# Ks3 mathematics sats past papers 2010

Electromagnetism and the strong and weak nuclear forces are now understood using quantum field theories. Quantum mechanics shows that at high energies, electromagnetism and the weak force combine to form a single force, known as the electroweak force. A theory that shows that the electroweak and strong nuclear force combine into a single force at high energies is known as a grand unified theory GUT. Inthe gram was defined as the mass of one cubic centimetre of water at the melting point of water . There are currently over 50 member states, which meet in Paris every four to six years .

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Inthe CGPM created an object that would be known as exactly a kilogram, and copies were taken to each member country. The terms 'mass' and 'weight' were still often used interchangeably when referring to objects on Earth. The CGPM clarified this inwhen they declared that the kilogram was a unit of mass, not weight.

These work using the law of torqueswhich state that two objects on a pivot, like a seesaw, will balance when the torque is the same on each side, where [7b]: The downwards force that an object exerts on a balancing scale is equal to its weight.

If you place the CGPM's prototype kilogram on one side of a balancing scale, then you can work out how much another object weighs by placing it on the other side and moving it until the scale is balanced. An object with twice the weight of the prototype kilogram will need to be twice as close to the pivot than the prototype kilogram in order to make the scales balance.

We also often weigh things on Earth using spring scales, like those found in bathroom scales. These use the law of torques combined with English natural philosopher Robert Hooke's law [7c].

Hooke's law shows that the force needed to stretch a spring is proportional to the distance it's stretched. The proportionality constant depends on how stiff the spring is.

This is known as the stiffness constant, where stiffer springs have higher stiffness constants. When you weigh an object using a spring scale, the force on the spring is due to the object's weight, and so if you take an object with a known weight, like the CGPM's prototype kilogram, then you can measure how much the spring stretches and work out the stiffness constant.

You can then measure the mass of anything using the spring, as long as it retains its elasticity. In bathroom scales, a person stands on a lever, which is like a seesaw with only one side. Because they stand very close to the pivot, their torque is small, and so the lever does not need as much space to move as a real seesaw.

The edge of the lever is attached to a spring, and so when the level goes down, the spring is stretched by the force due to the person's weight. The movement of the spring moves the scale.

The more force on the scale due to the person's weight, the more the lever moves, the more the spring stretches, and the more the dial turns. Mass can be determined from weight since the gravitational field is known, and so the dial is calibrated to show mass.

In digital scales, the force of a person due to their weight causes a strain on a conductive material, like foil.

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This increases its electrical resistance. Ohm's law shows that : This means that a heavier object will cause more strain on the conductive material, this causes it to have a higher electrical resistance. The mass needed to produce that voltage is then calculated and displayed. This is because if your apparent weight is zero, like it would be on the International Space Station, then the scales will be moving towards the Earth at the same rate that you are being pulled towards them by gravity.

To measure the mass of a person in space, the mass must be derived from something other than the force of gravity.

On the International Space Station, the mass of an astronaut is measured by applying a force to them using a spring. Two devices are generally used: Russia's BMMD also determines a person's mass by applying a force using a spring. Instead of measuring a person's acceleration, however, BMMD measures their frequency.

The force of the spring makes them oscillate in simple harmonic motion. Simple harmonic motion refers to repetitive motion around a central position, like the swing of a pendulum, or the up and down motion of an object attached to a spring, like a pogo stick.

The number of times a simple harmonic oscillator oscillates per second is known as its frequency, and this depends on its mass. The more mass they have, the slower they oscillate, and so the lower their frequency.

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Work as quickly and as carefully as you can. You have 45 minutes for this test. If you cannot do one of the questions, go on to the next one. You can come back to it later, if you have time. Around this time, American physicist Itzhak Bars showed that the mathematics needed to describe a universe with one observable time dimension, and three observable spatial dimensions, is the same as that needed to describe a universe with two observable .

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