Pulley Problem
In the figure, a particle \(A\) of mass \(m\) is connected to another particle \(B\) of mass \(2 m\) by an inextensible string which passes over a smooth fixed pulley. A third particle \(C\) of mass \(m\) is connected to \(A\) by an elastic string of natural length \(L\). All the particles are initially held with the elastic string just unstretched and are then released from rest. You can assume that the tension of the elastic string is directly proportional to the extension of the string beyond its natural length and the proportionality constant is \(m g / L\).
(a) Show that the coordinates of \(A\) and \(C\) as measured from the initial level of \(C\) are related by \(3 y_{A}+y_{C}=3 L\)
(b) Show that particle \(A\) performs a simple harmonic motion (SHM). What is the period of the SHM?
(c) Determine the greatest length of the elastic string during the motion.
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Two masses M and m are connected by a light, inextensible string that passes over a...
Two masses M and m are connected by a light, inextensible string that passes over a smooth pulley. The mass m is connected to one end of a Hooke's Law spring of force constant k, the other end of which is anchored to the floor, in such a way that the spring remains vertical. The system is released from rest, with the spring at its natural length, as shown. Show (a) that mass m executes simple harmonic motion (SHM) and...
Spring-Mass Problem
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2. An elastic string of m attached to it at a distance ' The other end...
2. An elastic string of m attached to it at a distance ' The other end of the string is fixed to a point B so that the string is just unstretched t held at B (by stretching the length a of the string) and then released. Show thatit will oscillate to andfto natural length (a + b) where a s b and modulus of elasticity y has a particle of mass a from one end, which is fixed to...
For the arrangement shown below, the inclined plane and the small pulley are frictionless; the string...
For the arrangement shown below, the inclined plane and the
small pulley are frictionless; the string supports the object of
mass M at the bottom of the plane; and the string has mass m. The
system is in equilibrium, and the vertical part of the string has a
length h. We wish to study standing waves set up on the vertical
section of the string.
For the arrangement shown below, the inclined plane and the small pulley are frictionless; the...
As shown in the figure below, two blocks are connected by a string of negligible mass passing over a pulley of radius 0...
As shown in the figure below, two blocks are connected by a
string of negligible mass passing over a pulley of radius 0.270 m
and moment of inertia I. The block on the frictionless incline is
moving with a constant acceleration of magnitude a = 1.20 m/s2.
(Let m1 = 15.5 kg, m2 = 22.0 kg, and θ = 37.0°.) From this
information, we wish to find the moment of inertia of the
pulley.
(a) What analysis model is appropriate...
(a) Consider a pendulum with a mass m suspended at the end of a light string...
(a) Consider a pendulum with a mass m suspended at the end of a light string of length l. As it moves through the air the mass experiences a damping force that is proportional to its speed, with constant of proportionality y. (i) Show that the angle θ that the string makes with the vertical is governed by the ordinary differential equation dt2 m dt l in the limit of small θ. 1) State the natural frequency wo of the...
Please show work Two particles of m_1 and m_2 are connected by a light, inextensible string...
Please show work
Two particles of m_1 and m_2 are connected by a light, inextensible string of total of mass length L, which passes through a smooth hole in a smooth horizontal table. The mass m_2 is suspended below the table, and the mass m_1 moves in a circular motion on the table with an initial distance R_0 from the hole. A gravitational field g acts on this system. The mass m_1 starts out with speed v_0 on the table...
Hi, can you solve the question for me step by step, I will rate up if the working is correct. I will post the answer together with the question. Answer: Question 7 Implement the following: A reel co...
Hi, can you solve the question for me step by step, I will rate
up if the working is correct. I will post the answer together with
the question.
Answer:
Question 7 Implement the following: A reel consists of two solid uniform circular discs, each of mass m and radius 2R, attached to two ends of a solid uniform cylindrical axle of mass m and radius R. The reel stands on a rough horizontal table. A light inextensible string has...
A.) Determine the tension in the cord before the string is burned B.) Show that the cord, strong ...
A.) Determine the tension in
the cord before the string is burned
B.) Show that the cord, strong enough to support the object
before the string is burned, is also strong enough to support the
object as it passes through the bottom of the swing
C.) The motion of the pendulum after the string is burned is
periodic. Is it also simple harmonic? why or why not?
Cord p 60° String A pendulum consists of a small object of mass...
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Two masses M and m are connected by a light, inextensible string that passes over a smooth pulley. The mass m is connected to one end of a Hooke's Law spring of force constant k, the other end of which is anchored to the floor, in such a way that the spring remains vertical. The system is released from rest, with the spring at its natural length, as shown. Show (a) that mass m executes simple harmonic motion (SHM) and...
2. An elastic string of m attached to it at a distance ' The other end of the string is fixed to a point B so that the string is just unstretched t held at B (by stretching the length a of the string) and then released. Show thatit will oscillate to andfto natural length (a + b) where a s b and modulus of elasticity y has a particle of mass a from one end, which is fixed to...
For the arrangement shown below, the inclined plane and the
small pulley are frictionless; the string supports the object of
mass M at the bottom of the plane; and the string has mass m. The
system is in equilibrium, and the vertical part of the string has a
length h. We wish to study standing waves set up on the vertical
section of the string.
For the arrangement shown below, the inclined plane and the small pulley are frictionless; the...
As shown in the figure below, two blocks are connected by a
string of negligible mass passing over a pulley of radius 0.270 m
and moment of inertia I. The block on the frictionless incline is
moving with a constant acceleration of magnitude a = 1.20 m/s2.
(Let m1 = 15.5 kg, m2 = 22.0 kg, and θ = 37.0°.) From this
information, we wish to find the moment of inertia of the
pulley.
(a) What analysis model is appropriate...
(a) Consider a pendulum with a mass m suspended at the end of a light string of length l. As it moves through the air the mass experiences a damping force that is proportional to its speed, with constant of proportionality y. (i) Show that the angle θ that the string makes with the vertical is governed by the ordinary differential equation dt2 m dt l in the limit of small θ. 1) State the natural frequency wo of the...
Please show work
Two particles of m_1 and m_2 are connected by a light, inextensible string of total of mass length L, which passes through a smooth hole in a smooth horizontal table. The mass m_2 is suspended below the table, and the mass m_1 moves in a circular motion on the table with an initial distance R_0 from the hole. A gravitational field g acts on this system. The mass m_1 starts out with speed v_0 on the table...
Hi, can you solve the question for me step by step, I will rate
up if the working is correct. I will post the answer together with
the question.
Answer:
Question 7 Implement the following: A reel consists of two solid uniform circular discs, each of mass m and radius 2R, attached to two ends of a solid uniform cylindrical axle of mass m and radius R. The reel stands on a rough horizontal table. A light inextensible string has...
A.) Determine the tension in
the cord before the string is burned
B.) Show that the cord, strong enough to support the object
before the string is burned, is also strong enough to support the
object as it passes through the bottom of the swing
C.) The motion of the pendulum after the string is burned is
periodic. Is it also simple harmonic? why or why not?
Cord p 60° String A pendulum consists of a small object of mass...
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