In Utah, almost certainly not.
I cannot think of a scenario in which a parent (mother or father) has sole physical custody of the children and would have to pay any child support to the noncustodial parent. In that scenario it doesn’t matter if he/she earns more than the other parent; he/she will have no child support obligation to the noncustodial parent. It is possible, however (though not likely), that if the custodial parent earns more than enough to support the children on his/her own the court could order that the noncustodial has little to no child support obligation.
It gets more interesting if the parents are awarded joint physical custody. In Utah “joint physical custody” means that a parent who has the children no less than 110 overnights with the children is a joint physical custodian. Custody does not have to 50/50 for there to be joint custody awarded.
So I ran some calculations where the parent who has the child in his/her custody more nights than the other joint custodial parent grosses $10,000 per month and the other parent makes minimum wage (i.e., grosses $1,257 per month). This little hypothetical proves that, depending upon the division of overnights, a parent who makes more money than the other parent AND who has the children in his/her custody more than the other parent can, under Utah’s statutory child support guidelines, wind up being ordered to pay child support to the other parent.