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 needed to lift the end of the top slab of the viaduct, we can use the equation for mechanical advantage in a simple machine:

Mechanical Advantage = Load Force / Effort Force

In this case, the load force is the weight of the top slab of the viaduct, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2). The effort force is the force we want to calculate.

1. Calculate the load force:
Load Force = mass * acceleration due to gravity
Load Force = 20000 kg * 9.8 m/s^2
Load Force = 196,000 N

2. Determine the distance over which the effort force is applied:
The length of the lever arm is given as 60 cm, but we need to convert it to meters to maintain consistency with the units of other measurements.
Lever Arm Length = 60 cm = 0.6 m

3. Calculate the distance moved by the effort force:
The distance moved is determined by the pitch of the jackscrew, which is given as 5 mm. Again, we need to convert it to meters.
Distance Moved = 5 mm = 0.005 m

4. Calculate the mechanical advantage:
Mechanical Advantage = Distance Moved / Lever Arm Length
Mechanical Advantage = 0.005 m / 0.6 m
Mechanical Advantage = 0.00833

5. Rearrange the equation for mechanical advantage to solve for the effort force:
Effort Force = Load Force / Mechanical Advantage
Effort Force = 196,000 N / 0.00833
Effort Force ≈ 23,527 N

Therefore, the effort force required to lift the end of the top slab of the viaduct is approximately 23,527 Newtons.