Motion Definition and 999 Threads

Homework Statement The task is to design a highway. I did a similar project last year but I have completely forgotten and have no clue what to do. You have to design a banked, circular, clockwise highway exit. you knwo you have 5000 sq. meters. of land to build it on..you also know that the...

Homework Statement Homework Equations L = T-V For constant frequency tangential velocity is (radius)*(w) The Attempt at a Solution I need to find r(t) using the Langrangian L = T-V I just was not sure whether I am on the right track for calculating the total kinetic energy for the above...

I have a question to a physical task in Mathematica. We have this equation of motion: For energy of masspoint there is the condition : I have to write a procedure that uses the law of the conservation of energy for the potential V(x) to calculate t(x_1) - t(x_0) when there are given two...

Homework Statement [/B] picture 1: picture 2: Homework EquationsThe Attempt at a Solution For the first picture I was thinking answer B because at the start velocity increases, but as terminal velocity is hit the velocity doesn't increase as much.. why is it graph A? For the second...

Homework Statement Calculate the angle of Projection for which Kinetic Energy at the highest point of trajectory equal to one-fourth of its kinetic energy at point of projection? Homework Equations Range and height of Projectile equations The Attempt at a Solution [/B] I've made two...

The thought of increasing a satellite's (for example) speed to allow it to transfer from a "higher energy" elliptical orbit to a "lower energy" circular orbit (in reference to the effective potential energy plot that arises after introducing the concept of an effective mass to simplify the...

Homework Statement A vertical block-spring system on Earth has a period of 6.0 s. What is the period of this same system on the moon where the acceleration due to gravity is roughly 1/6 that of earth? Homework Equations w = √(k/m) w = (2Pi)/T T = 2Pi*√(m/k)[/B] The Attempt at a Solution So...

Homework Statement [see attached photo] I seek specific help with (a) only. The answers to this question are provided in the back of the textbook, so I know the answers (I hope). Homework Equations ##x(t)=Acos(\omega t+\phi _{0}),## ##v_{x}(t)=-A\omega sin(\omega t+\phi...

Homework Statement Object A is stationary while objects B and C are in motion. Forces from object A do 10 J of work on object B and –5 J of work on object C. Forces from the environment do 4 J of work on object B and 8 J of work on object C. Objects B and C do not interact. What are ΔKtot and...

Homework Statement Hookes Law gives: F = -kx. This is SHM. But I cannot see how to get to the sinusoidal expression from this. (In all the explanations, they cheat, and just introduce de novo Omega or Omega^2.) But how do you get to m. d2x/dt^2 = -x.(omega) ^2 Homework Equations F = -kx. m...

For a null particle, ds^2 = 0, Timelike, ds^2 >0, spacelike, ds^2 < 0, how would you characterize the motion of each particle?

Homework Statement A bus is traveling at a constant speed of 6.2ms-1 along a section of road that is inclined at an angle of 6.0degrees to the horizontal. a) the total output power of the engine of the bus is 70kW and the efficiency of the engine is 35%. calculate the power to the engine b)...

Hi everyone! I recently came across the Lyusternik-Fet theorem concerning closed geodesics on a compact manifold. For simplicity of description, take the 2-torus, and imagine it represents the configuration space of a double pendulum. For every pair of integers m, n (where m represents the...

Hi! I was trying to understand circular motion and came across two problems. I would really appreciate if you could help me with those. Question 1: In the picture below let's assume that the angle θ is 1 radian, i.e. 57.3°, radius is 1 m. It would mean that the length of arc AB is also 1 m...

Homework Statement ##\ddot{\Phi_i}-\frac{k}{ml^2}\Phi_i+\frac{k}{ml^2}\Phi_{i+1}=0## This is the equation of motion of a series of pendulums linked by a torsion spring in the case where ##g=0## Homework EquationsThe Attempt at a Solution I haven't really met this type of equation before. I...

Homework Statement You need to derive a formula for undamped pendulum simple harmonic motion; 1. Starting from the middle point 2. Starting from the extreme point Homework Equations The solutions are; 1. s = s0 sin(2 pi f t) 2. s = s0 cos(2 pi f t) The Attempt at a Solution I can derive the...

