Final answer:
The required acceleration for the robot's foot to generate the correct force on the soccer ball is approximately 9.8 m/s^2, equivalent to the acceleration due to gravity.
Step-by-step explanation:
To determine the acceleration required to give the robot's foot in order to generate the correct force on the soccer ball, we can use Newton's second law of motion:
F = m . a
where:
- F is the force,
- m is the mass,
- a is the acceleration.
If the robot's foot exerts a force on the soccer ball, the force required is equal to the mass of the soccer ball m_ball times the desired acceleration a:
F_robot = m_ball . a
The robot's foot, in turn, needs to exert a force on its 2-kilogram weight. If the weight is experiencing a force F_robot, and the weight has mass m_weight = 2kg, then we can use Newton's second law again:
F_robot = m_weight . a
Now, equating the two expressions for F_robot, we get:
m_ball . a = m_weight . a
Since a is a common factor on both sides, it cancels out:
m_ball = m_weight
Therefore, the acceleration required a is the same as the acceleration due to gravity, approximately 9.8 m/s^2 .
Your complete question is: The students must determine the acceleration that the robot needs to give its foot (the 2-kilogram weight), in order to apply the correct force to the soccer ball. What is that acceleration required to give the robot’s foot in order to generate the correct force?