When opening a door, you push on it perpendicularly with a force of 55.4 N at a distance of 0.728m from the hinges. What torque are you exerting relative to the hinges? (Does it matter if you push at the same height as the hinges?)
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To determine the torque exerted relative to the hinges, you need to use the equation:
Torque = Force x Distance x sin(θ)
Where:
- Torque is the rotational force or moment, measured in Newton-meters (Nm)
- Force is the applied force perpendicular to the door, measured in Newtons (N)
- Distance is the perpendicular distance from the hinges to the point where the force is applied, measured in meters (m)
- θ is the angle between the force vector and a line perpendicular to the door, measured in degrees
In this case, the force is given as 55.4 N and the distance is given as 0.728 m.
Now, to answer the second part of your question, whether it matters if you push at the same height as the hinges, the answer is that it does matter. When you push on the door at the same height as the hinges, the distance component in the equation becomes zero. Therefore, the torque exerted relative to the hinges will be zero as well.
To calculate the torque exerted relative to the hinges using the given values, we need to know the angle θ between the force vector and a line perpendicular to the door. Without knowing the angle, it is not possible to calculate the torque accurately.