A bank vault is opened by applying a force of 300 N perpendicular to the plane of the door, 1.2 m from the hinges. Find the torque due to this force about an axis through the hinges.Select one:a.660 N·mb.330 N·mc.300 N·md.250 N·me.360 N·m
Question
A bank vault is opened by applying a force of 300 N perpendicular to the plane of the door, 1.2 m from the hinges. Find the torque due to this force about an axis through the hinges.Select one:a.660 N·mb.330 N·mc.300 N·md.250 N·me.360 N·m
Solution
The torque (τ) due to a force can be calculated using the formula:
τ = r * F * sin(θ)
where:
- r is the distance from the axis of rotation to the point where the force is applied (in this case, 1.2 m),
- F is the force applied (in this case, 300 N), and
- θ is the angle between the force vector and the line from the axis of rotation to the point where the force is applied.
In this case, the force is applied perpendicular to the door, which means it is also perpendicular to the line from the hinges to the point where the force is applied. Therefore, θ = 90 degrees, and sin(90 degrees) = 1.
So, the torque due to the force is:
τ = 1.2 m * 300 N * 1 = 360 N·m
So, the correct answer is e. 360 N·m.
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