Answer Happy

H: Adding Forces - Potter's Pull Bookmark this page You and Harry are using two ideal ropes (massless, supporting any amount of tension) to pull a dragon of mass M out of a frictionless mud puddle. The dragon was trying to take a bath but found out it is a bad idea for dragons to bathe. With your rope you pull with a force of magnitude F₁ at angle 8₁ to the -+-axis. Harry pulls his rope with a force of magnitude F₂ at angle 62 to the +-axis. Before starting, sort out which vectors in the diagram below can be used to represent the two pull forces and which can be used to represent the total force. 14 1102₂2 191 The goal is to find the magnitude and direction of the acceleration of the dragon.
Force Components 0.0/10.0 points (graded) Calculate the components of the force vectors F, and F, having magnitudes F and F, respectively. Enter your responses in terms of some or all of F1 for F₁, F2 for F₂, theta 1 for 0₁, and theta 2 for 0₂. FLz F1 F2, F2 = 11 SUBMIT You have used 0 of 10 attempts Total Force Components 0.0/10.0 points (graded) Calculate the components of the total force on the dragon F= (F₂, F,). Enter your responses in terms of some or all of F1 for F₁, F2 for F2. theta_1 for 0₁, and theta 2 for 8₂. F₂ SUBMIT You have used 0 of 10 attempts
Acceleration Components 0.0/10.0 points (graded) Being a frictionless puddle the dragon begins to accelerate. Calculate the components of the total acceleration on the dragon a = (a,. Enter your responses in terms of some or all of M for M. F.1 for F₁, F2 for F₂. theta_1 for 0₁, and theta_2 for 0₂. A₂ = aby SUBMIT You have used 0 of 10 attempts Total Force Magnitude 0.0/10.0 points (graded) Calculate the magnitude of the total force on the dragon, here expressed through it square F². Enter your responses in terms of some or all of F1 for F₁, F2 for F₂, theta 1 for 0₁, and theta 2 for 02. F2 SUBMIT You have used 0 of 10 attempts
Simplifying Total Force Magnitude 0.0/10.0 points (graded) Now simplify the previous expression by expanding the squares and collecting terms. Use the fact that sin² (2) + cos² (x) = 1 to simplify the expression, and recall the facts to write the write the total force using only the angle = 0₂-0₁- Enter your responses in terms of some or all of F1 for F₁, F2 for F₂. theta_1 for 0₁, and theta 2 for 0₂, and phi for d. F² = Ft + ( ) cos($) + F2 SUBMIT You have used 0 of 10 attempts sin(utv) = sin(u) cos(v) + cos(u) sin(v) cos(utv)= cos(u) cos(u) + sin(u) sin(v) Angle of Total Force and Acceleration Vectors 0.0/10.0 points (graded) Calculate the cosine, sine, and tangent of the angle with respect to the z-axis of the total force vector. The acceleration vector has the same direction as the force vector because F -Ma Enter your responses in terms of F for . Ex for F. Fy for F, a for läl. ax for a,. and ay for a,, and M for M. cos(0) = sin (0) tan (0)