a) Copy and complete the following statement: The moment of a force about a point is ...... multiplied by.......
b) The diagram shows a uniform iron bar B of weight 30 N and length 1.40 m. The bar is being used to lift one edge of a concrete slab S. A stone, placed 0.20 m from one end of B, acts as a pivot. concrete slab S 0.20m stone ******* 1.40m iron bar B force 40 N
i A force of 40 N pushing down at the other end of B is just enough to lift the slab and hold it as shown. Copy the diagram and draw an arrow to show the weight of bar B acting from its centre of mass.
ii State the distance d of the centre of mass of bar B from the pivot.
iii Calculate the total clockwise moment, about the pivot,
iv Calculate the downward force which the slab S exerts on the end of bar B.
v Suggest a change to the arrangement in the diagram that would reduce the force required to lift the slab
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Ответы
Ответ:
a) The moment of a force about a point is the product of the force applied and the perpendicular distance between the point and the line of action of the force.
b) The problem describes a scenario where a uniform iron bar, B, of weight 30 N and length 1.40 m, is being used to lift one edge of a concrete slab, S, with the help of a stone acting as a pivot placed 0.20 m from one end of the bar. A force of 40 N pushing down at the other end of the bar is just enough to lift the slab and hold it in place.
i) The weight of bar B acts vertically downwards from its centre of mass, denoted by C, located at the midpoint of the bar's length.
ii) The distance d of the centre of mass of bar B from the pivot can be calculated by finding the midpoint of the bar's length, which is 1.40m / 2 = 0.70m from either end.
iii) To calculate the total clockwise moment, about the pivot, we need to find the moments of the two forces acting on the bar. The moment of the force applied at the end of the bar is equal to the force multiplied by the perpendicular distance from the pivot, which is (40 N x 1.20 m). The moment of the weight of the bar is equal to the weight multiplied by the perpendicular distance from the pivot, which is (30 N x 0.70 m). The total clockwise moment is the difference between these two moments, which is (40 N x 1.20 m) - (30 N x 0.70 m) = 36 Nm.
iv) The downward force which the slab S exerts on the end of bar B is equal in magnitude to the force required to lift the slab, which is 40 N.
v) To reduce the force required to lift the slab, one could either move the stone pivot closer to the end of the bar where the force is being applied, which would reduce the lever arm and the moment required to lift the slab, or use a heavier stone as the pivot to increase the lever arm on the other side of the pivot and reduce the force required to lift the slab.