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Finding the Resultant of Perpendicular Forces Two 40.0 N forces, □(→┬F_1 ) and □(→┬F_2 ), directed at 90.0° to each other, act on a hook, as shown in Figure 2-6. Use the geometric approach to vector addition to find the resultant force acting on the hook. Find the components of each force along the x- and y-axes. Find the components of the net force (resultant vector). Compare your results from parts (b) and (c). What conclusions can you draw? Fig. 2-6 Two 40.0 N forces are acting on a hook.
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Civil Engineering
Finding a Unit Vector perpendicular to two Given Vectors Two forces are described as F ⃗1 = (i ̂+2j ̂-3k ̂) N and F ⃗2 = (-2i ̂+3j ̂) N. Find an expression for a unit vector directed perpendicular to both of them.
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Civil Engineering
Relationships between the Coordinate Direction Angles Prove that the coordinate direction angles for any 3-D vector F ⃗ satisfy the equation 〖cos〗^2∝+〖cos〗^2 β+〖cos〗^2 γ=1 (2-13)
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Civil Engineering
Finding a Unit Vector in the Direction of a Given Force A force vector is described as F ⃗=(3i ̂+4j-5k ̂ ) N. Express the unit vector in the F ⃗ direction using Cartesian notation
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Civil Engineering
Forces Acting on a Student on a Slippery Ramp A 51.0 kg student steps onto a slippery 10.0° ramp (the force of friction between the ramp and the girl can be neglected). Two forces are acting on her: the force of gravity exerted by Earth, which is Fg = 500 N directed down (toward the centre of Earth), and the normal (perpendicular to the surface) force exerted by the ramp, which is N = 493 N, directed perpendicular to the ramp, as shown in Figure 2-9.
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Civil Engineering
The Dot product and Simple Coordinate Transformations Two forces, F ⃗1 andF ⃗2 are described as F ⃗1 = (3.00i – 2.00j) N and F ⃗2 = (-1.00i ̂ + 3.00j ̂) N. Find the angle between the forces. Verify that the x- and y-components of the forces, F_1x,〖 F〗_(1y,) 〖 F〗_(2y ) and F_2y, are their projections onto the x- and y-axes, respectively. Find the components of forces□( ) F ⃗1 andF ⃗2 in the orthogonal x’y’-coordinate system that is rotated by 30° counterclockwise about the origin, as shown in Figure 2-18(a). Calculate the magnitudes of the forces using their components in both coordinate systems, and compare the results. Suppose that we move the xy-coordinate system in a plane such that the new coordinate axes remain parallel to the original axes, but the origin O moves to a new location (Figure 2-18(b)). Find the components and the magnitudes of forcesF ⃗1 andF ⃗2 in the x’y’-coordinate system.
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Civil Engineering
How Fast Are the Molecules Going? At standard temperature (0 °C) and pressure (101.325 kPa), or STP, a mole of gas occupies a volume of 22.4 L. The molar mass of an atom of nitrogen is approximately 14 g/mol. Nitrogen is diatomic, that is, its atoms bond in pairs to form N2 molecules. Estimate the average speed of a nitrogen molecule at STP.
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Civil Engineering
Thermal Expansion of a Rod A long, thin rod of aluminum is measured to have a length of 0.250 m at 20.0 °C. By how much will the length of the rod increase if it is heated to 30.0 °C?
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Civil Engineering
