Final answer:
The force exerted on the lawnmower by the person is 73 N. This is found by adding the net external force and the frictional force together.
Step-by-step explanation:
The student asks what force F is exerted on a 24-kg lawnmower if the net external force is 51 N and there's a frictional force of 22 N opposing motion. To find the force exerted by the person, we simply add the force of friction to the net external force because the net force is a result of the person pushing minus the frictional force working against it.
F_{net} = F_{push} - F_{friction}
51 N = F_{push} - 22 N
To isolate the force exerted by the person (F_{push}), we add 22 N to both sides of the equation:
F_{push} = 51 N + 22 N
F_{push} = 73 N
So, the force the person is exerting on the mower is 73 N.