Using only one arm/leg on machines?

Question

My dad doesn't want me to lift more than 20kg (44 lbs) in any exercise because I'm 14. I know a lot of teenagers don't take this seriously and do bad form just to lift more weight, but I don't wish to do that.

The problem is that I can easily do more than 15 reps with 20kg in almost every machine and as we know what I'm targeting here when doing more than 15 reps is mainly resistance, I know I won't become Schwarzenegger (I don't take steroids); but, I know I can get a little more muscular and mainly increase my strength, so the question is:

Can I only use one arm on machines without damaging my muscles (or something like that) yet still target the muscles in a correct way? For example on Lat Pulldowns (obviously with one hand grip) or Inclined Bench Press Machines.

Meaning that I would still lift no more than 20 but just with one arm, so in theory I would be able to lift about 35-40 with the 2 arms.

Answer 1

As @Alex L points out in the comments: yes you can, but why not just use your body weight or free weights instead?

Instead of doing one-armed lat pulldowns, do pull ups: it's the same motion, but there isn't a machine stabilising the weights for you and you are lifting your entire body weight. If that's too difficult you could also consider a one-armed dumbbell row.

There are plenty of isolated and compound exercises you can perform with free weights or just your body weight that should keep you going!

Answer 2

As others have mentioned, start doing dips (you can even add weight when it gets too easy), pull-ups and chin-ups, same principle, add weight when you can do more than 8 for example. Those three exercises there will bulk your biceps, triceps, chest, back.

Bent over rows with free weights would be good too, standing shoulder press also if you want to target shoulders, standing makes it more difficult.