2. A door knob is located as far as possible from the hinge line for a good reas
ID: 1398620 • Letter: 2
Question
2. A door knob is located as far as possible from the hinge line for a good reason. If you want to open a heavy door, Where you apply a force and in what direction you push are important. Consider a vector force F acting on a body that is free to rotate about a point O. The force is applied at a point P whose position determines the vector r. The directions of F and r make an angle of phi with each other as in the figure to the above. (a) Decompose the force into a radial component Fr (in the direction of r) and the tangential component Ft (perpendicular to r). So F = Fr + Ft Which of these components acts to move the body? What happens to the other component of F? (b) Define torque as the vector tau = r x F. Derive a formula for ||tau|| in terms of ||Ft|| and ||r||.Explanation / Answer
a) tangential component of force(Ft) turns the door.
The other force can not rotate the door.
b) Torque, T = r cross F
= r*F*sin(theta)
= r*Ft (since F*sin(theta) = Ft)
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