4 . An eight-spoke wheel with a radius of R is free to rotate on a horizontal axis with masses hung from
the end of three of the spokes, as shown in the figure. The spokes are evenly spaced, and the wheel is
in equilibrium. Two masses are known and have a mass of m . What must the third mass be in order to
maintain equilibrium?
(A) m
(B) 2m(C) m (sin 45°)(D)
(E) m =0 because the two existing masses already create equilibrium.Answers
1 . E —Gravity (mg ) always points downward, and normal force (FN ) is always perpendicular to the
contact surface. Finally, you need friction to keep the car stationary in equilibrium. Friction is always
parallel to the contact surface and opposite to the direction the object is trying to slide.2 . B —
3 . A —The forces in the horizontal direction must cancel each other out because the object is moving at
a constant velocity; thus, it is in dynamics equilibrium. The horizontal forces are from the student to
the right 80 cos 60° and from friction μFN . to the left, where FN = mg - 80 sin 60°. Equating the
forces in the positive and negative directions we get