WJEC Physics for AS Level Student Book 2nd Edition

25 1.1 Basic physics Test yourself 1.1 1. A student gave the following definition of the moment of a force: Moment is the force multiplied by the distance from the pivot. What is wrong with this definition? Give a better one. 2. A constant called Planck’s constant has the unit J s [joule second]. Express this in terms of the base SI units, kg , m and s . 3. A student is asked to calculate the acceleration of an object and gives the answer as 7.5 m s – 2 . Why is this not a complete answer? 4. The diagram shows all the forces acting on a rod. Explain why the rod is not in equilibrium. 5. A force of magnitude 100 N acts at an angle above the horizontal of 40° . Calculate (a) the horizontal; and (b) the vertical component of the force. 6. Two forces act on an object of mass 5.0 kg : a horizontal force of 12.0 N and a vertical force of 5.0 N . Calculate (a) the resultant force; and (b) the acceleration of the object. 7. A student determines the density of aluminium by taking measurements on a rectangular block. Using vernier callipers with a resolution of ± 0.1 mm , she determines the dimensions of the block to be 10.30 cm × 4.75 cm × 3.21 cm , by taking one measurement of each length. An electronic balance gives the mass to be 427.32 g . (a) Use these data to calculate the density of the aluminium. (b) State which length reading has the greatest percentage uncertainty. Explain your answer. (c) The student assumes that the uncertainty in balance reading can be neglected. Calculate the percentage uncertainty and the absolute uncertainty in her value for the density and hence express the density to an appropriate number of significant figures. (d) Evaluate whether the student’s assumption in part (c) was a reasonable one. 8. A bacterium has a mass of 0.95 pg . Estimate its volume (in m 3 ), assuming its density is 1000 kg m – 3 . 9. The pressure, p , at a depth, d , below the surface of a liquid of density ȡ is given by p = p A + JȡG where ȡ A is the air pressure at the liquid surface and g is the acceleration of free fall. (a) State the units of p , g and ȡ in terms of the base SI units. (b) Show that the equation is homogeneous. (c) Calculate the pressure 25 m below the surface of the sea. ( p A = 101 kPa , g = 9.81 N kg – 1 , ρ sea water = 1030 kg m – 3 ). 10. A uniform rigid plank of weight 30 N and length 4.8 m , with a load of 20 N at one end, is supported between two fulcrums, X and Y, which apply forces F 1 and F 2 , as shown. (a) Calculate the moments of the 20 N load and the 30 N weight of the plank about fulcrum X. (b) Take moments about X and use the principle of moments to calculate the value of F 2 . (c) Explain why F 1 = F 2 + 50 N . Hence calculate the value of F 1 . 11. Newton’s law of gravitation states that two small bodies of masses M 1 and M 2 , separated by a distance d attract each other with a force, F , given by: F = GM 1 M 2 d 2 , where G is the universal gravitational constant. (a) Show that [ G ] = N m 2 kg – 2 . (b) Express [ G ] in terms of the base SI units, m , kg and s . 12. A cylinder of length 1.5 m and diameter 60 mm is made from iron of density 7900 kg m – 3 . Calculate its mass. 13. (a) Find the horizontal and vertical components of each of v 1 and v 2 . (b) Hence find the sum of v 1 and v 2 , expressing the direction as an angle to the dotted line. (c) By a similar method, find the difference ( v 2 − v 1 ) of the vectors. 1.5 N 1.0 N 2.5 N 1.2 m 1.2 m 2.4 m 20 N 30 N X Y F 1 F 2 v 1 = 30 m s – 1 v 2 = 20 m s – 1 30°