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The wave speed can be related to the tension and the mass per unit length of the string by the following equation: $$ v = \sqrt{\frac{T}{\mu}}$$ Here, $T$ is the tension, $\mu$ the mass per unit length and $v$ the speed of waves on the string. For a derivation of this equation refer to this or to any first year Physics textbook (e.g. Halliday & Resnick)...


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To answer to a real world problem assumptions have to made. In this case an assumption is made, the thread is massless and inextensible, which leads to a solution, for an instant of time the thread exerts an infinite force on the mass, the mass undergoes an infinite acceleration, the speed of the mass becomes zero instantaneously, which is not the experience ...


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If the thread is inextensible and massless, the body will immediately come to a stop the moment the thread becomes taut. Since this happens instantaneously, the force experienced by the string will be infinite for that small moment. However, realistically no string satisfies the above conditions. The threads will have some elasticity as well as a limiting ...


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According to @weeeeliam's answers to the following questions: What is the formula for calculating the tension of the rope section? There is a circle of rope that rotates at a uniform angular velocity $ω$. What is the formula for calculating the tension of the rope section? Without gravity, the density of the rope is $ρ$, the radius of the rope circle is $R$...


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Consider an infinitesimally small section of the of the string $d\theta$. The following diagram illustrates this: The tension is of the same magnitude throughout the rope, and it acts perpendicular to the vector from the center of the string to the point of action. From this diagram, you can tell that only the x-components to the left matter, since the y-...


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An impulse acting at point A gives the 2m mass its velocity, and the center of mass a parallel velocity of (2/3)V. Since the impulse is not acting in line with the center of mass, it also provide an impulsive torque which causes the system to rotate around the center of mass. Working in the center of mass system is valid and gives a tension which is the ...


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A perfectly elastic object, when deformed, will immediately return to its undeformed shape when the deforming forces are removed. In so doing, it will dissipate zero energy: all the work done in deforming it is returned when it is allowed to relax again. This is true whether the object is stiff (like a cube of steel) or flexible (like a cube of rubber). A ...


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Welcome to Physics StackExchange! If both you and the sledge are on a frictionless surface, and the rope is massless, then yes, your application of Newton's third law is correct, you will accelerate towards the sledge at 1.6 $m/s^2$. If you are on rough ground (but the sledge is on a frictionless surface), then the ground exerts the same magnitude of ...


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D'Alembert principle is nothing but a prescription of a type of constraints -- also known as ideal constraints -- such that the equation of motion can be written in the form of Euler-Lagrange equations, by using an arbitrary system of coordinates obtained by "solving the constraint equations". The definition requires that, at fixed time, the total (...


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The author of the excellent book where I found this problem (The Lazy Universe) explains in another part of the book: A surprisingly tricky example is the case of a sliding block which is pushed across a table-top by a force, say, pushed by your finger (we ignore friction). The displacement of the block is anywhere on the surface whereas the ...


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Whether the tension is a constraint, or not, depends how you model the problem. Method 1: consider "the two masses plus the rope" as one body, and use just one coordinate to measure its position. Obviously the "single body" changes shape as it moves, and one mass moves up and the other moves down, but that doesn't affect the general principle of calculating ...


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Gravity is pulling the weights down, the cable provides a directly opposing restraint, to keep the weights from accelerating downwards at 9.8 meters per second per second. The actual work is done by using the heavier weight's gravitational potential.


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What is the constraint enforce by the tension? How does it show up in your generalized coordinates? As I noted in the comments it is usual to chose a set of generalized coordiantes with a single position for each rope (and the location of the other end found by calulating from there); this form has the constraints built-in, so that there is no way to ...


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To solve it in the ground plane you need to separate out in your mind the rotation about a common centre of mass and the movement of the centre of mass. You might then need to think about the special case of such motion in which one of the masses stops moving from time to time in a particular reference frame. Googling 'cycloid' might also shed some light. ...


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This is a complex question. The pure vibration of a string at a single frequency takes on a sine wave pattern. The plucking of a string deforms the string in a non-sine shape, so the disturbance is a linear combination of sine and cosine (a $\pi/2$ phase shift of sine) of multiple frequencies which are determined by properties of the string. The string acts ...


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[Refer to the diagram] When the man pulls the rope downward with a force $T$ the rope too pulls him up with the force $T$ (Newtons 3rd law). Also this force gets transfered via the rope to the the man and it pulls him with a force of $T$. So the total force acting on him is $2T-mg$ but if he is at rest or moving with constant velocity then $T =mg/2$.


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This is a simple analysis; Take an object, and hang it from a pulley with two ropes coming to the object.What is the force on the pulley? The weight of the object, you could measure with a proper scale. This means that , all other things being equal, the tension on each rope is half the weight of the object, by construction. Now if it is a girl being the ...


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The velocity of propagation of a wave in a string ( v ) is proportional to the square root of the force of tension of the string ( T ) and inversely proportional to the square root of the linear density ( $\mu$ ) of the string: $$ v=(T/\mu)^{1/2} $$ Once the velocity of propagation is known the fundamental harmonic frequency is given by: $$ f=(v/(2L))=(1/...


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