Homework Statement
A red ball is thrown down with an initial speed of 1.0 m/s from a height of 27.0 meters above the ground. Then, 0.4 seconds after the red ball is thrown, a blue ball is thrown upward with an initial speed of 24.8 m/s, from a height of 0.8 meters above the ground. The force...
We have a Newtons cradle , when you let go of one ball at one end you know what happens. Rlease one ball and the other side has a ball osciallte.
But if you release two balls (with a 5 ball cradle) , why is that two balls on the other side of the middle ball also rise in response. How does...
Homework Statement
A bag contains 4 balls. Two balls are drawn at random, and are found to be white. What is the probability that all balls are white?
2. Relevent equations
At school, I'm currently learning Bayes' theorem, probability disribution and Bernoulli trials.
The Attempt at a...
I'm trying to work out the following problem: Find the first two terms of the power series expansion for the volume of a ball of radius r centered at p in a Riemannian Manifold, M with dimension n. We are given that
Vol(B_r(p)) = \int_S \int_0^r \det(d(exp_p)_{tv})t^{n-1}\mathrm{d}t...
Homework Statement
From a bag containing 4 white and 6 black balls, 2 balls are drawn at random. If the balls are drawn one after the other, without replacement, find the probability that
The first ball is white and the second ball is black
Homework Equations
The Attempt at a...
Homework Statement
Suppose x,y \in X which is a normed linear space and x\neq y
. Prove that \exists r>0 such that B(x,r) \cap B(y,r)=∅
Homework Equations
Epsilon Ball
B(x,r)={z \in X:||x-z||<r}
The Attempt at a Solution
So my attempt here is via contradiction and its not...
Homework Statement
A 0.155-kg ball, moving in the positive direction at 13 m/s, is acted on by the impulse shown in the graph below. What is the ball's speed at 4.0 s?
The graph is attached below.
Homework Equations
J = F Δt
The Attempt at a Solution
I thought that it might...
What is the significance of gravity on the torque of balls rolling down an incline?
I know that gravity is able to exert a force, or torque by acting on the center of mass, causing an object to rotate. But what about rolling motion? Where would the axis of rotation be for a ball rolling down...
One ball is thrown upwards at 10 m/s, the other is thrown straight down (not dropped) also at 10 m/s. Which ball arrives first?
This is more of a theoretical question than anything. I know the relevant equations such as v^2=u^2 +2as, but I was thinking that the height of the building has to...
HELP PLEASE! My friend is suffering huge depression and stress and she really needs to hand in this assignment or she will fail... please if you can answer any of these questions!
A bag contains x pink balls and y yellow balls. Three balls are randomly selected from the bag.
a) Write down an...
Hey! (First post)
We're conducting an experiment as a part of a couple of problem sets in preperation for the IYPT, and we're a little stuck in terms of the research we need to have to solve the problem. Basically, (I'm not going to copy paste the question in here, I'd be cheating) We've...
Homework Statement
A small ball of mass m is aligned above a larger ball of mass M = 0.63kg (with a slight separation), and the two are dropped simultaneously from height h = 1.8m. (Assume the radius of each ball is negligible relative to h.)
a. If the larger ball rebounds elastically from...
Hi, I'm having a bit of trouble with the below practice problem from my textbook. The answer given in the back is -9.52 m/s, but there is no explanation. Thanks for any help.
Homework Statement
Two balls are thrown off of a 7.25 m high building both at an initial speed of 63.5 mph. However...
Homework Statement
The entire problem is in the attachment.Homework Equations
F = k*(|q||q0|)/(r^2)
The Attempt at a Solution
F = 8.99e9(.450uC*.450uC)/(3cm^2) = 6.068e8
This problem has me completely lost and I am turning to you guys as my last resort. I solved for F and have no idea what to...
Homework Statement Small masses m1 (m1 = 30 kg) and m2 (m2A = 5 kg; m2B = 10 kg; m2C = 40 kg; m2D = 50 kg; m2E = 30 kg) are each attached to a string of length 2.0 m. The other end of each string is attached to a common point on the ceiling. The masses are raised until each string is at an...
Homework Statement
http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w09_qp_41.pdf
number 6III...
There are 5 players and me.
If I throw numerous balls in the air and the chances of each individual player catching a ball is as follows:
player 1: 13%
player 2: 16%
player 3: 14%
player 4: 15%
player 5: 18%
Please show working:
1) What is the chance that at least one player catches a...
