How might the industrial revolution and the birth of capitalism motivate countries to dominate other countries a claim ?

To secure natural resources and labour force. Wealth resulting from industry empowers the wealthy to seduce, buy and/or corrupt the elite of other nations. In Victorian Britain there was a genuine belief among some that other nations benefited from being annexed. Whilst the British elite were terrible imperialists they also built infrastructure such as transport, sewers etc, everywhere they went. Brits arent evil but we do always think we know best...unfortunately.

people can eat food during that time

in the 1800s, chinese workers migrated to the united states, first to work in the gold mines, but also to take agricultural jobs, and factory work, especially in the garment industry. chinese immigrants were particularly instrumental in building railroads in the american west, and as chinese laborers grew successful in the united states, a number of them became entrepreneurs in their own right. as the numbers of chinese laborers increased, so did the strength of anti-chinese sentiment among other workers in the american economy. this finally resulted in legislation that aimed to limit future immigration of chinese workers to the united states, and threatened to sour diplomatic relations between the united states and china.