Many of the social tensions of the early republic were rooted in conflict between humane considerations and the desire for economic and political growth. Where can you see these tensions at work? Is there any instances of successful resolution?

The early republic was marked by tensions between an effort at reform (a humane consideration) and the desire of the country to grow economically and politically. The Second Great Awakening, a religious movement which occurred around 1800, gave rise to many different types of reform movements, including abolitionism, temperance, and women's rights. However, these movements struggled to achieve their goals in the midst of the national fervor for economic and political growth.
Abolitionism in particular ran up against the fervor for growth. While many people came to believe that slavery was morally wrong, slavery was integral to the agricultural economy of the South. Cotton in particular became very profitable following the development of Eli Whitney's cotton gin in the late 1700s, as the gin made it possible to remove seeds quickly from different varieties of cotton plants that grew all over the South. Cotton was the "king" of Southern agriculture, and abolitionists were met with the refusal of the South to give up a labor system that fed the growth of cotton. In addition, abolitionism ran up against political demands for western growth. As settlers moved west, they often brought slavery with them (in particular to Texas over time), and the desire for westward growth caused slavery to grow rather than to be eradicated.
There were few successful resolutions of this conflict, as compromises such as the Missouri Compromise of 1820 only caused a delay in outright warfare rather than resulting in a compromise that pleased both sides. In the Missouri Compromise, one state (Missouri) was admitted to the Union as a slave state while another state (Maine) was admitted to the Union as a free state. This only delayed the outbreak of the Civil War and did not prevent it. As a result, humane considerations were in opposition to political and economic demands in the early republic, and this conflict in part led to the Civil War.