A girl uses a plank to lift a box of 200N. The BOX is 20cm from the fulcrum. What is the effort the girl needs to exert?
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To solve this problem, we can use the principle of moments.
The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point, provided the object is in equilibrium.
In this case, the box is being lifted using a plank as a lever. We need to find the effort that the girl needs to exert to balance the box.
Let's assume that the distance between the girl's effort and the fulcrum is 'd'. We need to find the value of 'd'.
According to the principle of moments, the moment on one side of the fulcrum (caused by the weight of the box) is equal to the moment on the other side of the fulcrum (caused by the effort exerted by the girl).
The moment on one side (clockwise) is given by the formula: Moment = Force x Distance.
So, the clockwise moment caused by the weight of the box is: Moment_box = 200N x 20cm.
On the other side (anticlockwise), the moment caused by the effort exerted by the girl is: Moment_girl = Effort x d.
Using the principle of moments, we can set up the equation:
Moment_box = Moment_girl
200N x 20cm = Effort x d
To solve for Effort, we need to convert the distance 'd' from cm to meters. There are 100 cm in 1 meter, so d = 20cm / 100 = 0.2m.
Now we can substitute the values:
200N x 20cm = Effort x 0.2m
4000 N.cm = Effort x 0.2m
To solve for Effort, we can rearrange the equation:
Effort = (4000 N.cm) / (0.2m)
Effort = 20000 N
Therefore, the effort the girl needs to exert to lift the box is 20000 Newtons.
To determine the effort the girl needs to exert, we need to use the principle of moments. The principle of moments states that the sum of the moments (torques) acting on an object in equilibrium must be zero.
In this case, the girl is using a plank as a lever, with the box acting as the load and the girl's effort acting as the force that balances the load. The effort is the force the girl needs to exert to lift the box.
To apply the principle of moments, we need to consider the distances from the fulcrum to the load (20cm) and the fulcrum to the effort. Let's denote the distance from the fulcrum to the effort as "d" (in centimeters).
The moment of the load (box) can be calculated by multiplying its weight (200N) by its distance from the fulcrum (20cm). So, the moment of the load is 200N * 20cm = 4000 N•cm.
Similarly, the moment of the effort can be calculated by multiplying the effort required by its distance from the fulcrum (d cm). So, the moment of the effort is Effort (unknown) * d cm.
Since the system is in equilibrium, the sum of the moments must be zero:
4000 N•cm + Effort * d cm = 0.
Now, we can solve this equation for Effort:
Effort * d cm = -4000 N•cm
Effort = -4000 N•cm / d cm
Given that d = 20 cm, substituting this value into the equation, we can calculate the effort:
Effort = -4000 N•cm / 20 cm
Effort = -200 N.
So, the effort the girl needs to exert is 200 N. It has a negative sign because it acts in the opposite direction compared to the load (box), as illustrated by the negative value in the calculation.
Note: The negative sign indicates the direction of the force. In this case, it means that the effort of the girl must be applied in the opposite direction of the weight of the box.