Question

PHYS 3043, Spring 19, HW#1 due Wed, Jan 23, by 3:00 pm 1) Show that sing + a) + sin侄-a)s cos(a) 2) (a) Given two vectors ธิ (2,2,1) and Ce(1,2,-6), what is xc? (b) Are B and C orthogonal to each other? How can you tell? 3) Given vectors A and E a) Define the dot product mathematically in two different ways. One way involving the components and the other the length/angles b)Define the vector cross product mathematically two different ways. 4) (a) Given the function f(x.y,z)-xy+z, what is the gradient of f, Vf. (b) Given the function F zi + rVJ + k, what is the curl of F, ▽ × F?" c) Given the function F i+zy+ k, what is the divergence of F 5) For an arbitrary function f(x.y,a) show that Vx Vf in Cartesian One way involving the components and the other the length/angles. Is it a vector or a scalar? Is it a vector or a scalar? V F? Is it a vector or a scalar? coordinates is 0. 6) Use an appropriate volume integral to find an expression for the vol- ume enclosed between a sphere of radius 1 centered on the origin and a circular half-angle β with its vertex at the origin. Show that in the limits where β=0 and β=π that your expression gives the expected results. 7) A 3-kg block is moved up a 370 incline relative to the horizontal under a) Determine the work done by the 40 N force b) Determine the work done by friction c) If the block is initially at rest, how long does it take the block to travel the action of constant horizontal force of 40 N. The coefficient of kinetic friction is 0.1 and the block is displaced 2m along the incline. 2m along the incline?

Answer 1