A viaduct is being re-levelled by using a jackscrew with a pitch of 5mm. The mass of the top slab of the viaduct is 20 tonnes (20000kg) and its length is 40m. The lever arm used to turn the jackscrew is 60 cm long.
Calculate the effort force to be applied to the end of the lever arm of the jackscrew in order to lift the end of the top slab of the viaduct.
To calculate the effort force required to lift the end of the top slab of the viaduct, we need to consider the principle of moments. The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
In this case, the clockwise moment is created by the weight of the top slab of the viaduct, and the anticlockwise moment is created by the effort force applied to the jackscrew.
1. First, let's calculate the weight of the top slab of the viaduct:
Weight = mass * acceleration due to gravity
Weight = 20000 kg * 9.8 m/s^2
Weight = 196,000 N
2. Now, let's calculate the clockwise moment created by the weight of the slab:
Moment = Weight * lever arm
Note: The lever arm is given in centimeters, so we need to convert it to meters.
Lever arm = 60 cm = 0.6 m
Moment = 196,000 N * 0.6 m
Moment = 117,600 Nm
3. Next, let's calculate the effort force required:
We know that the pitch of the jackscrew is 5 mm, which means for every full turn of the jackscrew, it raises the slab by 5 mm.
The length of the slab is given as 40 m. Therefore, the number of full turns required can be calculated as:
Number of turns = Height of slab / Pitch of jackscrew
Number of turns = 40 m / 0.005 m
Number of turns = 8000
Since each full turn creates a change in the vertical position of the slab equal to the pitch, the total vertical displacement of the slab is:
Vertical displacement = Number of turns * Pitch of jackscrew
Vertical displacement = 8000 * 0.005 m
Vertical displacement = 40 m
Now, we need to calculate the effort force required to lift the slab to this height.
Effort force = Moment / Vertical displacement
Effort force = 117,600 Nm / 40 m
Effort force = 2940 N
Therefore, the effort force to be applied to the end of the lever arm of the jackscrew in order to lift the end of the top slab of the viaduct is 2940 Newtons.