A sprinter with a mass of 57.0
kilograms accelerates at 3.922 meters per second squared. What is the magnitude of the net
external force on her?
We can call this magnitude of the
net external force acting on the sprinter capital 𝐹. We’re told the sprinter’s mass,
57.0 kilograms, which we’ll label 𝑚 and also her acceleration, 3.922 meters per
second squared, which we’ll name 𝑎. As the sprinter runs, it’s the
frictional force of the track on her feet that push her forward and give her a net
forward force. It’s that force magnitude we want
to solve for. And to do it, we’ll recall Newton’s
second law of motion.
Newton’s second law says that the
net force acting on an object equals the object’s mass times its acceleration. In the case of our sprinter, we’re
working with magnitudes rather than vectors. And we’re given values for the
sprinter’s mass as well as her acceleration 𝑎. When we plug in for those two
values and calculate this product, we find it’s equal to 224 newtons. That’s the net force magnitude
causing the sprinter’s acceleration.