Mechancis Definition and 137 Threads

I am struggling through a problem in one of my designs and would appreciate some help. Please refer to the image attached. Problem Description: S = Torsion spring F = fixed point T = tire A tire is attached to a torsion spring through an arm as shown in the image. The torsion spring has one...

3. Find the hamilton equations 4. using 3. prove the the angular momentum in the z axis ##L_z=m(x\dot y-xy\dot)## is preserved. I got in ##3##: How can I prove 4?

My approach: Let us take two orthogonal axes: x, parallel to the racket's plane and y, perpendicular to it. For the ball to not spin, the components of initial velocities of the racket and the ball along x-axis must be same. Also, as the line of collision is along the normal to the racket's...

So I am a bit stuck on this question as my result using the above equations dose not give an numerical value which I assume from the question is needed. So here my method for solving My first thought was that if on the planet the person can throw a rock 10 time further then that it implies in...

On object 2: There are only 2 horizontal forces - Friction and Tension (of the spring). T = km2g On Object 1: There are 3 horizontal forces and the minimum value for F is when: F - km1g - km2g = 0 F = kg(m1 + m2) However, Solution is: F = kg(m1 + 0.5 m2) Any opinion?

<< Mentor Note -- thread moved from the technical forums, so no Template is shown >>[/color] Show, from the first principles, that the equation of motion of a mass (m) on a spring, subjected to a linear resistance force R, a restoring force S, and a driving force G(t) is given by d2x/dt2+...

Homework Statement A frog jumps at t=0s and follows a projectile motion. The maximum height he reaches is 0.45m. The air resistance can be neglected. a) What is the initial speed of the frog in y-direction and how long is the total time until he lands on the ground? b) At which degree should...

Hello everyone, I need some help to calculate the force required to bend a tor steel bar of dia 20mm and 12 m long from the centre. I want to bend it like a hair pin and need to know how much force is exactly required to do so. Any help or resource would be great. Regards, Mradul

Homework Statement A “superball” of mass m bounces back and forth with speed v between two parallel walls, as shown. The walls are initially separated by distance l. Gravity is neglected and the collisions are perfectly elastic. If one surface is slowly moved toward the other with speed V...

So I tried solving the differential equation for a spring - mass system using Euler's Algorithm in Python. The equation being d2x/dt2= -4π2x (The equation was obtained by Dimensional Analysis) here x and t are both dimensionless equivalents of position...

Homework Statement A circular plate with radius 0.5 m and mass 5 kg is hung on the wall, fixed at a point that is 0.3 m above its center. The plate can freely rotate about the fixed point with no friction. A very short-duration impulse of 5 N sec, along a direction that is tangential to the...

Homework Statement We have an Atwood machine like the picture below. one side (left) is a bucket full of water which has a hole on the bottom and the water is flowing with rate ##dm/dt = \alpha = const##. The initial mass of bucket with the water is ##m_0##. On the other side (right) we have a...

Homework Statement This question is actually two question. We have two hollow frames - one is rectangular and another is triangular. the rectangle is rotated and fixated such that the angles in shape are ##\alpha , \beta = 90 - \alpha## and the angle of triangle is ##\alpha##. We have two balls...

Homework Statement Question from fundamental of physics, Halliday Resnick Walker In Figure below, a ##m=0.250## kg block of cheese lies on the floor of a ##M=900 kg## elevator cab that is being pulled upward by a cable through distance ##d1 =2.40 m## and then through distance ##d2 = 10.5 m##...

Homework Statement We shot a projectile with mass ##m## and velocity ##v_0## with angle ##\phi## it collide with a box with mass ##M## at the maximum height of its path. Then, they both start to move with another speed. (We define ##t=0## at this time) (Completely Inelastic Collision). The box...

Homework Statement Question from Fundamentals of Physics (Halliday, Resnick, Walker) This figure below shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction...

