A crowbar is 4.000 metres long and has its pivot 50.000 centimetres from one end. A force of 2000.000 newtons is applied to the end closest to the pivot. What effort must be applied to the other end of the crowbar to keep it in equilibrium? (Round to 3 decimal places)
The effort required to keep the crowbar in equilibrium is 1000.000 N.
To solve this problem, we can use the principle of moments, which states that for an object to be in equilibrium, the sum of the clockwise moments must equal the sum of the anticlockwise moments.
First, we need to convert the length of the crowbar and the distance of the pivot from centimeters to meters for consistent units.
Length of the crowbar: 4.000 meters
Distance of the pivot from one end: 50.000 centimeters = 0.500 meters
Force applied to the end closest to the pivot: 2000.000 newtons
Now, let's calculate the effort that must be applied to the other end of the crowbar to keep it in equilibrium.
Since the force is applied at one end of the crowbar, the moment of the force is given by the formula:
Moment = Force * Distance
The distance of the force from the pivot is the length of the crowbar minus the distance of the pivot from that end:
Distance of the force from the pivot = Length of the crowbar - Distance of the pivot
Distance of the force from the pivot = 4.000 meters - 0.500 meters
Distance of the force from the pivot = 3.500 meters
Now, let's calculate the moment of the force:
Moment of the force = Force * Distance of the force from the pivot
Moment of the force = 2000.000 newtons * 3.500 meters
Moment of the force = 7000.000 newton-meters
To keep the crowbar in equilibrium, the clockwise moment and anticlockwise moment must be equal. Since there are no other forces mentioned in the question, the only force acting is the effort applied to the other end.
Therefore, the effort required can be calculated using the formula:
Effort = Moment of the force / Distance of the effort from the pivot
Effort = 7000.000 newton-meters / 0.500 meters
Effort = 14,000.000 newtons
Therefore, the effort that must be applied to the other end of the crowbar to keep it in equilibrium is 14,000.000 newtons.
To answer this question, we can use the principle of moments. The principle of moments states that the sum of the moments acting on a system in equilibrium is equal to zero.
The moment of a force is calculated by multiplying its magnitude by its perpendicular distance from the pivot point.
In this case, we have a force of 2000.000 newtons applied to the end closest to the pivot point, which creates a clockwise moment. The perpendicular distance from the force to the pivot point is 50.000 centimeters (or 0.500 meters).
To keep the crowbar in equilibrium, there must be an equal and opposite anticlockwise moment. The other end of the crowbar is 4.000 meters long, so the perpendicular distance from the pivot to the other end is 4.000 meters - 0.500 meters = 3.500 meters.
We can now calculate the effort required to keep the crowbar in equilibrium:
Moment of the force = Moment of the effort
2000.000 newtons * 0.500 meters = Effort * 3.500 meters
1000.000 Nm = Effort * 3.500 Nm
Effort = 1000.000 Nm / 3.500 meters
Effort ≈ 285.714 newtons (rounded to 3 decimal places)
Therefore, to keep the crowbar in equilibrium, an effort of approximately 285.714 newtons must be applied to the other end.