A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide (frequently flat) pieces along certain routes (usually on a board) to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a larger picture (like a jigsaw puzzle), numbers, or letters.
Sliding puzzles are essentially two-dimensional in nature, even if the sliding is facilitated by mechanically interlinked pieces (like partially encaged marbles) or three-dimensional tokens. As this example shows, some sliding puzzles are mechanical puzzles. However, the mechanical fixtures are usually not essential to these puzzles; the parts could as well be tokens on a flat board that are moved according to certain rules.
Unlike other tour puzzles, a sliding block puzzle prohibits lifting any piece off the board. This property separates sliding puzzles from rearrangement puzzles. Hence, finding moves and the paths opened up by each move within the two-dimensional confines of the board are important parts of solving sliding block puzzles.
The oldest type of sliding puzzle is the fifteen puzzle, invented by Noyes Chapman in 1880; Sam Loyd is often wrongly credited with making sliding puzzles popular based on his false claim that he invented the fifteen puzzle. Chapman's invention initiated a puzzle craze in the early 1880s.
From the 1950s through the 1980s sliding puzzles employing letters to form words were very popular. These sorts of puzzles have several possible solutions, as may be seen from examples such as Ro-Let (a letter-based fifteen puzzle), Scribe-o (4x8), and Lingo.The fifteen puzzle has been computerized (as puzzle video games) and examples are available to play for free on-line from many Web pages. It is a descendant of the jigsaw puzzle in that its point is to form a picture on-screen. The last square of the puzzle is then displayed automatically once the other pieces have been lined up.
The context is going down a hill in rollerblades: when people fall and they come to a quick stop (due to not having protective gear and there being lots of friction), they always end up with major injuries, while people with protective pads can sometimes fall and slide for 60+ feet and often be...
So basically I need to find the coefficient of friction given the listed information.
What bothers me is that I am getting two different accelerations for two different approaches. When I calculate acceleration using Fg=mgsin60 I do it this way: Fg=mgsin60 -> ma=mgsin60 ->a=gsin60 -> a=8.66. But...
For this problem,
The solution is,
However, is the reason why they don't do ##-0.5a_xt^2## because the negative of the acceleration has already taken care of itself?
Many thanks!
I reason the frictional force on the plate from the ice is doing work first 3 meters (while the motorbike is moving on top) and then an "x" distance after the motorbike has left it. Does anybody have an idea of how one might solve this problem?
In both the cases 7 kg mass accelerates towards the right because of the 50N force. The unbalanced forces in both the cases are the force of gravity due to 5kg block and force of friction. Applying Newton's second law of motion to cases 1 and 2 yields the following results for acceleration...
What force causes the surface to move to the left?
Can I say that it's due to the force component of the weight along the vertical force of the surface?
First, I solved for the firefighters mass and got 82.9kg.
Then, I plugged in the mass and the 1.8m/s2 acceleration into a=Fnet/m
This is where I get confused. I think I'm supposed to use Fnet = F-fk to solve for fk (and that would be the answer?) but I don't know what to input for F.
So, when the mass reached the peak, its horizontal velocity will be the same as the wedge's. Using conservation of momentum :
$$ mu = 2mv$$
$$v = \frac u 2$$
With v is the final velocity for both objects.
Now, what we need is the acceleration of the wedge, which we can find by using Newton's...
1)When a wheel is stuck in mud it rolls with slipping ,this means that at the point of contact it has a net velocity
As we can see from the image Kinetic Friction acts in the direction opposite to the resultant velocity ,this effectively reduces the tangential velocity at the surface and tries...
While coming across a question on Newton's laws,I found a case when a block slides on another block kept horizontally as in the figure.All surfaces are frictionless.
My concern is for the blocks to be in contact that is to move together will the horizontal velocities of both the blocks be the...
I have no idea how to start this other than that I think that Fn is 17.64N and Fnet is 0. But I don't have the mew, so I am not sure how I am going to get the force of static friction.
