Mechancis Definition and 109 Discussions

Problem: a particle of mass m is in a circular orbit around a planet at a distance R from the center. The planet mass is M and it's radius is R_0. What is the tangential impulse that will cause the particle to brush against the back of the planet? Describe the orbit. The attempt at solution...

Could I please ask for help with the following: Here's my diagram: The forces at the hinge (green) are internal forces. For the whole system resolving vertically gives: R1 + R2 = 4W and horizontally gives: F1 = F2 For the rod of weight 3W only, taking moments about B gives: F1 * L *...

Question: A string spring is connected between two bodys with a rope above them. M1 = 25Kg M2 = 50KG Distance between them is 100m. I answered a bit and got to the point where the distance between the two masses are 110m ( the mass below got 10m lower and is on balance, I mean, acceleration = 0...

What I do not get is why should a stress much lower than yield point cause deformation in a material? If temperature is high intermolecular attraction is reduced and thus even low stress can deform things. But if it is low Then a force lower than yield point should be less than intermolecular...

Goldstein 3 ed, pg 171, under" rate of change of a vector " : The author derives the relationship between the change of a vector in a stationary and rotating coordinate system. In the process he uses this assumption : >It is no loss of generality to take the space and body axes as...

I am trying to code collision of two objects. When they collide, instead of rebound or motion of them according to their velocity, i want them to stick together and move in direction of resultant normal velocity. It is not plastic collision. I want a force that stops the rebound. how can i...

I apologize in advance for any errors in my concepts or assumptions. Feel free to correct me wherever I am wrong. Thanks in advance for the help. There is a vertical shaft which will be operated at around 600 rpm (N) which can be achieved in 2 seconds (or even 4 just an assumption). The shaft...

Could I please ask for help with the following question: A lamina is in the shape of an equilateral triangle ABC, and D, E, F are the midpoints of BC, CA, AB respectively. Forces of magnitude 4N, 8N, 4N, 3N, 3N act along AB, BC, CA, BE, CF respectively, the direction of each force being...

Hello there, I have a question regarding this problem. I have no problem with part A. However, in part B, my solution manual states that the hollow cylinder will reach the bottom last. Why is it? I mean shouldn't the solid cylinder and the hollow one reach the bottom at the same time? you know...

Can anyone please help me with the following? Three forces which act along the sides AB, BC and CD of a regular hexagon ABCDEF of side 2a, have a resultant which acts along DF. When a couple of 4Pa in the sense CBA is added in the plane of the hexagon, the resultant acts along CA. Find the...

Hello there, I was trying to solve this problem. I have no problem with part A and C. But in part B, my guidebook arrived with different answer. Can anybody point out what my mistake is? I am using the same method as the elevator motor problem which states : "A 650-kg elevator starts from rest...

What came to my mind for this question is: Consider one of the cars. The velocity and mass of this car are V and M respectively. And the velocity and mass of the piece attached to the car are m, v respectively. Before the collision, the velocity of this piece relative to this car is zero. So its...

qvB=mv^2/R R=mv/qB= p/qB ! As you can see, the difference between this relation and the relation in question is in 'c'. Maybe my way is wrong. Maybe I should get help from relativity because the speed of light is involved here. Please help. Thankful

If M moves ##x## along the plane, her height variation in ##x \cos(\alpha)##, and, but I don't know how to find the variation of the height of ##m##

Could I please ask for help on the last part of this question: So, part b, I get the right time but not the right distance. Book answers are: distance = 1/6 and time = a/V. Here's my (faulty?) reasoning (LaTeX isn't working for me): The boat is steered due east and so would have a velocity...

Can anyone please help me see if my reasoning is correct regarding the following question? I'll just solve for the case where the dinghy tracks so as to just 'touch' the exclusion zone on the 'high' side So, in the diagram below: The dinghy tracks along the red path, inclined at x degrees...

I have general equation for undamped forced oscillations (no friction) which is: I just wonder about,what type of motion should occur when initial conditions are both 0 (i.e v0=0 and x0=0). My intuitive expectation is that as there is no 'natural' oscillations at beginning,vibration has to be...

Could I please ask for help with the following question (the second part): A cruiser sailing due north at 24 km/h sights a destroyer 48 km due east sailiing at 56 km/h on a course (360-a) degress where cos(a)=11/14. Show that the destroyer's course realtive to the cruiser is on a bearing of...

Could I please ask for help regarding my answer to the following question? I've done the first part and get the answer of 500 seconds. I anticipated no problem with the second part, it is the same problem with different inputs, but I have disagreed with the provided answer of 1754 seconds. I...

I have computed that the acceleration in my problem is a(t) = -gj - k/m(|r(t)| - L_0) * r(t)/|r(t)| Where a(t) is the acceleration vector, g is the gravitational acceleration, j is the unit vector in y-direction, k is the spring constant, m is the mass, r(t) is the position vector, |r(t)| is...

So far, I have this: For Part ii) I know that: mgh = xmgsin(theta), but I don't know how to go further

Please refer to the image

Firstly I only consider one of the wheels. This wheel consists of a big wheel (black) with mass M and radius R and inside it a circular region with a negative mass (-m) and radius R/2. (I assume they have same mass density but with opposite signs. I do this because I don't know where the center...

I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong

Problem Statement: How to calculate minumum angular velocity of a mass on a spinning plate Relevant Equations: f=mrw^2 Hi, here's the question: a) A rough horizontal plate rotates with a constant angular velocity of w about a fixed vertical axis. A particle of mass m lies on the plate at a...

I'm reading Mechanics by Landau and Lifshitz, chapter IV, and trying to understand how in a (closed) center of mass system, with randomly distributed and oriented particles that disintegrate, "the fraction of particles entering a solid angle element ##do_{0}## is proportional to ##do_{0}##, i.e...

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 >> 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+ 2K(dx/dt) +...

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 this 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 a given velocity for a given time, a smaller spring will...

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 just wanna 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...