EXAMPLE 8.2 The Swinging Door GOAL Apply the more general definition of torque. 300 N (a) Top view of a door being pushed by a 300-N force. (b) The components of the 300-N force. PROBLEM (a) A man applies a force of F = 3.00 x 102 N at an angle of 60.0 to the door of Figure (a), 2.00 m from well-oiled hinges. Find the torque on the door, choosing the position of the hinges as the axis of rotation. (b) Suppose a wedge is placed 1.50 m from the hinges on the other side of the door. What minimum force must the wedge exert so that the force applied in part (a) won't open the door? STRATEGY Part (a) can be solved by substitution into the general torque equation. In part (b) the hinges, the wedge, and the applied force all exert torques on the door. The door doesn't open, so the sum of these torques must be zero, a condition that can be used to nd the wedge force. SOLUTION (A) Compute the torque due to the applied force exerted at 60.0. rFsin 6 = (2.00 m)(3.00 x 102 N) sin 600" (2.00 m)(2.60 x 102 N) = 5.20 x 102 N - m Substitute into the general torque TF equation. (B) Calculate the force exerted by the wedge on the other side of the door. Set the sum of the torques equal to Ihinge + Twedge + IF = 0 zero. The hinge force provides no torque o + Fwedge(1'50 m) sin {90.00) + 5.20 x 102 N - m = because it acts at the axis (r = 0). The 0 wedge force acts at an angle of _ o _ Fwedge 347 N 90.0 , opposrte the upward 260 N component. LEARN MORE REMARKS Notice that the angle from the position vector to the wedge force is 90. This is because, starting at the position vector, it's necessary to go 90 clockwise (the negative angular direction) to get to the force vector. Measuring the angle in this way automatically supplies the correct sign for the torque term and is consistent with the right-hand rule. Alternately, the magnitude of the torque can be found and the correct sign chosen based on physical intuition. Figure (b) illustrates the fact that the component of the force perpendicular to the lever arm causes the torque. QUESTION To make the wedge more effective in keeping the door closed, should it be placed closer to the hinge or to the doorknob? O closer to the hinge O closer to the doorknob PRACTICE IT Use the worked example above to help you solve this problem. (a) A man applies a force of F = 3.00 X 102 N at an angle of 60.0 to a door, x = 1.90 m from the hinges. Find the torque on the door, choosing the position of the hinges as the axis of rotation. (b) Suppose a wedge is placed 1.50 m from the hinges on the other side of the door. What minimum force must the wedge exert so that the force applied in part (a) won't open the door? :lN EXERCISE HINTS: GETTINGSTARTED | I'M STUCK! A man ties one end of a strong rope 8.96 m long to the bumper of his truck, 0.520 m from the ground, and the other end to a vertical tree trunk at a height of 3.04 m. He uses the truck to create a tension of 8.29 X 102 N in the rope. Compute the magnitude of the torque on the tree due to the tension in the rope, with the base of the tree acting as the reference point