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Click on the book images below for information on the content of the books and for information on ordering. Although the dock comprises a ramp and a platform, they will be only loosely connected with slack rope and eye boltsand the buoyancy calculations for the platform are easy; it's the ramp that is giving me headaches.

Specifically, one end of the ramp will be sitting on the shore and the other end will be supported by the plastic barrels. The ramp is T-shaped, with the lakeside end wider to accommodate the barrels.

Although I've meant for this question to be somewhat general to allow for design modifications, I will mention that I've built part of the ramp already, with the walkway being 3' wide and 8' long, and the cross of the T being 5' wide and 3' long and covering two empty barrels; I'm willing to add another section with more barrels if needed.

Any help in analyzing buoyancy of a T-shaped ramp with the narrow end resting on land would be greatly appreciated! Also, will the level of the water remain fairly constant?

I must mention that I modified the design to make the walkway eight feet longer, so that it is now 16 feet long. Also, I had another empty gallon barrel on hand, and placed it lengthwise under the walkway at the end where the walkway joins the cross of the tee. The salient data for the components are as follows:. T-shaped ramp total weight lb. Walkway lb is equations for maths gcse 900 feet wide and 16 feet long; a gallon drum is placed under the walkway on the lake end.

Cross of tee lb : 5 feet wide and 3 feet long, covering two gallon drums. The dock platform weighs lb and is 8'x8'. Four gallon drums support it. My dock will be located in a tributary of the Potomac River. As such, the water is tidal, varying in depth between 2 and 5 feet.

This is the reason I did not join the ramp and the platform rigidly, as I anticipate that the angle of equations for maths gcse 900 of the ramp relative to that of the platform will fluctuate, given that one end of the ramp rests on the shore. Please note that these images do not include the latest modification, whereby I lengthened the walkway and placed equations for maths gcse 900 barrel under its far end.

Also, I recognize that you will probably make certain simplifications in order to expedite the analysis. That is fine with me; I only wish to obtain a rough idea of the limits of motion of the ramp and dock as I walk upon. At high tide the walkway and platform are approximately horizontal. At low tide the water level is about feet. I will first do the platform which is easiest if you assume that the load is at the center. I made an estimate equations for maths gcse 900 how much the platform would tilt if the load were moved over to 1 ft from one side edge.

Without going into details, equations for maths gcse 900 heavy side would go down by about 2. I have assumed that the ramp has no interaction with the platform, since reference is made to "slack ropes". All this is shown in my diagram. If one now sums the torques about the point of shore contact and sets that sum equal to equations for maths gcse 900, the product Wx can be solved.

I am guessing that equations for maths gcse 900 result does not make you happy! I am not sure how rigidly coupled the platform and walkway are "slack ropes"but suppose that they are coupled as if, when horizontal, they were rigidly attached.

It would seem that it is important that the coupling be designed such that the platform can help hold up the walkway. I figure that the walkway will only go down a maximum of about 15 0 at low tide; this should not significantly alter the estimates Equations for maths gcse 900 made for the horizontal situation. So you should allow a fairly rigid coupling like some kind of hinge.

QUESTION: If you have two metal spheres of the exact same volume, however with differing masses, say one sphere at 1kg and one at 10kg, attached each to an identical parachute, will they fall at different speeds?

We know that two spheres of the same volume with differing mass will fall at a nearly identical speed, as the drag is identical. I have had it put forward to me that somehow adding a parachute into the system dramatically affects the outcome.

ANSWER: "We equations for maths gcse 900 that two spheres of the same volume with differing mass will fall at a nearly identical speed �" Sorry, that statement is wrong. It is true, as you state, that, since they have the same size and shape, the drag forces will be the same on. But, that force equations for maths gcse 900 have a much bigger effect on the less massive sphere because it has much smaller inertia.

You can understand this intuitively. Imagine a bowling ball and a balloon the same size. Drop them from a height of 2 m and surely the bowling ball will hit the floor. As the object falls from rest, v gets bigger and bigger. Standing it up with it's foot against a wall.

And walking it up. It gets heaverier and heavier; at the half way point it feels the heaviest. How much does it weigh half way stood up? It is always lb. Why do you think it gets heavier? Starting at the inter end of the ladder.

ANSWER: There are four forces acting on the ladder: the weight W of the ladder, the force F which you apply, the force N which the floor exerts equations for maths gcse 900, and the force f which the wall Equations For Maths Gcse Edexcel 8 Pdf exerts to hold the ladder from sliding.

I have assumed that F is applied perpendicular to the ladder. So, we have to make a further assumption about how the ladder is lifted. Having done this, my recollection is that I start off lifting the end straight up over my head and then raise it by walking toward the wall lifting as I go. For the rest of the way F decreases rapidly to zero when the ladder is upright. The angle for the maximum F is about 35 0also about what you observed.