Hey Everybody, I am supposed to model the trajectory of a golf ball. I have been given the equations for velocity as a function of its derivative with respect to time. I am supposed to find the x-range as a function of the angle θ. (Pardon my bad latex skills, I will fix mistakes)...
Homework Statement
Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Initially ball A is moving along the y axis at +2.0 m/s, and ball B is moving to the right along the x axis with speed +3.7 m/s. After the collision (assumed elastic)...
Bob has two balls. He releases one ball from a platform of height H. Just as that ball strikes the ground he releases the next ball from the same height H. Assuming that the first ball bounces perfectly, (i.e. reversing only the direction of its velocity when it strikes the ground), at what...
A box contains V balls of which N_{g} are green, N_{r} are red and V-N_{g}-N_{r}=N_{b} are blue.
Now somebody shakes the box vigorously, brings it to rest and then observes the
arrangement of the balls in the box. Suppose this is repeated many times so that
probabilities of different ball...
Homework Statement
Two balls are juggled so that each ball is in the air for 2.000s, and the second ball is thrown UP at the instant the first starts down. Find the height above the throwing hand where the two balls pass.
(Assume gEARTH = 9.800m/s2 down)
TT=2.000s
g=9.800m/s2 down...
Consider two balls on an inclined track with a constant angle. Ball Q is released from rest a tthe top of the track. Ball P is given an initial velocity directed up the track. Both balls have a constant acceleration directed down the track. at the instant that the balls collide, ball Q is going...
Six balls are thrown from the top of a building. Two balls are dropped from rest, two are thrown downward with a velocity of 10 m/s and two are thrown upward with a velocity of 10 m/s. Each ball has a differing mass as well, such as the two balls thrown from rest, one has a smaller mass than the...
Consider two balls on an inclined track with a constant angle. Ball A is released from rest at the top of the track. Ball B is given an initial velocity directed down the track. At the instant that the balls collide, Ball A is going 4 times as fast as Ball B. Ball B is still traveling upward...
Homework Statement
One charged plastic ball is vertically above another in a test tube as shown. The balls are in equilibrium a distance "d" apart. If the mass of the upper ball is reduced by a factor of four, the distance between the balls in the test tube would become :
1) 4d
2) 8d
3)...
Homework Statement
I dropped a ball from different heights, and got height they bounced up to, but I need a formula for it.
Data
Gravity = 9.800 m/s2
[Initial Height(cm)]----------[Bounced Height(cm)]
100.0---------------------------81.00
90.00---------------------------75.00...
Homework Statement
Ball A is dropped at t=0 from a window. At t=6, the ball hits the ground. Neglect air resistance for question
a) Suppose that at t=1, Balls B and C are thrown vertically down from the same window. Ball C has a greater initial velocity than Ball B, as shown by their...
Homework Statement
A blue ball is thrown upward with an initial speed of 20.4 m/s, from a height of 0.5 meters above the ground. 2.5 seconds after the blue ball is thrown, a red ball is thrown down with an initial speed of 9.8 m/s from a height of 23.9 meters above the ground. The force of...
One ball is selected from 100 at a time, without replacement. Of these balls, r of them are red.
What is the probability that the first ball picked will be red?
The 50th?
The last?
Solution:
I don't understand why it matters which pick it is. I know that "without replacement"...
1. Homework Statement [/b]
Two smooth uniform spheres, A and B, are of the same size, but A has twice the mass of B. They are placed at rest on a smooth horizontal table and A is projected directly towards B with speed U. The spheres collide, and then B strikes a barrier perpendicular to its...
Homework Statement
Let \displaystyle f:{{\mathbb{R}}^{n}}\to \mathbb{R} a continuous function. Proove that:
If \displaystyle f\left( p \right)>0 then there's a ball \displaystyle {{B}_{p}} centered at p such that \displaystyle \forall x\in {{B}_{p}} we have \displaystyle f\left( x...
Homework Statement
(It includes a diagram so I'm just going to link it)
#22 from Chapter 7 of the People's Physics Book (second to last page, with the table)
http://scipp.ucsc.edu/outreach/07Momentum.pdf
Homework Equations
p(i)=p(f)
p(f)x=m*v*cosin(theta) [I "made these up", so to speak, but...
