Claudia stubs her toe on the coffee table with a force of 100 N. What is the acceleration of Claudia’s 1.80kg foot? What’s is the acceleration of the table if it has a mass of 20.0 kg. Why would Claudia’s toe hurt less if the table had less mass?
To find the acceleration of Claudia's foot, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma). Rearranging the equation, we have acceleration (a) equals force (F) divided by mass (m).
For Claudia's foot:
Acceleration = Force / Mass
Acceleration = 100 N / 1.80 kg
Acceleration ≈ 55.56 m/s²
For the coffee table:
Acceleration = Force / Mass
Acceleration = 100 N / 20.0 kg
Acceleration = 5.00 m/s²
Claudia's toe would hurt less if the table had less mass because when Claudia stubs her toe, the force exerted on her toe depends on the acceleration of the table. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, when Claudia's foot collides with the table, there is a reaction force exerted on her foot in the opposite direction. This force causes the pain.
So, if the table has less mass, its acceleration will be greater for a given force (since acceleration is inversely proportional to mass). As a result, the reaction force exerted on Claudia's foot will be greater, causing more pain. Conversely, if the table has more mass, its acceleration will be lower (for the same force), resulting in a smaller reaction force on Claudia's foot and less pain.