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(4 marks.) Two block of equal hang over two pulleys (negligible size) as shown masses m...
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 plane pendulum of length L and mass m is suspended from a block of mass...
A plane pendulum of length L and mass m is suspended from a
block of mass M. The block moves without friction and is
constrained to move horizontally only (i.e. along the x axis). You
may assume all motion is confined to the xy plane. At t = 0, both
masses are at rest, the block is at
, and the pendulum has angular deflection
with respect to the y axis.
a) Using
and
as generalized coordinates, find the Lagrangian...
3. Two equal masses are connected by a light string via massless, frictionless set of pulleys,...
3. Two equal masses are connected by a light string via massless, frictionless set of pulleys, as shown in the figure. All surfaces in contact have negligible friction. a. What is the acceleration of mi? b. If both start from rest, how far has ma traveled after 3 seconds? m m2
two equal masses are connected by a light cord passing over a pulley of negligible mass. at the...
two equal masses are connected by a light cord passing over a pulley of negligible mass. at the moment the system is in motion, with the right hand block movingdownward at 1.2 m/s. what is the correct free body diagram?
Consider two masses: M = 2.0 kg and M2 =1.5 kg. Mass M moves on a...
Consider two masses: M = 2.0 kg and M2 =1.5 kg. Mass M moves on a horizontal surface where the coefficient of kinetic friction Ilk = 0.40. Mass M, is hanging freely. Two masses are connected by a strong cord of negligible mass that extends over a pulley. M-20 kg H-0.40 M. - 1.5 kg a) Draw Free Body Diagrams for the two objects b) Write the equations for the two masses in the direction of motion ( both x...
Consider two masses: M=2.0 kg and M2 =1.5 kg. Mass M, moves on a horizontal surface...
Consider two masses: M=2.0 kg and M2 =1.5 kg. Mass M, moves on a horizontal surface where the coefficient of kinetic friction Mk = 0.40. Mass M2 is hanging freely. Two masses are connected by a strong cord of negligible mass that extends over a pulley. M - 2.0 kg He=0.40 M = 1.5 kg a) Draw Free Body Diagrams for the two objects b) Write the equations for the two masses in the direction of motion ( both x...
Two masses mA = 2 kg and mB = 1 kg are connected by a stnall pulley Mass maks on an inclined plane at angle e-π/4 radians, and mB is allowed to hang freely. (a) Suppose the string has length 10 m....
Two masses mA = 2 kg and mB = 1 kg are connected by a stnall pulley Mass maks on an inclined plane at angle e-π/4 radians, and mB is allowed to hang freely. (a) Suppose the string has length 10 m. Take a coordinate system in which the pulley is at the origin. What is the potential energy of the system as a function of the height of mass mg? (b) Find the acceleration of mass ma (either using...
3. A frictionless and massless pulley with radius Ri and string of li is suspended as...
3. A frictionless and massless pulley with radius Ri and string of li is suspended as shown in Fig. 1. One end connects with a mass mi and the other with another frictionless pulley of mass m with radius R2 and string /2, joining two masses ms and ms at the two ends. (a) Find the equations of holonomic constraints. (b) Find the equations of motion for masses mi, m2, m3, and m4. (c) Find the solutions for the undetermined...
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...
1) Consider a block of mass M connected through the massless rigid rod to the massless...
1) Consider a block of mass M connected through the massless rigid rod to the massless circular track of radius a on a frictionless horizontal table (see the Figure). A particle of mass m is constrained to move on the vertical circular track. The distance between the center of the circular track and the center of mass of the block of mass M is constant and equal to L. Assume that there is no friction between the track and the...
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 plane pendulum of length L and mass m is suspended from a
block of mass M. The block moves without friction and is
constrained to move horizontally only (i.e. along the x axis). You
may assume all motion is confined to the xy plane. At t = 0, both
masses are at rest, the block is at
, and the pendulum has angular deflection
with respect to the y axis.
a) Using
and
as generalized coordinates, find the Lagrangian...
3. Two equal masses are connected by a light string via massless, frictionless set of pulleys, as shown in the figure. All surfaces in contact have negligible friction. a. What is the acceleration of mi? b. If both start from rest, how far has ma traveled after 3 seconds? m m2
Consider two masses: M = 2.0 kg and M2 =1.5 kg. Mass M moves on a horizontal surface where the coefficient of kinetic friction Ilk = 0.40. Mass M, is hanging freely. Two masses are connected by a strong cord of negligible mass that extends over a pulley. M-20 kg H-0.40 M. - 1.5 kg a) Draw Free Body Diagrams for the two objects b) Write the equations for the two masses in the direction of motion ( both x...
Consider two masses: M=2.0 kg and M2 =1.5 kg. Mass M, moves on a horizontal surface where the coefficient of kinetic friction Mk = 0.40. Mass M2 is hanging freely. Two masses are connected by a strong cord of negligible mass that extends over a pulley. M - 2.0 kg He=0.40 M = 1.5 kg a) Draw Free Body Diagrams for the two objects b) Write the equations for the two masses in the direction of motion ( both x...
Two masses mA = 2 kg and mB = 1 kg are connected by a stnall pulley Mass maks on an inclined plane at angle e-π/4 radians, and mB is allowed to hang freely. (a) Suppose the string has length 10 m. Take a coordinate system in which the pulley is at the origin. What is the potential energy of the system as a function of the height of mass mg? (b) Find the acceleration of mass ma (either using...
3. A frictionless and massless pulley with radius Ri and string of li is suspended as shown in Fig. 1. One end connects with a mass mi and the other with another frictionless pulley of mass m with radius R2 and string /2, joining two masses ms and ms at the two ends. (a) Find the equations of holonomic constraints. (b) Find the equations of motion for masses mi, m2, m3, and m4. (c) Find the solutions for the undetermined...
1) Consider a block of mass M connected through the massless rigid rod to the massless circular track of radius a on a frictionless horizontal table (see the Figure). A particle of mass m is constrained to move on the vertical circular track. The distance between the center of the circular track and the center of mass of the block of mass M is constant and equal to L. Assume that there is no friction between the track and the...
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