So my basic understanding of an integral is that it finds the area underneath a graph.
I understand the idea behind an integral being the summation of f(x) * delta x, where delta x approaches zero.
If I look at the integral it's telling me that there's a change in mass that is being...
So I need to find equations for the force required to tip over a cylindrical object. This is fairly straight forward in the case when the force is applied above the centre of mass, by taking moments about the pivot corner. However, in the case where the force is applied below the centre of mass...
When thinking over the method of finding the centre of gravity that Julius Sumner Miller shows in this classic video, I wondered about if it would work in some other extreme situations.
Imagine a uniform, continuous plank of length equal to 1 earth radii positioned at the surface of the Earth...
Homework Statement
Hey everyone,
I'm studying for my physics and came across a question for the COM of a hemisphere.I made my attempt to calculate the COM.
Homework Equations
The Attempt at a Solution
I tried to calculate the y coordinate of COM this way,please go through it-
But,I am...
I have a test coming up next week and while doing some practice questions I found one I can't wrap my head around. The question is:
A pyramid (assume uniform density) is divided in two parts by a horizontal plane through its center of mass. How do the masses of the two parts compare ? There are...
Homework Statement
Given a graph (see below) containing the velocities of two stars with respect to the sun, I am asked to calculate the velocity of the centre of mass of a binary system. I am not given the mass of either star, nor the shape of the orbit nor the velocity of the centre of mass...
Homework Statement
A uniform, rectangular sheet with sides of lengths a and b has a hole of dimensions a/4 by b/4 punched in it as shown below. Find the centre of mass of the sheet after the hole is made.
Homework Equations
CM= ∫xdm/∫dm
The Attempt at a Solution
I'm confused on what to...
Homework Statement
Jane and her little brother John are fishing, sitting at opposite ends of a boat (Jane on the left, John on the right). Jane is having incredible luck! John, not so much. Jane offers to switch places in the boat with John. Jane has mass of 50 kg, john has a mass 30kg, and the...
Homework Statement
I have an image with the question here: http://imgur.com/TGG9VTx.jpg
The red text is the answer. I havent been able to get it without contradicting what Ive been told.
Homework Equations
I know m1x1 + m2x / m1+m2 is centre of mass in 2d plane, but I dont know how that...
Hi all.
Our lecturer gave us an exercise the other day regarding an elastic gravitational collision between a planet and a satellite where the satellite slingshots using the gravitational field of the planet. The question asks to show that ##v_{f} - v_{i} = 2v_{0}## where ##v_{f}## is the final...
Homework Statement
a thin uniform wire is bent to form two equal sides AB and AC of triangle ABC , where AB=AC=5cm . the third side BC , of length 6cm is made from uniform wire of twice the density of the first . the distance of centre of mass from A is ?
Homework Equations
x centre of mass...
Homework Statement
An unstable ion of mass ##M##, energy ##E## emits a massless particle of energy ##E_\nu## at angle ##\theta##. In the rest frame of the ion, find ##E_\nu^*## and ##cos \theta^*##.
Ions are now accelerated to ##\gamma=100## and a detector with radius ##r=20m## is placed...
I have to calculate the centre of mass of the drawn hemisphere. I don't understand where I make mistakes. The process I followed on the above image is the following:
(I) Here I simply translated position vector components from cartesian to polar coordinates.
(II) Formula of x-component of...
Homework Statement
Find the centre of mass of solid cone.
Homework Equations
$$y_{cm}=\frac{1}{M}\int_0^Hydm$$
The Attempt at a Solution
First I took thin disks. I got the answer when I assumed its thickness to be dy but then dysecθ would be more accurate if half angle of cone is θ since...
Hello, I uploaded an image of the question so it becomes clear
my main doubt is which procedure should I follow
1) total object weight*PERP. Distance to toppling point=Moment of cylinder+moment of cone
2) moment of cylinder ≥ moment of cone
I tried doing method two since they asked for least...
Hi I am doing an assignment where I roll a tin can filled with car oil. This will affect its rolling because it distorts its centre of mass, resulting in an awkward rolling motion. I have already done the experiment, the first revolution is the slowest one by a lot because it slows down a lot...
Homework Statement
Lower surface of a plank is rough and is initially at rest on a horizontal floor. It's upper surface is smooth and has a smooth hemisphere place over it through a light string as shown. Find the trajectory of centre of mass of the sphere after the string is burnt.
Homework...
Homework Statement
a) Two astronauts, A of total mass 90kg and B of total mass 110kg are tied together by a light rope 15m long during a space walk. A starts to reel in the rope at her end. After 8.5s she has reduced the length of the rope by 5.5m. What distance does the centre of mass move in...
"if kinetic energy of system of particles is zero, then linear momentum of that system of particles is zero but the reverse is not true. That is if linear momentum of a system of particles is zero, then the kinetic energy may not be zero"
This is what I got from my text. Can you provide me with...