Homework Statement The Actual Question is that: A car is moving on a circular hill with radius R. what is the maximum speed it can have at the apex of the hill such that it doesn't jump of from the hill. I know the solution but I want to know how will be the equations if the velocity is...

Homework Statement The question is from Fundamental Physics 10th Edition, Walker Resnik Holiday: A banked circular highway curve is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day.What is the minimum...

While reading http://www.dartmouth.edu/~sullivan/22files/System_analogy_all.pdf article, i encountered the following sentence: Thus, we see that K is analogous to 1/C , which makes sense, because with a given current for a given time, a smaller capacitor will build up more voltage, whereas with...

Homework Statement We have two cars moving like the picture. we want to find their minimum distance using relative motion. I) Consider a coordinate system on M, which has two axis. one axis is in direction of MP and the other is perpendicular to that (Something like r_hat and θ_hat). Find the...

Hey guys, I am Yasmeen, a12th grader.I am taking my #SAT physics and maths1 test next month. Hope To find the help in here..

I just want to know the difference between those rules: 1. R^2 = F1^2 * F2^2 + 2*F1*F2*COS(the angle between F1 and F2) 2. The second is about the parallelogram rule, it says that the two vectors are added and their summation is the magnitude of the resultant. Which one is correct?

<<Moderator's note: Moved from a technical forum, no template.>> Description of the system: The masses m1 and m2 lie on a smooth surface. The masses are attached with a spring of non stretched length l0 and spring constant k. A constant force F is being applied to m2. My coordinates: Left of...

1. A weightless rod carries towards of masses M and M. The roads Hinge Joint to vertical axis OO', which rotates with an angular velocity ω. Determine the angle φ formed by the rod and there vertical. The attempt at a solution If I am not wrong, the two ways to ensure equilibrium are...

We have a cube on an inclined plane. The tipping condition is the presence of an unbalanced torque relative to the center of mass (contributing forces are: the normal force and the force of friction). However, is this conditions equivalent to the previous one: The line of action of the force of...

Homework Statement I know that a bead is threaded on an metal sring (no T), and the bead is not moving/ The metal string moves in circular motion at a slope of 60 degrees. The string moves one spin in one second/ which powers works on the bead? Homework EquationsThe Attempt at a Solution

Can anyone help me on this problem from this video starting from 8:03 , I've been working on it for a week ,and I couldn't find a solution.

Homework Statement A horizontal disc is rotating with an angular velocity w about its axis perpendicular to its plane. A small body of mass m moves with velocity v relative to the disc alog the diameter. Find the net force exerted by the disk on the body as function of radius from centre...

In Lagrangian mechanics, both q(t) and dq/dt are treated as independent parameters. Similarly, in Hamiltonian mechanics q and p are treated as independent. How is this justified, considering you can derive the generalized velocity from the q(t) by just taking a time derivative. Does it have...

I am getting correct equations on using the Lagrangian method in Systems with no non conservative forces, but when I use it in Systems with friction, sometimes I get correct equations, and sometimes I do not. Most of the equations have some problem with the coefficients of the frictional forces...

Homework Statement Homework Equations The Attempt at a Solution

Homework Statement A model yacht runs on a horizontal frictionless oval track as shown (viewed from above) in the figure. The curved parts of the track are semi-circles of radius ##R = 0.5 m##; the straight sides have length ##L = 1 m##. The mass of the yacht is ##m = 0.5 kg.## A force of...

Homework Statement A mass m is initially at rest. A constant force $F$ (directed to the right) acts on it over a distance d. The increase in kinetic energy is therefore $Fd$. Consider the situation from the point of view of someone moving to the left at speed $V$ . Show explicitly that this...

1.Problem statement Prove the average external force of a system of particles N starting from rest and ending at rest is zero.Homework Equations If the system moves periodically prove the av. external force is zero in a period The Attempt at a Solution I don't quite understand what i am asked...

