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 using the jackscrew, we need to use the principle of moments.
1. Determine the weight of the top slab of the viaduct:
Given: Mass of the top slab = 20 tonnes = 20000 kg (weight = mass x acceleration due to gravity)
Weight = 20000 kg x 9.8 m/s^2 = 196000 N
2. Calculate the torque exerted by the weight:
Torque = weight x lever arm (torque = force x perpendicular distance)
Given: Lever arm = 60 cm = 0.6 m
Torque = 196000 N x 0.6 m = 117600 Nm
3. Determine the pitch of the jackscrew:
Given: Pitch of the jackscrew = 5 mm = 0.005 m
4. Calculate the distance moved by the jackscrew for one rotation:
Distance moved = pitch x number of rotations
In this case, we need to find the number of rotations for the jackscrew to lift the end of the viaduct. Let's assume it is "n" rotations.
Since the length of the top slab is 40 m, we can set up the following equation:
Distance moved = n x pitch
40 m = n x 0.005 m
n = 40 m / 0.005 m = 8000 rotations
Therefore, the jackscrew needs to make 8000 rotations to lift the end of the viaduct.
5. Calculate the effort force applied to the lever arm:
Effort force = Torque / (pitch x number of rotations)
Effort force = 117600 Nm / (0.005 m x 8000)
Effort force = 2.94 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 approximately 2.94 N.