Amother is her children, of unequal weight, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child simply sinking to the ground. given that her heavier child of weight w is sitting a distance l to the left of the pivot, at what distance l1 must she place her second child of weight w on the right side of the pivot to balance the seesaw?
express your answer in terms of l, w, and w.
l1= ?
now consider this problem as a more formal introduction to torque. the torque of each child about the pivot point is the product of the child's weight and the distance of the child (strictly speaking, the child's center of mass) from the pivot. the sign of the torque is positive if it would cause a counterclockwise rotation of the seesaw. the distance is measured perpendicular to the line of force and is called the moment arm.
the concept of torque requires both a force and a specification of the pivot point, emphasized by the first subscript on the torque.
part b
find ? p, w, the torque about the pivot due to the weight w of the smaller child on the seesaw.
express your answer in terms of l1 and w.
tp,
the children's mother wants the seesaw to balance, which means that there can be no angular acceleration about the pivot. the balanced seesaw will then be in equilibrium since it has neither linear acceleration nor rotational acceleration.
for the linear acceleration to be zero, the vector sum of forces acting on the seesaw and children must equal zero.
for the angular acceleration to be zero, the sum of the torques about the pivot must equal zero. this can be written
? i? p, i=0,
where ? p, i is the torque about the pivot due to the i th force.
part c
determine ? i? p, i, the sum of the torques on the seesaw. consider only the torques exerted by the children.
express your answer in terms of w, w, l, and l1.
the child with weight w has an identical twin also of weight w. the two twins now sit on the same side of the seesaw, with one twin a distance l2 from the pivot and the other a distance l3. (figure 2) part d
where should the mother position the child of weight w to balance the seesaw now?
express your answer in terms of l2, l3, w, and w. l=
bad news! when the mother finds the distance l from the previous part it turns out to be greater than lend, the distance from the pivot to the end of the seesaw. hence, even with the child of weight w at the very end of the seesaw the twins exert more torque than the heavier child does. the mother now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is a height h above the pivot. (figure 3)
part e
with what force in the rightwards direction, fx, should the mother push? note that if you think the force exerted by the mother should be toward the left, your final answer fx should be negative.
express your answer in terms of w, lend, w, l2, l3, and h.
fx=