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- A rectangular parallelepiped has dimensions a, b, and c as shown in the figure below (a) Obtain a vector expression for the face diagonal vector R. (Use the following as necessary: a, b, and c.) (b) What is the magnitude of this vector? (Use the following as necessary: a, b, and c.) R1 (e) Notice that R,, ck, and R, make a right triangle. Obtain a vector expression for the body diagonal vector R, (Use the following as necessary: 3, b, and c.) R2For numeric entry in the Bb system the standard guidance applies: enter more digits than are signifi- cant in the answer field to ensure correct answers are marked as correct,convert to standard units if necessary unless otherwise stated but do not enter the unit in the answer field, if you choose to use scientific notation 2.0563 x 10-4 is entered as 2.0563E-4 (no spaces, the E must be capitalized). 1) Calculate the density of a block of unknown metal that has mass 234.00 g and is a cube that measures 9.000 cm on a side. 2) Calculate the volume of a 5.00 kg nugget of pure gold. 3) If the nugget in the previous problem were cast into a cube, what would the length of one of the sides be, measured in centimeters? 4) Calculate the mass of blood in the average human body, given the average volume of 5.0 L. 5) If a cylindrical rod of uranium is 25.00 cm long and has mass 9.874 kg, what is its radius?In the diagram below there is a thick-walled cylindrical tube. Its height is H = 5.0 m, its inner radius is R1 = 1.0 m, its outer radius is R2 = 3.0 m and its mass is M = 10.0 kg. The volume density is proportional to the square of the height h measured from the top of the cylinder: p x h?. R2 a) Proof that the proportionality constant k (p = kh?) is k = , ms 100m b) Determine the position of the center of mass of this object. c) Determine I, the moment of inertia of the cylindrical tube around the axle going through the center of the top (as shown on diagram). You can use lying =mr? (the rotational inertia of a ring of radius r and mass m rotating around an axis parallel to it, through its center).
- Write down an expression for the angle in the previous problem if 0 is small (sin 0<<1). Please use appropriate algebraic symbols for multiplication (* for a × b), division (/ for a/b), exponents (a^b for a³), square root (sqrt(a*b/c) for √a × b/c) etc. Please use the "Display response" button to check you entered the answer you expect. 0=You purchased 5.2kg of apples from a store. You noticed that they used the smallest division of 4.2 g to weight them. What is the relative error of this weight measurement as a percentage. You want to calculate the area of your dorm which is in a rectangular shape. You measure the length and the width of the room as L= 4.8+(-.01) m, W= 4.4+(-.01) m. What is the absolute error in the area in m^2 units?A FIFA-approved size 5 soccer ball must have a circumference of 68.5 to 69.5 cm and a mass of 420 to 445 grams. a) What is the circumference in inches of a FIFA-approved size 5 soccer ball? b) How much does a FIFA-approved size 5 soccer ball weigh in pounds? Answer parts a-b. Please show all work.
- Please answer the following question(s): 1. Calculate the angle a person needs to lean from the vertical when 1. walking a 17 m (radius) circular track at 22 mins per mile, and Enter to 2 significant figures Angle with respect to the vertical = = 2. running at 4 min per mile. Enter to 2 significant figures Angle with respect to the vertical = Use 1 mile = 1609.4 m ✓ O OT The total surface area, A, of the cylinder can be expressed as A = (a) Find the value of k. (b) Find the value of that makes the total surface area a minimumThe dot product of vectors A and B is 6 sq. meters. If B = 3.5i + 5.1j – 3k meters and the angle between A and B is 63 degrees, what is the magnitude of vector A? Express your answers in meters and in two decimal places.
- UNIT VECTORS: 1. Given three vectors A = -2i + 3j + 4k, B = 3i + 1j - 3k and C = 3i -4j + 2k, do the following: a) Find the magnitude of each vector b) Write an expression for the vector sum A + B using unit vectors c) Write an expression for the vector difference A - C using unit vectors d) Find the scalar product A. B e) Find the cross product A x B f) Find the angle between A and B g) Find (Ax C). BA study fonds that the metabolic rate of mamals is proportional to the mass of the mamal carried to the exponent of (3/4). By what factor does the metabolic rate of a 70.0 kg human exceed that of a 6.30 kg cat?\ 70.0 3/4 kg = 6.09 6.303/4 kg I set up the values as a ratio and came up with 6.09. OK, I answered my own question. That is the correct answer.An Olympic-size swimming pool is 50 m long, 25 m wide, and 2 m deep. In terms of volume, this pool, when full, holds how many kilogallons of water? Use the following equivalences: 1 gallon = 3.8 L 1 kilogallon = 103 gallon 1 L = 103 mL for water: 1 mL = 1 cm3 1 m = 100 cm [Numerical Problem: Just write the numerical answer without units. Express your answer to 2 significant figures in standard notation]