Hi so with this question, I am really confused. Even from the start. Like it doesn't tell us where the force is acting on. From top of block, middle of block etc? And I know how to determine the direction of moment for something on a pivot, not in this scenario though. The answer is A. They did...
The best I could do was draw a forces diagram. I know that friction would be working up when the block is on the point of slipping down the plane and friction will be acting down the slope against the direction of motion when the block is on the point of slipping up the slope. (not even sure if...
hey i would like to understand something, i solve this question but i don't understand why my answer is right, first of all we learn that in problems like this we need to disassemble into components the mg and that what i try to do here but i didnt get the right answer so then i try to do same...
When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 2.19 m/s. The mass stops a distance S2 = 2.1 m along the level part of the slide. The distance S1 = 1.18 m and the angle θ = 28.10°. Calculate the coefficient of kinetic friction for the mass on...
Summary:: What is the sliding resistance of an eccentrically loaded block on a flat surface?
If a 1000kg block is placed on a flat surface (say coeff. of friction = 0.4), what force does it take to slide if it loaded eccentrically, i.e. at the far edge of the block?
My thinking is there is...
For lower half ,$$Fnet=-\mu F_N+mg\sin \phi$$
For upper half,
$$v^2=u^2+2as$$ (s is half of the total slant distance)
$$v^2=0+2\frac{mg\sin \phi}ms$$
$$v=\sqrt{2g\sin \phi s}$$
again for lower half,
$$v^2=u^2+2as$$
$$0=2g\sin \phi s+2\frac{-\mu F_N+mg\sin \phi}ms$$
$$\mu=\frac{2gm\sin...
Hello all,
I am a graduate student working on a thesis in tire dynamics and simulation.
I have came across the following equation for sliding adhesion coefficient for the HSRI tire model (source: Schramm et. al. Vehicle Dynamics, Modeling and Simulation, pg. 182):
Unfortunately, Schramm et...
Attached are some Sliding doors images.
Can they be operated with a remote control device?
The remote control device will have buttons for opening & closing the left and right door.
What will be the design & construction changes in the sliding doors so that they can be operated using a remote...
In the solution for question ##(a)##, it is written that the equation of translational motion for the center of mass is ##N-mg=ma_y##
Why ##N## is also included inside of the equation? In my opinion, the rail does not exerting force (N) to slow down the mass' acceleration. Instead, the purpose...
Let's say you are riding a bike very fast, and then you sharply turn into a slide (where the bike is sliding perfectly sideways).
I'm trying to calculate the angle that the bike would be leaning at, but I'm having trouble creating the free body diagram.
Right now I have the normal force and...
Hi everyone is able to help solve this question for my assignment in university?
I've draw a free body diagram for each component of the question but now i am stuck.
[Mentor Note -- Poster has been reminded to show their work when starting a new schoolwork thread]
hello , I am adding pdf with the questions and what i tried to do to solve them.
in the first question my teacher just taught us that if there is a frictionless floor and i push the upper block (m) with force F toward me then if the static friction will be toward me too. so the lower block M is...
I tried using Newton's first law as the net force in both the x and y directions should be zero in this case. In the free body diagram you need to consider weight, friction, normal force, and the horizontal force. I got a result that said that the horizontal force F you apply is at most W(mu_s +...
To be honest I am a bit clueless first with how to interrupt this question I think the bead is going around a wall type thing where there is friction both in the up and X direction. Some hint to get some ideas running would be great
1) To be in equilibrium, it must be $$\begin{cases}F_{centr}-T=0\\ T-mg=0\end{cases}\Rightarrow F_{centr}=T=mg\Rightarrow m\omega^2 R_0=mg\Rightarrow R_0=\frac{g}{\omega^2}$$
2) It is intuitive that this equilibrium is unstable but I don't know how to formally prove this.
3) In ##R_0## the...
A block slides on a frictionless wedge which rests on a smooth horizontal plane. There are two constraints in this system. One that the wedge can only move horizontally and another that the block must remain in contact with the wedge.
We want to find the virtual displacements for the two block...
