WEBVTT
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When opening a door, you push on it perpendicularly with a force of 55.0 newtons at a distance of 0.850 meters from the hinges.
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What torque are you exerting relative to the hinges?
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The force applied weโre told is 55.0 newtons; weโll call that ๐น.
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Weโre also told that this force is applied at distance of 0.850 meters from the hinges; weโll call that distance ๐.
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If we were to draw a diagram, looking down on the door from above of the action going on, we would see that weโre applying the force ๐น perpendicularly to the door a distance of ๐ meters away from the doorโs hinge.
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We want to solve for the torque that weโre exerting relative to the hinges, which weโll call ๐.
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To begin, we can recall the definition for torque.
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In general, the torque is equal to the cross-product of the radius ๐ with the applied Force ๐น.
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When ๐ and ๐น are in the same plane as they are in our example, we can write a simplified version of this equation for torque.
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Torque is equal to ๐ times ๐น times the sin of the angle between them.
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In our case, ๐ and ๐น are at right angles to one another.
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So when we use this simplified equation for torque, since the sin of 90 degrees is equal to one, the equation simplifies to simply torque equals ๐ cross ๐น.
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When we plug in for the given values of ๐ and ๐น and multiply them together, we find that the resulting torque is 46.8 newton meters.
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This is how much torque the force ๐น exerts relative to the hinges.