Hi guys, really simple question but...
http://img341.imageshack.us/img341/5447/ballsra.jpg
I'm not quite sure on how they ended up with the expression for P(exactly one match). I would have done it in a more straight forward way, simply define A: matching the colour red in the red box only. B...
Homework Statement
Three balls are drawn one after the other with replacement, from a bag containing 5 red, 9 white and 4 blue identical balls. What is the probability that they are one red, one white and one blue?
Homework Equations
The Attempt at a Solution
The question...
The jar has a radius of 6" and a height of 24" and each ball has a radius of 1".
So I found the volume of the jar which is \pi6^{2}(24) = \approx 2,714.33605 and the volume of the balls which is \frac{4}{3}\pi1^{3} = \approx 4.1887902
And then I divided how many of the balls can go into the...
Homework Statement
A ball of mass m = 1.9 kg moving with a speed of v0 = 20.1 m/s strikes an identical ball which was initially at rest. After the collision, the incoming ball (ball 1) goes off at q1 = 26° relative to its original direction and the struck ball (ball 2) moves off at q2 = 36° as...
Homework Statement
Question: A 12kg ball traveling at 5 m/s strikes a stationary ball of 7kg. After the collision the balls are 60 degrees apart, each 30 degrees either side of the original path of the striking ball.
Calculate the speed of both balls after collision?Homework Equations...
Homework Statement
A tennis ball of mass m_t is held just above a basketball of mass m_b. With their centers vertically aligned, both are released from rest at the same moment, so that the bottom of the basketball falls freely through a height h and strikes the floor. Assume an elastic...
Homework Statement
Two elastic balls of mass m1 = 0.3kg and m2 = 0.2kg are hanging on a thin rope so that their centre of gravity is on the same height. ball 1 goes out of balance raising it up to h0 = 0.05m
Then letting it go hitting ball 2. Calculate the maximum height of both balls reaching...
Homework Statement
Homework Equations
I=mr^{2}
L=ωI
ω=\frac{L}{I}
The Attempt at a Solution
I thought that since the moment of inertia was larger for the ball on the outside its angular speed would be slower. So then it would take longer to hit the wall.
1. A ball is dropped from a height of 79 m. Simultaneously a ball is thrown upward from the ground at a velocity of 28 m/s. How much time passes until the balls are at the same height.
I'm not really sure what equation to use or how to approach.
Could someone please show that an open ball is open where the definition of "open" is: A set is open if for each x in U there is an open rectangle A such that x in A is contained in U. Where an open rectangle is (a_1,b_1)×…×(a_n,b_n). I also realize that one can use rectangles or balls, but I...
I'd like to simulate the interaction between these magnetic balls on my computer.
I suppose they are magnetic dipoles, how would I go about finding out the forces applying between 2 of them in a specific configuration ?
Do I need to find the magnetic field and then apply the Lorentz force...
If i have 2 circular objects like coins and their moving on a frictionless surface and i know their velocity angles mass, how can i find the angle of each object after they collide, an example
A is the first coin, B the second their masses are the same. X will be the x of a vector and Y the y...
two balls, one made of iron and one made of lead with same radius and mass. which one will roll down the slope faster?
i don't really know where to begin, since everything is the same, the only idea i had was to somehow relate Ek=(J.ω2)/2 => Ek= m.r2.(ω2/2) to the question since i imagine...
Suppose you have 3 balls, all of equal mass, M. They are connected to each other by equal-length (each length L) strings of negligible mass, such that one ball is suspended in the middle and the two balls at the end are themselves suspended from the ceiling at two points, a distance X from one...
Homework Statement
This figure shows two identical billiard balls before and after a glancing collision. Determine the speed of the other ball.
Homework Equations
0=mv1sin30- mv2sin60
The Attempt at a Solution
v1= [(0.05m/s)sin60]/(sin(30))= 0.087 m/s
Here I am...
Homework Statement
by rolling 5 different balls down a ramp from 5 different heights onto 5 different surfaces i recorded the time taken from when the ball leaves the ramp until it stops, also recording the displacement of the ball from the the bottom of the ramp. with these results i need to...
Homework Statement
A ball of mass 4.5 kg is moving 16 m/s east when it collides with a stationary 6.2kg ball, which moves at a velocity 10 m/s after the collision. Was this an elastic or inelastic collision? Explain your choice.
Va = 16 m/s
Ma = 4.5 kg
Mb = 6.2 kg
Vb' = 10 m/s...