When a wood shelf of mass 7.2 kg is fastened inside a slot in a vertical support as shown in (Figure 1) , the support exerts a torque on the shelf. Assume that the slot exerts two vertical forces on the shelf, at points A and B.
To determine the torque exerted by the support on the shelf, we first need to understand what torque is and how it is calculated.
Torque, denoted by τ (tau), is a measure of the force that can cause an object to rotate about an axis. It is calculated by multiplying the force applied to an object by the perpendicular distance from the axis of rotation to the line of action of the force. Mathematically, torque can be expressed as:
τ = r × F
where τ is the torque, r is the distance from the axis of rotation to the line of action of the force, and F is the force applied.
In the case of the wood shelf in a slot, when the support exerts a torque on the shelf, it means that it is applying a force that tends to rotate the shelf about an axis. The two vertical forces exerted by the slot at points A and B will create a torque about points A and B respectively.
To determine the torque at point A, we need to know the perpendicular distance from point A to the line of action of the force. Similarly, to determine the torque at point B, we need to know the perpendicular distance from point B to the line of action of the force.
Once we have these distances, we can calculate the torque at each point by multiplying the force applied at each point by their respective distances from the axis of rotation.
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