A person exerts a horizontal force of 42 N on the end of a door 96 cm wide. What is the magnitude of the torque if the force is exerted

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. We consider part (a) where the torque is calculated by multiplying the length of the door or the lever arm which is 0.96 meters—I guess that's called the width of the door— either way, the distance between where the force is applied and the hinge is 0.96 meters and in part (a), the force is perpendicular to that lever arm so sin Θ is just 1 because the angle is then 90 degrees in this case and sin of 90 is 1. So we have 42 newtons times 0.96 meters gives 40 newton meters and I write that in scientific notation just to be clear that the zero is significant here and so 4.0 times 10 to the 1 newton meters. And then for part (b)—it's the green arrow here— we have the force applied at an angle of 60 degrees to the door and we need to find the component of the force perpendicular to the lever arm and multiply that by the lever arm. So this is the opposite leg of this triangle so we use sin of 60 degrees to calculate it. So sin 60 times the length of the hypotenuse which is 0.96 and that gives force perpendicular and multiply that by the lever arm of well I guess that's 42 newtons times sin 60 there because force perpendicular times 0.96 meters gives 35 newton meters and so as expected when the force is at an angle here that's not 90 degrees, the torque is gonna be less. So as the force becomes more and more parallel to the door, the torque becomes less and less to the point where if the force was directly at the hinge, there would be no torque.