A. Write a vector expression for each force. B. Determine the resultant of the t

Question

A. Write a vector expression for each force.

B. Determine the resultant of the three forces.

C. Determine the direction angles for the resultent.

F=100N Q=300N P=200N

Explanation / Answer

These force vectors act in the 3D plane x , y , and z first thing we do is break them up to each component lets start with F F has a 60 degree angle with the x axis, lets call Fx the x component of F Fz is the z component of F and so on... Fx = 100 N * cos (60) = 50N Fz = 100 N * cos (60) = 50N Fy = - 100N * cos (45) = -100/sqrt(2) N do the same for the other 2 vectors Qz = - 300 N * cos (60) = -150 N Qy = - 300N *sqrt(3)/2 *1/ sqrt(2) *first calculate the length of the vector projected on to the x-y plane ... then use the 45 degree to caculate the x , y components Qx = - 300N *sqrt(3)/2 *1/ sqrt(2) Pz = - 200 N * 8/17 (based on the ratio of in the picture) to find Px and Py first project the vector on to the x-y plane and then use the 30 degrees to find Px and Py Px = 200N * 15/17 * 1/2 Py = 200N * 15/17 * sqrt(3) / 2 Now to find the total vector, sum up all the x components , that is the new x component. sum all the y components ---> new y component sum all the z components ---> new z component to compute the magnitude of this vector Magnitude = sqrt ( x^2 + y^2 + z^2) to compute the angles, first consider only the x-y plane, based on the length of the x and y vector, you can compute the angle. Now combine the x, y vector... the length is sqrt(x^2 + y^2) . Now use this new vector to compute the angle with the z axis . good luck have fun

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.