## J. Pickles's Applied Mathematics by Example - Exercises PDF

By J. Pickles

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Extra info for Applied Mathematics by Example - Exercises

Example text

2 m. 3 m/s towards B. 2 m/s. What is the speed of A? 1 m/s. What is the speed of B? Check that the total momentum of A, B and C after both collisions have happened is still the same as their total momentum before the collisions. Will there be any more collisions? com 37 Questions Applied Mathematics by Example: Exercises 9. 3 m. 10. A spherical egg of diameter 5 cm and mass 60 g is dropped from a height of 2 m onto a concrete floor. (a) Calculate the speed at impact. (b) What is the change in momentum of the egg?

C) How will the speed of delivery of the cotton from the reel to the sewing machine operator vary over the lifetime of a reel if it is rotated at constant frequency? (d) Consider now the reel itself spinning without any cotton on it. What is the speed of a point at radius rh < r < r0 if it is spun at a frequency f ? (e) * A solid object is rotated about an axis passing through the object at a constant frequency. By referring to your answer to part (d) or otherwise, sketch a graph of how the speed of the parts of the object vary with their perpendicular distance from the axis of rotation.

P receives an impulse in a collision after which its velocity becomes 5i + 4j m/s. What is (i) the change in velocity of P, (ii) the increase in speed and (iii) the angle through which its direction of motion has been deflected? 24. Three forces F1 , F2 , and F3 are represented by vectors 10i + 20j, 20i − 30j and −6i + 20j newtons respectively. Draw a sketch showing their magnitudes and directions. Determine their resultant, expressed as a vector, and find its magnitude. An additional force F4 = xj is now applied so that the resultant of F1 , F2 , F3 and F4 has magnitude 30 N.