Suppose the density of an object is given by xz, and the object occupies the tetrahedron with corners (0,0,0), (2,0,0), (0,2,0) and (0,0,2). Find the mass of the object.

To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0 cm long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0 kg person, the mass of the upper leg would be 8.80 kg, while that of the lower leg (including the foot) would be 5.30 kg. Take that x-axis is directed horizontally and the y- axis is directed vertically downward. ▾ ▾ Part A ▾ Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. Zc = ▾ Part B Submit Yc= Part C ΤΥΠΙΑΣΦ Submit Zc = Find the y-coordinate of the center of mass of this leg, relative to the hip joint, if it is stretched out horizontally. Part D Submit Request Answer Vez A ■ ΠΑΣΦ 6 A • IE Request Answer ΠΑΣΦ A Find the x-coordinate of the center of mass of this leg, relative to the hip joint, if it is bent at the knee to form a right…

If the cross product of two vectors vanishes, what can you say about their directions?

A painter (of mass 72 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 64 kg directly over one of the bars (see figure). You can assume the plank is massless, and is long enough to reach to the other building.  -If the bars are separated by a distance 1.4 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall?

A painter (of mass 75 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 72 kg directly over one of the bars (see figure). You can assume the plank is massless, and is long enough to reach to the other building. If the bars are separated by a distance 2.6 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall? d =

(b) A particle moves from position A to position B in the following Cartesian coordinate system. (Not drawn to scale) (i) B 9 Z -6 Fig Q1b Find the displacement vector AB. 9 A (ii) Using dot product, find the angle that the displacement vector AB make with the x axis.

"If vectors A = 4i + 3j + 2k and B = 2i + 3j + 2k, then the dot product A.B will be equal to... "

(b) A particle moves from position A to position B in the following Cartesian coordinate system. (Not drawn to scale) (i) 7 6 de B Z X Fig Q1b Find the displacement vector AB. A (ii) Using dot product, find the angle that the displacement vector AB make with the x axis.

What is the difference between the scalar product and the cross product of two vectors? While the composition of two vectors into a single vector is unique, the decompositionof a vector into two vectors is not. Why? and What happens with the vector product when the order of the two vectors which arebeing multiplied is reversed?