Dynamics Definition and 1000 Threads

Imagine that we have a closed plastic bottle filled with water and then we punch a hole with area A in its cap. How can I find the initial velocity the water will he "fired" with if we squeeze the bottle applying stress S? Assume that we know all about the bottle (moduli, change in volume etc...

Homework Statement A 0.1-kg block moves along the x-axis. The resultant of all forces acting on the block is F = -1.2tiN, where t is in seconds. When t=0, x=0 and v=54i m/s. Determine the distance traveled by the particle during the time interval t=0 to t=4s. Homework EquationsThe Attempt at...

I have been reading quite a lot about the Physics behind car dynamics and I have gotten to a point which keeps confusing me, namely - brake locking. I understand brake locking as the situation when the wheels of the car do not rotate anymore but the car is still moving - this causes the tires...

In basic car aerodynamics car manufactures know the basic design in every car creates lift. Let's take the Prius for example, very aerodynamic but does not have any downforce due to the shape of the vehicle (air travels farther on top of the car) being shaped like a wing of an airplane. My...

I am stuck on the questions, 5.3.10 and 5.3.11 which are part of a chapter on dimensional analysis in fluid mechanics by Streeter. Question 5.3.10 (see also the attachment): It asks me for the given fluid dynamic problems, where is the inertial force not important. It lists several fluid...

Let's imagine that we fire a cannon located on a platform high above the ground and we want to compute the time after which the horizontal velocity of the cannonball will be zero. Let's assume that we shoot at 0 degree angle. 1. Air resistance force F = C_d \frac{\rho v^2}{2}S 2. Assuming that...

Imagine such situation: There is a sniper who fires his rifle, the bullet travels at the initial speed of, say, 1400 m/s. His target is standing 2000 meters away and the wind is blowing at 30 m/s opposing the bullet's motion. Let's assume that the bullet is fired in a straight lane and it may...

I wonder if it is possible to at least estimate the stress (or the impact force) that the cube in question will experience due to the collision with the concrete floor. Assumptions: 1. The cube is dropped from height h 2. The cube is relatively small, thus we can neglect air resistance...

Homework Statement Homework Equations F_spring = ks and F_spring potential = 1/2ks^2 The Attempt at a Solution So I recognize that @ theta = 0 it is a 3/4/5 triangle. The length of the spring is at .5m...furthermore the given spring force at that angle is 100 N. So why is it wrong to do...

Homework Statement the plane C is being tracked by radar stations A and B. At the instant shown, the triangle ABC lies in the vertical plane, and the radar readings are θA=30o, θB = 22o, θA(dot) = 0.026rad/s and θΒ(dot) = 0.032rad/s. Determine (a) the altitude y; (b) the speed v; and (c) the...

Homework Statement A rocket engine takes 8 seconds after firing to reach its full thrust. Assuming that the rocket was fired at t=0, use the following time-elevation data to estimate the velocity and acceleration (a) at t=0; and (b) at t=8s Homework EquationsThe Attempt at a Solution I don't...

Homework Statement When a particle moves along the helix shown, the componentsof its position vector are x=Rcosωt , y = Rsinωt , ##z=-\frac h {2π} ωt## where ω is constant. Show that the velocity and acceleration have constant magnitutes, and compute their values if R=1.2m, h=0.75m, and...

Homework Statement Problem: [/B]During a pond hockey game, a puck accelerates from rest at 5.0 m/s 2over a distance of 80.0 cm. The puck then slides with a constant speed for 4.0 s until it reaches a rough section which causes it to stop in 2.5 s. a. What is the speed of the object when it...

Today I've come across the statement that the coefficient of static friction of rubber tires on asphalt is bigger than that of tires on concrete. Does it mean that the maximal acceleration a car can attain on asphalt will be greater than that on concrete? My assumptions: 1)The force of friction...

Homework Statement An automobile goes down a hill that has the parabolic cross section shown. (see image attached) Assuming that the horizontal component of the velocity vector has a constant magnitude v0, determine (a) the expression for the speed of the automobile in terms of x; and (b) the...

Homework Statement m1= 0,05 kg, m2= 0,03 kg, mass of spring is omitted. We look at movement after spring stopped vibrate. How long does the spring measure during the movement if not stretched spring measure 0,1 meter and if we use force 0,1N elongation measures 0,02 meter. (sorry, English isn't...