I was thinking about this and couldn't really figure it out. You are standing on a cliff and you have two identical balls. In this case, air resistance is to be ignored. The only thing different is that you throw the ball horizontally at different speeds. Let's say you threw ball one at a speed...

Homework Statement ##\ddot{r} = c \frac{1}{r^2}##, where ##c## is a constant, and ##r## is the position of one object with respect to the other. I need to find the function ##\dot{r}(r)## We are in one dimension. Homework EquationsThe Attempt at a Solution I don't really have any idea how to...

I'm having trouble understanding the forces involved when defining the equation of motion for this particular problem. So... I've seen the answer for the eq. of motion worked two different ways. The first way involves combining the spring series into Keq = K1⋅K2/(K1+K2). The answer, plugging...

Homework Statement If an object moves in a circular path with a speed that increases at a constant rate, which of the following can be concluded? (A) The radial component of the force acting on the object is zero. (B) The net force acting on the object is zero. (C) The net force acting on...

Homework Statement A cat spots a flowerpot that sails first up and then down past an open window. The pot is in view for a total of 0.50 s, and the top-to-bottom height of the window is 2.00 m. How high above the window top does the flowerpot go? 2. Relevant equation Not sure but the theory of...

Homework Statement An archer launches an arrow from coordinates ##(0, 0)## at an angle ##\alpha## and with an initial velocity ##v_0##. There's a target located ahead of the archer and the center of that target is at coordinates ##(d, h)##. At what ##v_0## and at what angle ##\alpha## does...

I'll attach a picture of what I mean but essentially I wanted to know if it was possible to (under circumstances where the Earth and moon do not change angle of rotation when orbiting the sun) create a perpetual motion machine using orbit as a means to turn a giant gear circling the Earth in...

Homework Statement "A compact disc (CD) stores music in a coded pattern of tiny pits 10−7m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD...

Homework Statement A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.381m. The maximum transverse acceleration of a point at the middle of the segment is 8600 m/s and the max. transverse velocity is...

Homework Statement The vector position of a 4.00 g particle moving in the xy plane varies in time according to 1 = (3i+3j)t +2jt^2 where t is in seconds and is in centimeters. At the same time, the vector position of a 5.95 g particle varies as 2 = 3î − 2ît^2 − 6ĵt. Determine the acceleration...

Homework Statement A projectile is fired with an initial speed of 46.6 m/s at an angle of 42.2 ∘ above the horizontal on a long flat firing range. 1-Determine the maximum height reached by the projectile. 2-Determine the total time in the air. 3-Determine the total horizontal distance...

Homework Statement How would the motion of the block look like when the Force of kinetic friciton is more than the Limiting value of static friction? Homework Equations Kinteic Friciton=μN The Attempt at a Solution I think the block after overcoming the limiting value of static friction will...

Homework Statement While learning to drive, you are in a 1 320-kg car moving at 34.0 m/s across a large, vacant, level parking lot. Suddenly you realize you are heading straight toward a brick sidewall of a large supermarket and are in danger of running into it. The pavement can exert a...

Homework Statement A projectile is launched at an angle of 60° from the horizontal and lands 99 s later at the same height from which it was launched. 1) What is the initial speed of the projectile (in m/s)? I already figured this out to be 560.16 m/s 2) What is the maximum altitude (in m)...

Homework Statement Two identical trucks traveling at different constant speeds are about to collide. The trucks are traveling in opposite directions with truck A going at a velocity of 3m/s right and truck B going at 4m/s left. During the collision, will the magnitude of the acceleration of...

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...

I have been reading Feyman Lectures Volume 1 and I am stuck on the example or proof given in the book about how no machine can be more efficient than a reversible machine. http://www.feynmanlectures.caltech.edu/I_04.html Section 4-2 A very simple weight-lifting machine lifts weights three...

I'm a little confused with the application of laws of motion on a man climbing a rope. Suppose a man of mass Mg is climbing a rope with an acceleration a. Rope is massless. Now if look through the frame of the piece of rope held by the man, there is a force Mg downward by man, ma downward...