I can evaluate the first beads motion easily A to B is -2Rj considering the point B as y=0 the motion of the bead will be -gt^2/2+2R=0 which implies t=2√(R/G) , this is ok but what I am struggling with is A to C I can see that the angle between the beads weight and it's negative normal force...
A ramp rises 10cm for every 80cm along the sloping surface. A box of mass 50 kg slides down the ramp starting from rest at the top of the ramp. The coefficient of friction between the ramp and the box is 0.03 and no other resistance acts.
The box is traveling at 2 m/s when it reaches the bottom...
A tile of mass 1.2 kg slides 3m down a roof that makes an angle of 35 degree to the horizontal. Find the decrease in potential energy.
Iam getting the ans 24.8J
PE = mgh= 1.2× 12 sin 35 ×3
The ans in the textbook is 20.6J
Hi
I am working through some notes and came across this example. The wire rotates at angular frequency ω so the polar angle is given by θ = ωt. The generalised coordinate is r. Using the Euler-Lagrange equation leads to
d2r/dt2 = rω2
The notes then state that this leads to the solution r = Aeωt...
My two questions:
The author claims that ##T_1=T_2## and ##\alpha = \beta##, and this is supposed to be clear the force triangle. Why is this so?
Is it possible to use calculus of variation to find the lowest point C? That is, by maximizing the triangle ABC (Area of ABC = ##\frac{1}{2}(line...
This question is from the David Morin ( Classical Mechanics ) - problem 3.7. I spent some time trying to figure it out the solution by myself, but since I couldn't, I looked into the solution in the book, but I got even more lost. So I searched for an online solution that could help me at least...
I solved this problem easily using Newton's second law, but I had problems trying to use mechanical energy conservation to solve it.
How I solved using Newton's second law:
##\text{(part of the rope that is on the left)}\, m_1=x\rho g,\, \text{(part of the rope that is on the right)}\...
So for this question, when using point B as the centre of the moment, I get different sign for the mad term. If you take clockwise as positive than 100N force and the force at point G are causing a positive moment and gravity is causing an negative moment. But the solutions have different signs...
Hi,
I'm missing something really stupid here...
The problem is the usual one with a block sliding down (or moving up, it should be the same) a frictionless inclined plane,which itself is free to move on a orizontal frictionless surface.
These problems are usually solved stating that only...
Hi,
I solved this prolem in the following way.
I have started with the angular momentum theorem:
Iα=fR
As the force of friction vector is attached on point of contact of the ball and the supporting surface, the moment of inetria is:
Ic= MR^2 + Icm = MR^2 + (2/5)MR^2
Ic*a/R=μMgR
tr=7/5(v0/μg)...
When the mass starts sliding down, it will induce a current due to the cutting of B field.
By fleming right-hand rule, the B field points into the field, charge going in the direction down the ramp (current pointing down the ramp?),
therefore the force should be in the same direction of normal...
The soultion used polar corrdinates. Acceleration in polar corrdinates have radial and transeverse components.When calculating the acceleration of collar respect to the rod, the solution only calculates the radial component of acceleration. Is it because the collar is on the rod, so the...
Look on picture two for my equations, I’m pretty sure my first three equations are correct as it’s the same on the answer paper I got. Answer paper only shows the three equations and correct answer so I have no idea how they got to it.
When I put the equations togheter And solve out ”h” i get...
My attempt:
When the body is about to overturn backwards, the normal force and frictional force are applied on point A.
If I want to avoid overturning, torque must be 0. Then, I calculate torque with respect to A.
The value I get for h is negative, implying there is no minimum value for h...
I have just watched a video lecture about the Tomlinson model (aka Prandtl–Tomlinson Model) which explains the friction mechanism at a nanoscale by analogy with a tip dragged by a spring. The video has prompted me to ask several questions.
The spring is dragged over a corrugated substrate, as...
I thought in this equations
f is the man's pull\
f + dm*g = T < 600
Where dm is equal to the mass of the string that pull the up part (15-x) after descending x meters.
dm/(15-x) = m/15
And, to the man: W - f = Mx''
I can solve this, and i got ~8m/s
Is this right?