Kara (55kg) is standing next to her brother Ben (80kg) on a large piece on frictionless ice. Kara decided to push her brother with a force of 200N expecting him to slide across the ice while she remains standing in the middle of the ice rink laughing.
a) Describe the motion that will actually be experienced by Kara and Ben. Use the appropriate vocabulary to describe the motion. Describe the motion from beginning, middle and end
b) What is Ben's acceleration and Kara's acceleration?
I will be happy to critique your thinking.
a)
Since the ice is frictionless, there is no opposing force to Kara's push, which means there will be no external force acting on Ben once Kara pushes him. According to Newton's second law of motion, F = ma, where F is the force applied, m is the mass of the object, and a is the resulting acceleration.
At the beginning, when Kara pushes Ben, an external force is applied on him. This force causes Ben to initially resist motion. However, since there is no opposing force, Ben will gradually start to accelerate in the same direction as the force applied by Kara.
Meanwhile, Kara, who is standing in the middle of the ice rink, does not experience any external force after she pushes Ben. Therefore, she will remain stationary throughout the entire process.
In the middle, as time progresses, Ben's acceleration will gradually increase as the force applied by Kara remains constant. This is because his mass is greater than Kara's, meaning it takes more force to accelerate him compared to her.
At the end, Ben will continue accelerating until another force acts upon him or until he encounters an object that stops his motion. Kara, on the other hand, will remain stationary and observe Ben's motion.
b) To determine Ben's acceleration and Kara's acceleration, we need to use Newton's second law of motion. For Kara, since she is not experiencing any force, her acceleration will be zero (a = F/m = 0/55kg = 0 m/s^2).
For Ben, since an external force of 200N is acting on him, we can use the same formula to calculate his acceleration. Given that his mass is 80kg, we can substitute the values into the equation:
F = ma,
200N = 80kg * a
Now, solving for a, we have:
a = 200N / 80kg
a ≈ 2.5 m/s^2
Therefore, Ben's acceleration is approximately 2.5 m/s^2.