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Draw a right-handed 3D Cartesian coordinate system (= x, y and z axes). Show a vector A with tail in the origin and sticking out in the positive x, y and z directions. Show the angles between A and the positive x, y and z axes, and call these angles α₁, α₂ and α3 Prove that Ax Acos α₁ Ay = Acos α₂ A₂- Acos α3
solve for Vo
Draw a third quadrant vector C. (remember that boldface characters represent vector quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x- axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally, show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these angles p1 and p2, repectively. a) Prove the following formulas for the components of C involving the standard angle (hint: start with the formulas for the components based on the angle & and then use (look up if necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 = 3π/2-8 (this will switch cosine and sine around and eliminate - signs as well)) - C=Ccose C₁=Csine b) Prove the following formulas for the components of C: C=Ccosp1 C=Ccosp2

Chapter 12 Solutions

Modified Mastering Physics without Pearson eText-- Instant Access -- for Physics for Scientists & Engineers with Modern Physics

Ch. 12 - A ground retaining wall is shown in Fig. 1240a....Ch. 12 - Can the sum of the torques on an object be zero...Ch. 12 - A ladder, leaning against a wall, makes a 60 angle...Ch. 12 - Prob. 8QCh. 12 - Prob. 9QCh. 12 - Place yourself facing the edge of an open door....Ch. 12 - Prob. 11QCh. 12 - Prob. 12QCh. 12 - Prob. 13QCh. 12 - Which of the configurations of brick, (a) or (b)...Ch. 12 - Is the Youngs modulus for a bungee cord smaller or...Ch. 12 - Examine how a pair of scissors or shears cuts...Ch. 12 - Materials such as ordinary concrete and stone are...Ch. 12 - Prob. 1MCQCh. 12 - Prob. 2MCQCh. 12 - Prob. 3MCQCh. 12 - Prob. 4MCQCh. 12 - Prob. 5MCQCh. 12 - Prob. 6MCQCh. 12 - Prob. 7MCQCh. 12 - Prob. 8MCQCh. 12 - Prob. 9MCQCh. 12 - Prob. 10MCQCh. 12 - Prob. 11MCQCh. 12 - (I) A tower crane (Fig. 1248a) must always be...Ch. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4PCh. 12 - (II) Calculate the forces FA and FB that the...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - (II) Find the tension in the two wires supporting...Ch. 12 - Prob. 12PCh. 12 - (II) The force required to pull the cork out of...Ch. 12 - Prob. 14PCh. 12 - (II) Three children are trying to balance on a...Ch. 12 - Prob. 16PCh. 12 - (II) A traffic light hangs from a pole as shown in...Ch. 12 - Prob. 18PCh. 12 - Prob. 19PCh. 12 - Prob. 20PCh. 12 - Prob. 21PCh. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - (III) A door 2.30 m high and 1.30 m wide has a...Ch. 12 - Prob. 25PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - (III) A uniform ladder of mass m and length leans...Ch. 12 - (III) A refrigerator is approximately a uniform...Ch. 12 - (III) A 56.0-kg person stands 2.0 m from the...Ch. 12 - Prob. 31PCh. 12 - Prob. 33PCh. 12 - Prob. 34PCh. 12 - Prob. 35PCh. 12 - Prob. 36PCh. 12 - Prob. 37PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - Prob. 40PCh. 12 - (I) A sign (mass 1700 kg) hangs from the end of a...Ch. 12 - Prob. 42PCh. 12 - (II) How much pressure is needed to compress the...Ch. 12 - (II) At depths of 2000 m in the sea, the pressure...Ch. 12 - Prob. 45PCh. 12 - (I) The femur bone in the human leg has a minimum...Ch. 12 - Prob. 47PCh. 12 - (II) (a) What is the maximum tension possible in a...Ch. 12 - (II) If a compressive force of 3.3 104 N is...Ch. 12 - Prob. 50PCh. 12 - (II) Assume the supports of the uniform cantilever...Ch. 12 - Prob. 52PCh. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - Prob. 55PCh. 12 - (III) The truss shown in Fig. 1272 supports a...Ch. 12 - (II) How high must a pointed arch be if it is to...Ch. 12 - Prob. 60GPCh. 12 - A cube of side l rests on a rough floor. It is...Ch. 12 - Prob. 62GPCh. 12 - When a wood shelf of mass 6.6 kg is fastened...Ch. 12 - Prob. 64GPCh. 12 - Prob. 67GPCh. 12 - The mobile in Fig. 1274 is in equilibrium. Object...Ch. 12 - A 65.0-kg painter is on a uniform 25-kg scaffold...Ch. 12 - Prob. 70GPCh. 12 - Prob. 73GPCh. 12 - Prob. 74GPCh. 12 - Prob. 76GPCh. 12 - Prob. 77GPCh. 12 - Prob. 78GPCh. 12 - Prob. 79GPCh. 12 - Parachutists whose chutes have failed to open have...Ch. 12 - Prob. 81GPCh. 12 - One rod of the square frame shown in Fig. 1295...Ch. 12 - A uniform beam of mass M and length l is mounted...Ch. 12 - Prob. 84GPCh. 12 - A uniform 6.0-m-long ladder of mass 16.0 kg leans...Ch. 12 - In Fig. 1279, consider the right-hand...Ch. 12 - Assume that a single-span suspension bridge such...Ch. 12 - A uniform sphere of weight mg and radius r0 is...Ch. 12 - A uniform ladder of mass m and length leans at an...Ch. 12 - Prob. 90GPCh. 12 - Prob. 91GPCh. 12 - A 23-kg sphere rests between two smooth planes as...Ch. 12 - Prob. 93GPCh. 12 - Prob. 94GPCh. 12 - Prob. 95GP
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