By Jeremy Pickles

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**Extra resources for Applied Mathematics by Example: Theory **

**Sample text**

There is a resistance force of 300 N directly opposing the motion. ·what is the acceleration of the truck? 30.... ---- =tL... -- 11_. 1111111111111 P=SOO � ace=? In this example, we may presume that the truck will stay on the rails, so that we are only concerned with motion along the track. vVe therefore focus our attention only on the forces which act in this direction, or, for an oblique force like P, only on the component of P in the direction of the track. There are of course other forces acting, such as the weight of the truck, which acts downwards, and the transverse force from the rails which keeps the truck on line, but we do not include these in the calculation of the motion along the track.

8 m/s2 . This fixes the initial slope of the v-t graph. And secondly we know that the velocity can never exceed the terminal velocity. We expect therefore that the gradient of the graph reduces, as t increases and air resistance has a greater effect, becoming almost zero as it approaches the terminal velocity. 3 Dynamic friction Friction was first studied by Leonardo da Vinci but the formulæ we now use originate with Charles Coulomb, the same Coulomb whose name is commemorated in the name for the unit of electric charge.

5 Mr B is in his garden and places a pile of flowerpots against the shed door to stop it blowing shut. 7. 5kg each, are 20 needed to withstand a force from the door newtons of 20 newtons? 2: Flowerpots resisting a door. J,n newtons. 83, or, since pots come in whole numbers, n = 6. 6 Mr C puts his toolbox, total mass 15 kg, on the floor in the rear of his van. Later, while 2 driving, he is obliged to brake suddenly, decelerating at 5 m/s . 1, which will prevent the tools from sliding forwards when he brakes?