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Tutorial 1

Tutorial 1. GEM2507 Physical Question from Everyday Life. My Biodata. Name : Setiawan Office : S13-02-09 Phone no : 6516-2988 Email : physetia@nus.edu.sg Consultation hour : Monday 10.00-12.00.

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Tutorial 1

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  1. Tutorial 1 GEM2507 Physical Question from Everyday Life

  2. My Biodata Name : Setiawan Office : S13-02-09 Phone no : 6516-2988 Email : physetia@nus.edu.sg Consultation hour : Monday 10.00-12.00

  3. Would it be a good idea to measure the distance to the closest galaxy outside our own by triangulation? • No. Triangulation only works for distances up to about 50 pc. • Milky Way’s diameter ~ 30kpc with thickness ~ 300 pc. • Triangulation can only be used in the direct neighbourhood of sun

  4. 2. If we know that a star’s spectrum is blue shifted, what do we know about its distance? • Observation shows that all sufficiently distant celestial objects are red shifted. The distance can be calculated from Hubble’s law v =H0xd • If a star is blue shifted, it means it can’t be very far away from us. • Out of billions of galaxies, only somewhat more than 100 galaxies are blue shifted. One of them is Andromeda galaxy which is 2.57 Mly == 788 kpc and approching us whit a speed 301 km/s

  5. 3. With the help of mathematical induction, prove that for any n • The theorem is true for n = 1 because we have • Suppose that for some integer , , • We must show that for n+1 we have • Proof : QED

  6. 4. A slingshot consists of a rubber strap attached to a Y-shaped frame with a small pouch at the center of the strap to hold a small rock or other projectile. The rubber strap behaves much like a spring. Suppose that for a particular slingshot a spring constant of 600 N/m is measured for the rubber strap. The strap is pulled back approximately 40 cm (0.4m) prior to being released • What is the potential energy of the system prior to release? • What is the maximum possible kinetic energy that can be gained by the rock after release? • If the rock has a mass of 50 g (0.05 kg), what is its maximum possible velocity after release? • Will the rock actually reach these maximum values of kinetic energy and velocity? Does the rubber strap gain kinetic energy? Explain

  7. 4a) Each strap of the rubber band has a spring constant of 600 N/m. Since there are two straps acting parallely with each other. The total spring constant will be ktotal = 2k = 2(600N/m) = 1200 N/m • The elastic potential energy of the spring prior to release is 4b) 4c) 4d) The rock will not actually reach these maximum values of kinetic energy and velocity because some of the elastic potential energy will be converted to kinetic energy of the rubber strap, heat, sound etc

  8. 5. If the half-life of a radioactive substance is 12 years, how much of the substance will have decayed after 100 years? The substance remain after 12 years is of the original amount 6. Why is it reasonable to approximate atoms as billiard balls when discussing a gas at room temperature and one atmosphere pressure (STP)? • Ideal gas model assumes no interaction between the gas particles except the elastic collision between the particles which implies a large the distance between the gas particles. • The size of an atom or molecule is in the order of 10-10 m and hence its volume is (10-10)3. • The volume of 1 mol of atoms is then equal to 6.022 x 1023 x 10-30 m3 = 6.022x10-7 m3. • At STP, 1 mole of gas occupies a volume of 22.4 l or 2.24 x 10-2 m3. Therefore, the volume of the atoms is only 6.022x10-7/ 2.24 x 10-2 = 0.0026% of the space volume that the gas occupies. So, at STP, on average one gas particle is indeed very far away from the other. Hence, the ideal gas model is a suitable model to be used under such condition.

  9. 7. Which lattice is more efficient in packing atoms into a fixed volume of space: simple cubic or face centered cubic? • As can be seen from the picture, Face Centered Cubic (FCC) can pack more atoms into the same volume of space. • In simple cubic lattice, there are only 8 atoms situated at the corner while in FCC lattice, in addition to these 8 atoms there are also one atom at each face of the cube http://feynman.phy.ulaval.ca/marleau/bravais3D_1.htm

  10. 8. We have an incompressible fluid flowing into the opening of a canonical pipe. The radius of the opening is 1 cm and the fluid velocity is 2 m/s. If the outflow from the pipe end is 1 m/s, what is the radius of the pipe end? Since the fluid is incomprehensible, the amount of fluid that enters the cone is the same as the amount of fluid which exits the cone

  11. Toughness: the amount of energy that a material can absorb before rupturing (the resistance to fracture of a material when stressed). It can be found by finding the area (i.e. by taking the integral) underneath the stress-strain curve 9. In your own words, explain the difference between hardness and toughness. When a steel knife and a diamond are made to collide at high speed, which of the two is more likely to break?

  12. Q9. Hardness Definition: the resistance of a material to permanent deformation (plastic deformation). Hardness can be measured in various scales, depending on needs. For example, in mineralogy, the hardness of a material is measured against the scale by finding the hardest material that the given material can scratch, and/or the softest material that can scratch the given material (Mohs scale). Diamond is the hardest material in the world that can sustain high pressure without getting deformed. However, steel knife is tougher than diamond, in the sense that it can sustain high impact. So when the two collide at high speed, diamond will likely to shatter first.

  13. 10. The grain size in steel depends on a number of factors including the speed with which it is cooled. What kind of grain size (relatively large or relatively small) should I aim for if I want the steel to be very hard? During plastic deformation, slip or dislocation must take place across the boundary between grain A and B in the picture • Grain boundaries are barriers to slip for two reason • 1. Since the two grains are of different orientations, dislocation passing into grain B will have to change its direction of motion; it become more difficult as the crystallographic misorientation increases • 2. The atomic disorder in the grain boundary result in discontinuity of slip planes from grain into the other • High-angle boundaries are better in blocking slip ! • • Smaller grain size: • more barriers to slip. • The so called Hall- Petch eq. expresses this Adapted from Fig. 7.12, Callister 6e. (Fig. 7.12 is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.) σ0 and ky are material dependent σy = yield strength D = average grain diameter

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