Homework Statement We had a lab on projectile motion and one of the questions was this: Use your Vy versus t graph to determine the y-component of the acceleration of the puck. Should this be equal to the acceleration due to gravity (9.8 m/s)? Explain why it is or why it is not. The...

Homework Statement Imagine a vertically placed clock. What forces have an effect on the object when it is in the position of 3am? Homework Equations No need od equations i guess. The Attempt at a Solution So I figured out that when the object is in the position of 12am then weight of the...

We know that energy is a function of space and velocity and it’s constant (in ideal case) though time. So ## E(\vec{x}(t) , \vec{\dot{x}}(t)) = E_0## where ##\vec{x} , \vec{\dot{x}} \in \mathbb{R}^3##. So my function is ##E : \mathbb{R}^6 \rightarrow \mathbb{R}##. Then there is my question...

Homework Statement You swing a 1.60m long string with a metal ball attached to its end in a vertical circle, such that the speed of the ball does not change but the rope is always taut. The tension in the string when the ball is at the bottom of the circle is 60.0N more than the tension when...

Homework Statement A curious child finds a rope hanging vertically from the ceiling of a large storage hangar. The child grabs the rope and starts running in a circle. The length of the rope is 14.0m. When the child runs in a circle of radius 7.0m, the child is about to lose contact with the...

Homework Statement An object moves at constant speed in a circular path. True statements about the motion include which of the following? a) the velocity is constant b) the acceleration is constant c) the net force on the obj is 0 since its speed is constant Homework Equations hm none...

Homework Statement Two cars are facing each other on a long straight airport runway. They are initially separated by a distance of 1 km. Car A begins to accelerate towards the other car at a uniform 0.5 ms^-2. Ten seconds later car B begins to move towards the other car with a uniform...

Homework Statement A hammer bro is throwing hammers with a velocity of 1.7 E 1 m/s at 51 degrees down at Mario from a ledge that is 8.5 m tall. Assume that gravitational acceleration in the Mushroom Kingdom is the same as on Earth. Determine how long each hammer in in the air. Homework...

I'm a teacher at a Senior High School in Indonesia. I have two Senior High School physics books (Indonesian book) written about simple harmonic motion formula: y = A sin θ = A sin (ωt + θ0) = A sin 2πφ = A sin 2π (t/T + θ0/2π) phase angle = θ = ωt + θ0 phase of wave = φ = t/T + θ0/2π But I...

Homework Statement We have been given the following mass-spring-damper diagram, and are asked to derive the equations of motion. The positions of the two masses are given as q1 and q2. The Attempt at a Solution I began by drawing free-body diagrams for each mass. Then I set up the...

Homework Statement Satellite 1 has mass m1 & radius R1 and satellite 2 has mass m2 and radius 2R1 Which satellite’s speed is greater? Question and my attempt are shown in the attached file. Homework Equations V= √GM/R The Attempt at a Solution I am not sure if my steps are correct, but if...

Homework Statement :[/B] One swings a rock at the end of a string. We wish for the string to remain taut and for the rock to travel in a circulat path, in a vertical plane. What mathematical condition must the centripetal acceleration of the rock satisfy for the string to remain taut when the...

Homework Statement Projectile motion I have an an object that is shot at an angle of 55 degree's. (the velocity listed next to it was 35 m/s, which was not listed as Vo but I think I have to assume it is?) It is launched from the ground. it is meant to land to hit a button that is elevated by...

Homework Statement The figure below shows the speed of a person's body as he does a chin-up. Assume the motion is vertical and the mass of the person's body is 72.7 kg. Determine the force exerted by the chin-up bar on his body at the following times. My answers: Homework Equations F = ma...

Hi there, I just saw some lectures where they claim that the Klein Gordon equation is the lowest order equation which is Lorentz invariant for a scalar field. But I could easily come up with a Lorentz invariant equation that is first order, e.g. $$ (M^\mu\partial_\mu + m^2)\phi=0 $$ where M is...

Homework Statement In the attached file Homework Equations Kinematics equations. The Attempt at a Solution The question asks about vertical component. Isn’t this always 0? Like in C the intial velocity is the horizontal velocity but the vertical one is 0. Same applies to all. Am I correct?