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# U5 Forces (and their effects)

Resultant forces; Newton's laws; terminal velocity; acceleration due to gravity; work done and gravitational potential energy; Hooke's law and elastic potential energy; kinetic energy; power; stopping distances; momentum
by

## Tom Munoz-Britton

on 23 October 2017

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#### Transcript of U5 Forces (and their effects)

Forces (and their effects) Newton's laws Acceleration due to gravity Terminal velocity Work done & gravitational potential energy Hooke's law & elastic potential energy Kinetic energy Power Stopping distances Momentum Resultant forces The concept of a resultant force is in principle very simple... What does that mean? A force of 10 N is applied to a block in the +x direction. Q. What is the resultant force (and in which direction)? A. 10 N in the +x direction. Consider the effect of adding a second, 5 N, force in, which acts in the -x direction Q. What is the new resultant force (and in which direction)? A. 5 N in the +x direction. Seems so simple... It is really... that is unless the forces don't act in the same plane. Consider the size and the direction of the resultant force acting on the ball. At this stage things begin to get much simpler if: (a) we draw a diagram (b) we start treating forces as vectors Let's try something a bit trickier still... As before, find both the size and the direction of the resultant force acting on the ball. Still getting trickier Find the size and the direction of the resultant force acting on the ball. Newton's 1st law "A body at rest remains at rest and a body in motion continues to move at a constant velocity in a straight line unless acted on by an external force." "Every body perseveres in its state of rest or of uniform motion (in its right line) unless it is compelled to change that state by forces impressed upon it." Galileo Galilei (~1630 AD) Isaac Newton (~1680 AD) In plain(er) English... If the resultant force acting on an object is zero then its velocity is constant.

A body at rest will therefore remain at rest; a body moving at constant velocity will continue to move with the same constant velocity. If two (or more) forces are acting simultaneously upon an object they add together to give a single resultant force. Newton's 2nd law Newton's 2nd law is somewhat different to the other two in so far as it is mathematical in nature. "An apple, of mass 0.15 kg falls from a tree, accelerating due to gravity at 10 ms . What is the force acting on the apple?" In summary... At GCSE level at least, Newton's 2nd law is a fairly straightforward concept: Newton defined the idea of a 'force' as being the mass of a body multiplied by its acceleration: For example... -2 "Is that it? This all seems suspiciously simple..." "Well yes and no... Newton's 2nd Law is one of the most important equations in science, and correctly applying it to complex physical systems involves a good understanding of calculus... ...but for GCSE physics we only need to remember (and be able to use F = ma*." *You will also need to be able to re-arrange F = ma to get: This taxing piece of mathematics is left as an exercise to the reader... i.e. that the acceleration of an object is determined by the resultant force applied and its own mass. All you're required to do is be able to use this equation (though possibly in a re-arranged form). Newton's 3rd law Newton's 3rd (and final) law is perhaps the most famous of them all... While it is exceedingly unlikely that you would be asked to regurgitate Newton's 3rd law verbatim, it is a vitally important idea in modern physics and you do need to understand the principle... "To every action there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions." ...Furthermore, Newton's 3rd law is the underlying principle in understanding conservation of momentum, which we will be looking at in a few weeks. An example If a cyclist headbutts the floor, exerting a force F, the floor will simultaneously exert an equal and opposite force on the cyclist's chin. Gravitational potential energy Lifting an object up (against the gravitational force) involves expending energy. As your body converts chemical potential energy in your muscles, this must become a different kind of energy... Gravitational Potential Energy Gravitational potential energy is energy stored in an object due to its position in a gravitational field (usually that of the Earth). Changing Gravitational Potential Energy When an object moves up or down in a gravitational field, its G.P.E. changes: If it moves up, its G.P.E. increases.
If it moves down, its G.P.E. decreases. The amount by which the G.P.E. changes depends on three factors: the amount it moves by;
its mass;
The strength of the gravitational field. A little more mathematically, this can be written as: A quick example A 2.0 kg object is raised through a height of 0.4 m. Calculate the change of G.P.E. of the object. Does the object gain or lose G.P.E.?

Assume the gravitational field strength of the Earth to be 10 N/kg at its surface. The object has been raised in height and so this is a gain in G.P.E. Key points The gravitational potential energy of an object increases when it moves up and decreases when it moves down (both in a vertical direction).
The change in gravitational potential energy of an object depends on its mass, the gravitational field strength and the change in its height.
An object gains gravitational potential energy when it is lifted up because work is done on it to overcome the gravitational force (more on this next time...) Using Hooke's Law to measure the spring constant (of a spring) Hooke's Law (of elasticity) connects the amount by which a spring will extend with the load (weight) it is supporting. A couple of definitions before we get started... Elastic An object is elastic if it returns to its original shape when a force that is deforming it is removed. Extension When an object increases in length it extends. Its extension is the difference between its 'normal' length and its extended length: Stretch testing When weights are added to the bottom of a spring it will extend.

We find that as the weight suspended on a spring is doubled, the extension also doubles; i.e. the extension of the spring is directly proportional to the load. Hooke's Law Hooke's law states this relationship of direct proportionality mathematically: Kinetic energy is the energy something possesses due to its motion. While kinetic energy is not a new idea, at this point we will look at it a little more mathematically than in the past!
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