A force F is applied at the top of the tower at A. If it acts in the direction shown such that one of its components lying in the shaded y-z plane has a magnitude of 80 lb, determine its magnitude F A y 60° 60° 90 Ib F
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- y 1 40 4N 65° 6N (d) What is the magnitude of the total force | A+B|? (e) What is the angle between the total force and the +x axis?The force F is applied 45 degrees counter clockwise from the surface of the slope. The slope is 20 degrees counter clockwise from the horizontal. The magnitude of F is 60lbs. Determine the magnitude of the Force F applies along the slopeIn the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates where one of the C-H bonds is in the direction of i + j + k (i-hat + j-hat + k-hat) an adjacent C-H bond is in the direction of i - j - k (i-hat minus j-hat minus k-hat). What is the angle between these two bonds? " a) 100 degrees b) 109 degrees c) 200 degrees d) 209 degrees
- "In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates where one of the C-H bonds is in the direction of i+j+k (i-hat + j-hat + k-hat) an adjacent C- H bond is in the direction ofi-j-k (i-hat minus j-hat minus k-hat). What is the angle between these two bonds?" O 100 degrees O 109 degrees O 200 degrees O 209 degreesA force vector with magnitude R and making an angle α with the x-axis is having its component along x-axis and y-axis as:a) Rcosine (α) and Rsine(α)b) Rcosine (180-α) and Rsine(α)c) Rcosine (180-α) and Rsine(180+αTwo forces, F1 and F2, act at a point, as shown in the picture. (Figure 1) F1 has a magnitude of 9.60 N and is directed at an angle of a = 58.0 ° above the negative x axis in the second quadrant. F2 has a magnitude of 7.00 N and is directed at an angle of B = 53.7 ° below the negative x axis in the third quadrant. Figure 1 of 1 B F
- Create xand y vectors to represent the following data: 10 23 20 45 30 60 40 82 50 111 60 140 70 167 80 198 90 200 100 220 1. Plot the data on an x-y plot. 2. Usc lincar interpolation to approximate the value of y when x 15. 3. Usc cubic spline interpolation to approximate the valuc of ywhen x 15. 4. Usc lincar interpolation to approximate the value of x when y 80. 5. Usc cubic splinc interpolation to approximate the value of x when y= 80. 6. Usc cubic spline interpolation to approximate yvalucs for xvalues cvenly spaced bectween 10 and 100 at intervals of 2. 7. Plot the original data on an xy plot as data points not connected by a linc. Also, plot the values calculated in Excrcise 6.Why is the following situation impossible? A barge is carrying a load of small pieces of iron along a river. The iron pile is in the shape of a cone for which the radius r of the base of the cone is equal to the central height h of the cone. The barge is square in shape, with vertical sides of length 2r, so thatthe pile of iron comes just up to the edges of the barge. The barge approaches a low bridge, and the captain realizes that the top of the pile of iron is not going to make it under the bridge. The captain orders the crew to shovel iron pieces from the pile into the water to reduce the height of the pile. As iron is shoveled from the pile, the pile always has the shape of a cone whose diameter is equal to the side length of the barge. After a certain volume of iron is removed from the barge, it makes it under the bridge without the top of the pile striking the bridge.B1-1. A connection point has two force vectors with the magnitudes of F = 37 kN and F2 = 24 kN. The slope zılyn = 2/3 and the angle d= 53 degrees. 3 Y1 F, a) Determine the magnitude of the resultant force (kN). Answer: Check b) Determine the direction cosine of the resultant force vector for i direction. Answer: Check c) Determine the direction cosine of the resultant force vector for j direction. Answer: Check d) Determine the direction cosine of the resultant force vector for k direction. Answer: Check e) Determine the coordinate direction angle ß (degrees).
- Try and solve for the resultant of the two vectors. Also, determine the direction cosines of the resultant and sketch the resultant in the x, y, and z coordinate system. Determine the x-component of the resultant, the y-component of the resultant, the z-component of the resultant, the magnitude of the resultant , the angle made by the resultant force with the x-axis, the angle made by the resultant force with the y-axis, the angle made by the resultant force with the z-axis.Problem 17. For the tree in Problems 13 and 14. knowing the tension in cable AB 13 950 lbs 1bs and the tension in cable AC is 810 lbs. determine the magnitude and direction of the resultant force atA Write the force vector of the resultant A in terms of its unit vectors. 45° 25 40 P.The angle between the vectors that connect ther carbon atom to the hydrogen atoms in the methane molecule can be calculated using the dot product or the cross product rule. In the case of the dot product, we get the correct answer, which is 109.5 degree, but if we use the cross product, the answer might be 70.5 degree. Why?