Hello. Lets say I am riding a unicycle rolling along the wheels direction with some velocity v0. I know that for the unicycle to turn a curve the centripedal force must be provided by the static friction with the rode that acts against any slipping of the wheel. I am however having trouble...

Homework Statement Homework EquationsThe Attempt at a Solution Taking change in the kinetic energy per unit time as power, P = ## \frac {d W}{dt} = \frac {d K}{dt} = \frac 1 2 \frac { dm} {dt} v^2 = 36.75 ## watt...(1) ## P = \vec F \cdot \vec v = \frac{ dm} {dt} \vec v \cdot \vec v =...

Homework Statement Homework EquationsThe Attempt at a Solution Applying conservation of potential energy, ## mgL (1 - \cos{ \theta_0}) = mg(L + \delta ) (1 - \cos{ \theta_1}) ## ## \cos{ \theta_1} - \cos{ \theta_0} = \frac { \delta - \delta \cos{ \theta_1}} L ##Taking the...

Homework Statement One end of a light elastic string of stiffness mg/l and natural length l is attached to a point O. A small bead of mass m is fixed to the free end of the string. The bead is held at O and then released so that it will fall vertically. In terms of find the greatest depth to...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] The thing to remember is that inside the Earth surface, the gravitational field does not remain inversely proportional to ##r^2##. The equation of motion is ## \ddot r = \frac { -gr} R## ....(1) This means that the...

Homework Statement Homework EquationsThe Attempt at a Solution Trying to answer it before solving it, The maximum tension force is mg, so the average has to be less than this. Hence, the option (a) and (c) are not correct. ## T = mg \cos \theta ##, where ## \theta ## is the angle between...

Homework Statement A mass m1 collides with stationary m2 with velocity u1 u. Find the fraction of energy converted into heat and sound. Show that this energy is equal to the kinetic energy from centre of mass reference frame Homework Equations [/B] let v1 and v2 be velocity of m1 and m2 after...

Homework Statement Homework Equations friction force = F_v m=m1 The Attempt at a Solution is method 1 correct? if so, why method 2 came out with a totally incorrect answer. I understand that you can also set up acceleration equations for m1 and m2, since their acceleration are equal, and...

particles in plane polar coordinates r = rcosθ i + rsinθ k F = Fer + Feθ ∂r/∂r =|∂r/∂r|er = (cos2θ + sin2θ)½er = er why ∂r/∂θ =|∂r/∂θ|eθ = (r2cos2θ + r2sin2θ)½eθ = reθ I understand that ∂r/∂θ = -rsinθ + rcosθ but why ∂r/∂θ = (r2cos2θ + r2sin2θ)½eθ

Homework Statement A dinner plate, of mass 580 g is pushed 90.0cm along a dining room table by a constant force of F = 3.60 N directed at angle theta = 24.0 deg below the horizontal. If the coefficient of kinetic friction between the plate and the table's surface is 0.440 determine a. the...

I've been having some trouble with this problem for a while. (Its not a homework or coursework problem) Its a part of an experimental set up that I'm building and this is a simplified version of it. I have a rigid rod which is hinged at a point and can pitch or heave about that location. There...

Homework Statement A bead slides without friction on a horizontal rigid wire rotating at constant angular speed ω. The problem is to find the force exerted on the bead by the wire. Neglect gravity. Homework EquationsThe Attempt at a Solution The physical force acting on the bead is the force...

Homework Statement A particle of mass m and and velocity v collides with a square of mass M (at rest)whose movement is confined to rotation about its centet. I must now solve for the angular velocity and the velocity of the particle after the collision (elastic collision) Homework Equations...

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 person enters a curve of a waterslide with velocity v. The curve is fully horizontal and has the shape of a circle segment of radius R, there is no friction and width of the curve can be neglected for calculating the centripedal force. The waterslide itself can be described...

How can I simulate this spring system and see how they move and behave? Thank you.