By Christine Compston
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Additional resources for A Teacher's Guide to The American Revolution: A History in Documents (Pages from History)
Oil can make surfaces smooth and ice is often modelled as a smooth surface. 41 42 AN INTRODUCTION TO MATHEMATICS FOR ENGINEERS: MECHANICS When the contact between two surfaces is smooth, the only force between them is at right angles to any possible sliding and is just the normal reaction. 1 What direction is the reaction between the sweeper’s broom and the smooth ice? A TV set is standing on a small table. Draw a diagram to show the forces acting on the TV and on the table as seen from the front.
Ii) The section BC is much steeper than OA; what does this tell you about the motion? iii) Draw the speed–time graph for the person. iv) What simplifications have been made in drawing these graphs? 5 i) Calculate the acceleration for each part of the following journey. ii) Use your results to sketch an acceleration–time graph. 6 A particle moves so that its position x metres at time t seconds is x ϭ 2t 3 Ϫ 18t. i) Calculate the position of the particle at times t ϭ 0, 1, 2, 3 and 4. ii) Draw a diagram showing the position of the particle at these times.
The weights 2g N and 5g N are more appropriate. ii) When the block does not slip, the forces on B are in equilibrium so 5g Ϫ T ϭ 0 T ϭ 5g. The tension throughout the string is 5g N. For A, the resultant horizontal force is zero so TϪF ϭ0 F ϭ T ϭ 5g. The friction force is 5g N towards the left. iii) When the block slips, the forces are not in equilibrium and T and F have different magnitudes. The resultant horizontal force on A is (T Ϫ F)N towards the right. The resultant force on B is (5g Ϫ T) N vertically downwards.