Homework Statement A missile is launched from the surface of a planet with the speed v0 at t=0. According to the theory of universal gravitation, the speed v of the missile after launch is given by v2 = 2gr0(r0 / r -1) + v02 where g is the gravitational...

Hi! I have Pytel Mechanics Dynamics 2nd edition and revising for my own purposes (not a homework). I am trying to solve problem 12.4: A bead moves along a straight 1500-mm wire that lies along the x-axis. The position of the bead is given by x=t2 - 10t mm where x is...

Assuming we have a cylinder that is rotating on a single axis, how would I go about calculating the torque knowing the following information? m = 2000 kg w = 60 rpm r = 5 m

Homework Statement the moment of inertia of A cylinder of height 2h radius (a) and uniform mass density ρ about a line x=y=z using multiple integration. Homework Equations I=ρ∫s^2*dV where the integral is over the volume V of cylinder and s is the perpendicular distance to the axis of...

Hi All, Looking for some help (any is greatly appreciated). I've been tasked with the below, and am unable to find a worked example to cross check my work against. If anyone with a greater knowledge than me could have a look at the below and advise if I'm right the right track. Thanks 1...

Homework Statement A sphere of radius ρ constrained to roll without slipping on the lower half of the inner surface of a hollow cylinder of inside radius R. Determine the Lagrangian function, the equation of constraint Homework Equations v= ω × r The Attempt at a Solution NOT HOMEWORK-SELF...

Homework Statement circular hoop is suspended in a horizontal plane by three strings, each of length l, which are attached symmetrically to the hoop and are connected to fixed points lying in a plane above the hoop. At equilibrium, each string is vertical. Show that the frequency of small...

Homework Statement PROBLEM 7-10[/B] Two blocks, each of mass M, are connected by an extensionless, uniform string of length l. One block is placed on a smooth horizontal surface, and the other block hangs over the side, the string passing over a frictionless pulley. Describe the motion of the...

Homework Statement More a report question but unsure where to put it. Take a 5mL syringe and a 10mL syringe (both filled to 5mL) with the plungers removed. Time how long it take to full drain each syringe Make a statement regarding your results. Homework Equations Fluid flow rate = volume /...

1. For the mechanism shown in FIGURE 1 determine for the angle θ = 45°: (i) the velocity of the piston relative to the fixed point O (VBO) (ii) the angular velocity of AB about point A (i.e. ωAB) (iii) the acceleration of point B relative to A (aBA). (b) Determine the value of the angle θ...

Homework Statement A particle of mass m is on top of a frictionless hemisphere centered at the origin with radius a" Set up the lagrange equatinos determine the constraint force and the point at which the particle detaches from the hemisphere Homework Equations L=T-U The Attempt at a...

Homework Statement This is a common massless string and pulleys problem. I'd just like to understand why, according to the solution, l_2 + 2l_1 = constant. It doesn't seem to me that two times the l_1 length is equivalent to l_2. Can somebody explain? Homework EquationsThe Attempt at a Solution

Hello there, Situation I got a research position at my university in studying amyloidogenic proteins, which are associated with many different neuro-degenerative diseases. The professor has a NovoControl Dielectric Spectrometer in the lab, which will be the main equipment used to gather data...

1. Homework Statement Determine the total magnitude of angular momentum Ho of the particle about point O. The velocity of the particle is 5.5 m/s.Homework Equations Ho= r x mv The Attempt at a Solution The answer is 43.04. My question is, isn't the graph wrong? If you take the magnitude of the...

Hi all, i ask in advance sorry for my bad english, i hope you will understand my question. I'm studying the motion of a plume fluid in a fluid ambient, with ρ(plume) > ρ(ambient). Afterwards there si a transport of fluid ambient as an effect of the turbolence caused by the viscosity between...

Homework Statement In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture. The tire remains stationary in spite of the three pulls. Alex pulls with force \vec{F_A} of magnitude 220~N, and Charles pulls with force...

Hi. I am revising my Mechanics: Dynamics by reading the Beer 10th edition textbook and Pytel 2nd edition In Pytel pg 358 art. 17.3 the angular momentum about the mass center of a rigid body in general motion is being calculated...

