# physics-forces

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

This is what I think but it may not be correct. In the beginning, Kara and Ben are on the ice and as Kara tries to push Ben she ends up sliding across the ice since she weighs less and because the surface is frictionless while Ben moves slightly. In the middle, Kara would be moving away from Ben at a faster rate than Ben is moving. In the end, Ben would stop moving first and Kara would follow after. They would come to a stop because of air resistance. (I'm not sure what type of motion vocabulary I am to be using).

b) What is Ben's acceleration and Kara's acceleration?
Would Ben's acceleration be 2.5m/s^2 and Kara's be 3.6m/s^2?

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1. Since there is no external force on the system at the beginning (air and ice friction is later), the momentum of the center of mass will not move
That means:
Mass ben * Vben + mass kara * Vkara = 0

V kara = - V ben (Mass ben / Mass kara)

so at all times Kara's speed is greater than Ben's speed but in the opposite direction. Chances are she would drift further before stopped by friction

F = 200 call it + on Ben and - on Kara
a = F/m
a ben = 200/ 80
a kara = -200/ 55

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posted by Damon

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