a short phrase for 'exert strength with the hand'

I'm looking for a way to translate the Portuguese phrase 'fazer força com a mão', which literaly translates as 'to exert strength with the hand'.

I've searched the Internet and I came across a lot of 'hand grip strength' but not a verb that could fit the bill. I've also toyed with phrases such as 'apply strength', but they just don't feel natural.

I'd like something that could fit sentences such as:
- She exerted strength with her hand and hurt herself.
- She had to exert a lot of strength with her hand before she could open the lid.
- She couldn't exert strength with her hand because of her hurt thumb.

edit:
The phrase should imply that there is a strong grip (which is mostly stationary) followed by exerting strength to produce a (twisting, horizontal, vertical, what you may) movement. In a sense, it's a "strong grip immediately followed by strong production of movement".

Your direct translation could be improved. Although it is possible in English to "exert your strength" it is also possible to "exert a force". "Force" is a direct translation of "força" and is more appropriate in your examples.

In order to make your examples more natural in English, I've also reworded/added some extra words:

Instead of "She couldn't exert strength with her hand because of her hurt thumb" I would say:

She couldn't exert any force with her hand because of her hurt thumb

Instead of "She had to exert a lot of strength with her hand before she could open the lid" I would say:

She had to exert a lot of force with her hand in order to open the lid

Your first example, however, I am finding more problematic. Your example is "She exerted strength with her hand and hurt herself". As we don't really have a stock idiomatic phrase for "using the strength of your hand", this sentence feels to me like it's missing context, i.e. what she was trying to do with her hand. My best attempt would be to include the "lid opening" context:

She tried opening the lid by hand, but hurt herself.

yank

to pull something forcefully with a quick movement:

• She hurt her hand when she yanked the jar lid off.
• She couldn't yank the lid off because her thumb hurt.
• She yanked hard at the rope but hurt her hand in the process.
• ‘In a couple of strides, Sonrisa made her way to the door, yanking it open with force.’

and as a noun ...

• ‘Eventually with a hefty yank and a banshee-like howl, the damn thing came out.’
  ^{Oxford Dictionaries}