1. ### Conservation of energy problem: Two masses, a pulley and an incline

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##
2. ### Calculating the time to cross a river

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...
3. ### To find the time to nearest appoach of a dinghy and a buoy

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...
4. ### I Influence of initial shift on undamped frictionless forced oscillations

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...
5. ### To find the time for which a vessel is within range of these guns

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...
6. ### To find the time taken for one vessel to reach another

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...
7. ### I Finding motion where the acceleration depends on position and time

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...
8. ### Mechanics: Slope Friction Problem

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

10. ### A cart with two cylindrical wheels connected by a rod

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...
11. ### Velocity of an object on an inclined plane

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
12. ### Calculation of minimum angular velocity of a mass on a spinning plate

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...
13. ### I Distribution of particles

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...
14. ### Torsion spring problem

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...
15. ### Prove: angular momentum is preserved

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?
16. ### What is the angle between the velocity of and the normal to the racket?

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...
17. ### Relative Density Word Problem

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...
18. ### 2 objects connected by a spring - Minimum Force required to move the objects

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?
19. ### Using first principles, how to get the equation of motion?

<< 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) +...
20. ### Projectile motion, ideal angle

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...
21. ### Force Calculation for bending of TOR steel bars

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
22. ### Find the average force at distance x

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...
23. ### I The order of calculating velocity and position alters the solution?

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...
24. ### Year1 Mechanics (angular momentum)

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...
25. ### Atwood machine with variable mass

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...
26. ### Time of Fall in triangular and rectangular frame

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...
27. ### Simple question about a moving elevator cab

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##...
28. ### Finding the Work of a spring and friction with a changing angle

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...
29. ### Question about the Work-Kinetic Energy Theorem - Pulling a cart

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...
30. ### Question About centrifugal force of a moving car

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...