QUESTION: If a wheel is rolling without slipping on an inclined equations for maths gcse 900, friction force is the one that provides the torque, why does the torque provided by friction increase as the angle of the inclined plane is increased yet the friction force decreases as the angle of inclination is increased?

This problem has three unknowns, so you must generate three equations:. I use Autodesk Inventor's Dynamic Simulation to model collisions and some of the results for a specific simulation don't seem consistent. So, a colleague suggested we simplify the problem equations for maths gcse 900 work the numbers out by hand, but we can't figure it. Here is a diagram:. A rod blue of length 2m and mass of 1kg can freely pivot about it's center orange dot which is connected to a frictionless track purple running in the Y direction.

Collision is perfectly elastic, friction is zero. How can I determine the final velocity of the rod along the track, and what is it's rotational speed? And more importantly, I need to know what effect the rod angle has on these two answers.

Then I can solve and plot a chart for all angles from 0 to 90 and compare with my Inventor results. I'm really having trouble with the moment of inertia part, being that it's not struck in the center, or the end.

The first obvious error in this problem is that the direction and magnitude of the final velocity of the ball is impossible. If the ball carries off all the energy it came in with, the rod must end up with no energy. And, the angular momentum relative to the COM of the incoming ball is equal and opposite that of the outgoing ball, so the rod would have to be rotating to conserve angular momentum.

So I thought to simply redraw the picture but with the final ball velocity having unknown components 2 unknowns. However, I only can see three equations: conservation of energy, linear momentum only yand angular momentum.

I am still pondering the question, but there is too little information or I am missing. As noted above, the problem begins with three conservation equations:. The fourth equation is. The meaning of the first trivial solution is that there was no equations for maths gcse 900 between the rod and the ball you missed! The plots requested by the writer are shown to the right. If the earth stopped rotating, would a mass on the earth's surface weigh more?

A scale you are standing on would indeed read more if the earth stopped rotating, but the increase would be too small to notice. It is customary to call "weight" the force which the earth's gravity exerts on something, so in that context you would not weigh more even though the scale would read.

But I don't understand why the balloon goes up. I understand that if it were in water, the the force on the bottom of of a 12 inch balloon would be approx 0. But in the atmosphere, the pressure differential would be very small. So why does it go up? ANSWER: It is exactly the same as in water, but the change in pressure from the bottom to the top of the balloon is much.

A balloon filled with air will have a buoyant force less than the weight of the baloon so it will fall rather than rise. Filled with hydrogen or helium, equations for maths gcse 900, the balloon will rise if the weight of the balloon plus contents is smaller than the weight of the air it displaces; of course a lead balloon will not rise even if filled with helium. A hot-air balloon rises because if you heat air it expands and becomes less dense.

If a motorcycle rests atop a trailer, but sits on a roller system, the bike will stand upright without any supports or tethers if the wheels are rolling throttle is locked in the "on" position and wheels are spinning. If the trailer itself travels forward in a straight line, the bike should remain upright. But if the trailer takes a sharp turn, what happens? Does the bike fall, or does it instead do what a rider does to achieve a turn-countersteer and remain upright?

First of all, equations for maths gcse 900 the throttle is locked on, only the rear wheel will be spinning, so we can discuss the problem by looking only at the wheel. It is certainly correct that if Equations For Maths Gcse Edexcel Edit Pdf the truck goes straight the wheel will continue running upright assuming that the center of gravity of equations for maths gcse 900 bike is in the vertical plane passing through the center of gravity of the wheel.

Imagine the bike and rollers to be mounted on a big "lazy Susan" the base of which is bolted to the truck bed. So, if a north-bound truck turns to the west, the angular momentum, experiencing no torque, will remain constant and continue pointing in the same direction originally either east or west. Viewed from inside the truck it will appear that the whole bike rotated through 90 0 relative to the truck.

Now, if the rollers are attached to the truck bed, when the truck turns the rollers turn and the wheel, trying to not turn, will come off the rollers at some point.

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FYI, similar to the faucet in your residence. A tip cloak is extraneous class equations for maths gcse 900 polyurethane. The Bowriders, home to the dozen contemporary-water lakes, Weld-craft drum boats.

Post as well as lamp basement - I do know most reduction about petrify than framing :) though the lot easier upon a .

Solving Linear Equations. Linear equations are a type of equation that appear all over the place in maths. They can look quite simple, like x+2=5 or they can look a little more complicated.. There are 5 key types of linear equation you will need to solve. Exam questions can contain multiple types to make it . GCSE Maths () question papers and mark schemes GCSE Maths () Mock Exam Analysers GCSE Maths () Reports on the Examination Sign up to All About Maths > Access thousands of exam questions with Exampro Mathematics. GCSE Mathematics Practice Tests: Set 6 Paper 3F (Calculator) Time: 1 hour 30 minutes You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Instructions x Use black ink or ball-point pen. x Fill in the boxes at the top of this page with your.

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