and...
Use the 1D diffusion equation to find T(x,t):
2. A bar of length L has an initial temperature distribution T(x,0) = a + br ( x = L are the ends of the bar). The ends are insulated. Find T(x,t) for t > 0. 0 and си oFlu сх
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