Homework Statement Homework Equations This would be the part I think I'm missing The Attempt at a Solution In the fourth line, Ix, where is the justification for multiplying 1/3 by the first term? I believe they are using the center of inertia of a rod, which is mr2 and the first term...

Why does the planetary boundary layer velocity profile shows a sinusoidal variation with height? Reference: Fig:14.10 Page 576 Fluid Mechanics - Kundu and Cohen 2nd edition

Homework Statement In the given figure, a wedge of mass 2m is lying at rest on a horizontal surface. The wedge has a cavity which is the portion of a sphere of radius R. A small sphere of mass m is released from the top edge of the cavity to slide down. All surfaces are smooth.Prove the maximum...

Homework Statement A uniform circular disc of mass 2m and radius R placed freely on a horizontal smooth surface as shown in the figure. A particle of mass m is connected to the circumference of the disc with a mass less string. Now an impulse J is applied on the particle in the directions...

Homework Statement A block of mass M = 0.5kg, attached to a spring of elastic constant k = 3N/m on a vertical wall, slides without friction through an horizontal air table. A disk of mass m = 0.05kg is placed on the block, whose surface has a coefficient of static friction \mu _e = 0.8. What...

I am doing a review for a Dynamics exam, but I am having trouble with this one question (below). Please note the top of the picture contains the answers. What I have done is make a free body diagram that includes the tension of the cable and the weight of the rider/swing. So according to my...

Homework Statement Two spheres, with 0.5g each, are hanging by 30cm threads, tied on the same spot. The same electric charge is communicated to each sphere; in consequence, the threads move apart until they are about 60^\circ from each other. What is the value of the charge? \theta =...

Hi all, I am interested in rotating convection. Anyone know of any open questions, or where to find research topics in this area? Cheers.

Homework Statement A thin walled spherical shell with a mass of 0.605 kg and a radius of 0.0402 is released, from rest, at the top of an incline. The spherical shell rolls down the incline without slipping. The spherical shell takes 7.49 s to get to the bottom of the incline. A solid sphere...

Homework Statement potential energy function of : $$ U(x) = 4x^2 + 3 $$ And have to i) Work out the equation of motion ii) Prove explicitly that the total energy is conservedHomework Equations$$ F = \frac{dU}{dt} $$ The Attempt at a Solution I'm not too sure how to go about this...

Homework Statement Homework Equations The last part of this question is an example of this result: The Attempt at a Solution Here is the solution I think L' is missing a term: If we take the Earth as your frame of reference.(i.e. You are stationary, watching the movement of the railway...

Homework Statement I think I made a mistake somewhere.. Homework Equations T = Jα T = F*R The Attempt at a Solution A) I started with T = Jα Since there is no slip, αm = αL Thus: Tm / Jm = TL / JL Plugging in, we find TL = Tm * JL / Jm = 2560 Now use T = F*R. Tm = Fm * Rm Plugging in...

Homework Statement "Figure 5 depicts a 30 000 kg aircraft climbing at an angle θ = 15˚ when the thrust T = 180 kN. The aircraft’s speed is 300 km/hr and its acceleration is 2m/s2. If the radius of curvature of the path is 20 km (i.e., θ is decreasing), compute the lift and drag forces on the...

The integral formulation of Maxwell equations, for example the one called "Gauss' theorem", see the first equation here: https://en.wikipedia.org/wiki/Maxwell's_equations is still valid in dynamics, with rapidly varying sources? We know that a rapidly varying charge here gives a flux of an...

I recall reading somewhere (I can't remember where) that there is astronomical evidence that dark matter has different densities in different parts of the relatively near parts of the observable universe. Q1. Is this correct? If so, can someone please post a link to a relevant article? The...

Hi all, I encountered a fairly straightforward problem involving fluid dynamics, but the result I got is very confusing and I seem not to understand where I got wrong. This is the question: A rectangular flat-bottom barge with a bottom area A=50 m2A=50~\text{m}^2A=50 m2 is loaded so that the...

Good evening, good people of PF. I have a fairly simple question. Please see the attached drawing. My question is this: does the moment of inertia change from position one to position two (as the weight is rotating around a center line). In essence, does it maintain the same moment of inertia...