Video: Net Force Required to Accelerate an Object

A sprinter with a mass of 57.0 kg accelerates at 3.922 m/s². What is the magnitude of the net external force on her?

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Video Transcript

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.

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