物理 balancing point 寻找木棍平衡点 实验报告

Broom Balance

Jane

While a person is holding a broom in the hand, the front view is figure 1, the side view is figure 2 and the simplified version of side view is figure 3

Figure1 Figure2 Figure3

So it can be noticed that while hands holding the broom, hands are tangent to the broom, the force hands applied to the broom on the point of tangency and i perpendicular to it.

According to Figure1, the broom has 3 forces in vertical direction. (N1and N2 are exerted by hands)

Since two hands are sliding slowly from two ends towards the center of the broom

V1=V2

And two hands start to slide at the same time

V1t=V2t

So for lever arm 1 and lever arm 2

Since N1+N2=F g, two lever arms are equal and consider the center of gravity is the reference point

When two hands move towards the center, velocities are V1 and V2 respectively and cause forces N1 and N2 respectively as well. (Figure 4)

Figure 4

So left and right hand both exert a kinetic frictions f1 and f2 to the broom. And f1 and f2 is opposite to their own velocity(movement)’s direction. (Figure 5)

Since both f1 and f2 are caused between hands and the wood, so μ1=μ 2

And N1=N2 So f1=f2

Thus, forces the broom had in horizontal direction are the equal. It is to say that for the broom, there is no net external force in horizontal direction and the broom will not move.

While two hands sliding to the center of the broom,for the broom, in horizontal direction, the friction which exerted by left hand is equal but opposite to the friction which given by right hand, so F net is 0 in horizontal direction, the broom is in equilibrium. And since frictions exert in a straight line, so torque net is 0, torque is in equilibrium as well. Hence the broom is in equilibrium during sliding.