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- Q 1: Let å = -2 ỉ +3 j +6 k and b = 4 i + 6 j , Find ( 2 å + 3 b ,1-ål, å * å , å * b_ )Assume = 36 and H = 4. Determine the x-component of H.Which of the following statements is true Select one: O " ("f(x, y)dxdy gives the area of the graph of f(x. y) above a rectangular region in xy-plane. O If f(x, v. 2) = x² + y? - - xyz + 2. then f(x, y. z) =f(2. y. x), O if f(x, y, 2) = x² + y² - z? - xyz + 2, then f(x. y. ) = f(.x.2) O If f(x, y) is constant functionof y, then = 0
- 97 PROBLEMS 2-45. Describe how to determine whe ther an equilibrium is stable or unstable when (dUdx),0. 2-46. Write the criteria for determining whether an equilibrium is stable or unstable when all derivatives up through order n, (d" U/ dx ") 0. 247. Consider a particle moving in the rCrionD If A = 3î – 4j + 4k, B = 2î + 3j – 7k and C = -4î + 2j + 5k, Find: (a) Ā + B – C (b) Ả.B (c) AxBLet F(x,y) = 24x -y. If (x , y) changes from ( 7 , 3 ) to ( 5 , 4) , find A F and dF. Enter A F in Blank # 1 and enter dF in Blank # 2. Enter an integer or a fully reduced fraction such as -2 , 0, 15 , 3/4 , -7/9 , etc. No Spaces Please. Blank # 1 Blank # 2
- Evaluate the following: a) [P., A] where A =(P + P3 + P2) 2mLet a = (a)a + b and a-b b (b)-2ā + (c) The magnitude of a and b (d)a × b (e) Show that a. (axb) = 0 and b. (axb) = i-2j-2k and b= 61+31 + 2k; Find?Using spherical polar coordinates, find Vf for (a) f = r4 (b) f = 2+1 (c) f = r² sin 20 cos o
- docs.google.com a (a) A + B at P(0, 2, –5) (b) The angle between A and B at P (c) The scalar component of A along B at P aX - ay + 7az ; 143.26°, -8.789 aX - ay + 7az ; 193.26°, -10.789 aX - ay + 7az ; 143.26°, 30 aX - ay + 7az ; 98.789°, -8.789 8 نقاط In a certain region, the electric field intensity is given by (2cosp E = (20080) a, – (r sin ø)a, + (4z² cos 4) a, V/m , Find Qr 0 •..PROBLEMS 97 2-45. Describe how to determine whether an equilibrium is stable or unstable when (d²U/dx®), = 0. 2-46. Write the criteria for determining whether an equilibrium when all derivatives up through order n, (d"U/dx"), = 0. stable or unstablew = FjAc = F .Aë , W = m(v;)* - m(u,)* , v 1 zm(us)* - m(v,)* , W = Problem 1: (a) à = 3â – 2ŷ, B = 4â& – 5ŷ. à ·B =? Answer: 22 (b) à = -2â + 4ŷ, B = 3âu – lŷ. Ā·B =? Answer: –10 (c) à = 5â – 3ŷ, B = -3â – 5ŷ. ÷B =? Answer: 0 1 | F,dx , W = F. dř , F, dU W = -AU dx d = 4m F = 20 N 0 = 30° m = 4 kg Hk = 0.5) m = 2 kg F = 40 N Hk = 0.2 Ө — 30° Problem 2: In the figure above on the left we have a force F = 20 N pulling a box to the right at an angle 0 = 30° above the horizontal. The box has a mass m = 2 kg, the coefficient of kinetic firction between the box and the ground is uk = 0.2, and the block moves a distance d = 4 m to the right. (a) What is the work done by the force F? Answer: 69.3 J (b) What is the normal force from the ground? Use g = 10 m/sec² Answer: 10 N (c) What is the work done by the kinetic friction force? Answer: -8 J (d) What is Wnet, the net work done on the box? Answer: 61.3 J (e) The box has an initial speed of 4 m/sec. What is the speed of the box after it has…