# Motion and force

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## Force and Accelration

Everything has a force. For example, a car on a road has a driving force pushing it forward and friction and wind resistnce pushing it back. If the driving force is larger, we say the resultant force is larger, causing the car to accelerate.

Newton's first law: Objects either stay at rest or remain in uniform motion unless acted on by a force.

This means that an object will be at a constant velocity until a force acts on it, causing it to either change direction or speed.

Newton's second law: Force is proportional to mass and acceleration.

This gives us the equation F=ma where F = resultant force (N), m = mass (kg) and a = acceleration (ms^-2)

Newton's third law: Every action has an equal or opposite reaction.

This means that every force acting on something has a force acting back. When we sit on a chair we exert a force downwards. The chair has to exert the same force upwards to not fall through.

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## Using F=ma

Forces in opposite directions: If two unequal forces are acting in opposite directions, the object accelerates in the direction of the largest force so if F2 > F1 then we do F2 - F1 = ma. If there is tension in a tow bar then the T is the force so T=ma. however we still do F-T=ma because the force is bigger. Then we combine the two equations to get F=Ma+ma which can be writen as F=(M+m)a.

If a rocket is going up, T is the thrust and mg is the weight acting down. We would do T - mg = ma. As there would be more thrist than weight.

Pulley problems:

The resultant force on the larger weight is Mg-T, other it T-mg. We combine these to get the equation Mg-mg=(M+m)a.

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## Terminal Speed

Any object moving through a fluid experiences a force that drags on it due to the fluid. The drag force depends on: shape of the object, speed of the object, the viscosity of the fluid. The faster an object tavels in a fluid, the greater the drag force on it.

When something is acceleretaing, it will get to the point where the forces are balanced and it can't get any faster. This is the terminal velocity which means the object's maximum speed. A car travelling fast will have a driving force pushing it forwards and wind resistance + friction which will balance the forces and cause it not to accelerate. This can be a man jumping out of a plane or a ball falling through a liquid.

This can be presented on a speed/time curve where it will be steep at the start then reach flat as the gradient become flat to represent it has hit terminal velocity.

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## Cars

On the road:

Stopping distance is the thinking distance (speed x reaction time) and the braking distance (how long the car takes to come to a stop). Braking distance is v^2/2a where a is the constant decceleration. On bad road conditions, the braking distance will increase as the tyres on the car are likely to skid/less friction.

Vehicle safety:

Most car safety features increase the time of the impact. This comes from momentum which is force x time. So an increase in time means a decrease in force. Airbags, seatbelts, collapsing steering and crumple zones all increase the time of the impact. This leads to a decrease of force. Cars are designed to crumple to the momentum which propells the body forward won't be stopped immediately by a solid force.

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