ƏD дв [d³r (E. +H. B³) = −√æ³r (i, • E)–[d³r [V • (E×B)], U Ot [d³r UEM √EM = √ d'r H₁₁ = ± √ d³r (€ |E|³² + µ|H|”) du. dt tot dU mech + dU EM = dt dt == -JaAs S ди Ju EM EM+V.S=-j•E Ət
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- The radius of a circle is measured to be (10.5 0.2) m. Calculate (a) the area and (b) the circumference of the circle, and give the uncertainty in each value.Physics A distance R is measured to be 5.400±0.003m. What is the absolute uncertainty in R^-2?What's mu? If p has a unit of [kg/m³), v has a unit of [m/s], D has a unit of [m], and Ris unitless, what is the unit of u in the equation R = vDp/µ? O [s/kg] O [kg/(m• s)] O [kg/s] O [(m• s)/kg]
- w = 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…If H(0) = 8 cos 8, find H'(0) and H"(0). H'(0) = H"(0) =If x = 3.54 + 0.02 %3D y = 8.03 ± 0.04 z = 5.02 ± 0.02, what is the absolute uncertainty in f = (x + y - z) ? Report your answer to two decimal places.
- If $ (x,y,z) ху?г and A %3 xz i - xy? j + yz?k, find (OA) at the point (2,–1,1). %3D dx dz O 2i-4j O 4i - 2j O 2i+4j O 4i + 2jA typical atom has a diameter of about 1.0×10^−10m. Approximately how many atoms are there along a 5.0 −cm−cm line? Express your answer using two significant figures.of 1 estion Given the equation f =- where = 3.43±0.78. What is the value and the absolute uncertainty in f (with the correct number of significant figures)? Select one O 0.2 Ob. 0.78 0.8 Od 1.26 O 1 Clear my choice If the length of an object is /=18.0±0.2cm What is the object's length in units of 772? There are 100cm in 1 m Select one: O 0.2±0.2m Ob. 0 1800+20m d. 0.180+0.002m Clear my choice 0.000180±0.000002m
- A = (6.00i – 8.00j) units, 37. QC (a) (-8.00i + 3.00j) units, and C= (26.0i + 19.0j) units, determine a and b such that aA + bB + Ć = 0. (b) A stu- dent has learned that a single equation cannot be solved to determine values for more than one unknown in it. How you explain to him that both a and b can be deter- mined from the single equation used in part (a)? Taking wouldAn atom of rhodium (Rh) has a diameter of about2.7 * 10-8 cm. (a) What is the radius of a rhodium atom inangstroms 1A° 2 and in meters (m)? (b) How many Rh atomswould have to be placed side by side to span a distance of6.0 mm? (c) If you assume that the Rh atom is a sphere, whatis the volume in m3 of a single atom?f(o)= KBT Vc 1 |--ømø + (1 − 6) ln(1 − 6) + x6(1 − ø) N Π II = kBT [ф Vc N X In(1 - 6) - 6- x6² - to:²] = 1 1 + 21 6 No (2.62) (2.66) (3) Following Sec. 2.4.1, using the (mean-field) Flory-Huggin free energy of mixing for a polymer solution (Eq. (2.62)), derive Eq. (2.63) and hence the van't Hoff's law. Show that the coexistence curve is given by (2.66) and compute the critical point. (2.63)
