Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 10.4, Problem 10.8P
To determine
Whether Equation 10.65 satisfies Equation 10.52, by direct substitution.
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The force F= (yzi + zxj + xyz)/xyz acts on the particle P(x,y,z) which moves in space. (a) Using the relation derived in Prob. 13.79, show that this force is a conservative force. (b) Determine the potential function associated with F.Reference to Problem 13.79:Prove that a force F(x,y,z) is conservative if, and only if, the following relations are satisfied:
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- 3.3 Is the vector field V(r,@,z) = ÷f – 2n®, rotational? Support your answer with a calculation.arrow_forward4G li. 12:23 SDD1-4E7C-44C7-A86A-F33B0962698C.j → ... 8. Find the vector product of two vectors A = 50 and B| = 20, with an angle between them is 45°.arrow_forwardThe figure shows four vectors A, B, C and D having magnitudes 12.0 m, 10.0 m, 8.0 m, and 4.0 m, respectively. The sum of these four vectors is y B 30° + 30° X D 1076 2 48432 W S mand X M O a. 16.4 m at an angle 77.8° with respect to +X-axis. Ob. 16.4 m at an angle 12.3° with respect to +X-axis. c. 19.5 m at an angle 77.8° with respect to +X-axis O d. 19.5 m at an angle 12.30 with respect to +X-axis. O e. 8.20 m at an angle 77.8° with respect to +x-axis. F2 s # 3 E D 31, C M 80 $ 4 R F a FA % 5 V #tv ♫ T o FS G 6 B c Fo Y H & 7 N F7 p U 8 J DII FB 1 M ( 9 K F9 O A ) O 4 F10 L e e P il V F11 { 11 + [ C F12 command option Oarrow_forward
- rection: Calculate the following. (Three points each) 2. Sam has measured the end points of two poles, and wants to know the angle between them: 1. Calculate the dot product of vectors a and b: (11,5,8) A (3.60 m) a (4,8,2) az k 70.0 30.0 () ax y B (2.40 m) ay 3. Vector a has magnitude 3, vector b has magnitude 4 and the angle between a and b is 60°. What is the value of a. b.? 4. Vector a has magnitude 3v2, vector b has magnitude 5 and the angle between a and b is 135°. What is the value of a. b.? 5. What is the size of the angle between the vectors a = (2, 5, -1) and b = (-3, 2, 6)?arrow_forwardIf v×w =2i −3j+2k, v×w=2i−3j+2k, and v⋅w=5, and θ is the angle between v and w, thenarrow_forwardThe density of a star measured from the center of a star is equal to Z. a is constant. find the gravitational potential and g as a function of r.arrow_forward
- Compute for the unit vector of the V V =arrow_forwardQuestion 1.1: Calculate the dot product of vectors A and B, where JA|=5 and |B|=3 and EXPLAIN. А B a.arrow_forwardA 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEarth = 5.97 x 1024 kg. A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy Ei. B) Can it escape Jupiter? Justify your answer. C) What is the angular momentum of the spacecraft around Jupiter? Call this Li.arrow_forward
- Two vectors A and B are shown in the figure. The magnitude of their dot product is C, and the magnitude of their cross product is 1.094 C. Find cos(0). B A.arrow_forward→ Let 2 vectors à anb b a in the plane of modules. 12=5 ²161 = 5 e 161=5 How much is the magnitude of their vectors d=a-b knowing that the angle between the two vectors is to 60°?arrow_forwardI am not sure how to work on this problem, the answers are Na=29.8N, Nb=8.12N. They gave a hint which says to find the acceleration of the system first.arrow_forward
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