How strong would I have to be to be able to pull a syringe that's been pushed all the way to squeeze all the air out of the tube and sealed shut so...

The plunger of a 60 mL syringe has been pushed all the way through to expel any air and its end has been sealed. The plunger now has to be pulled down to the 60 ml mark. The syringe is at sea level and it is strong enough to withstand the force exerted when the plunger is pulled down without the walls caving in.

At sea level, the atmospheric pressure is 101325 N/m^2. When the plunger of the syringe is pulled down, a vacuum is created. As a result, the surrounding air exerts a force on the plunger to push it back up. Pressure is force exerted per unit area. In the problem the cross sectional area of the plunger is not given. As a result, it is not possible to determine the force required to pull t down. Assuming the area of cross section as 1*10^-5 m^2, the force required to pull down the plunger is 1.01325 N. This force does not change as the plunger is moved lower and the vacuum is maintained.

The total work done to create the vacuum in 60 mL is equal to 101325*6*10^-5 = 6.0795 J.