Charlie and Nate are ice skating. The ice can support 3028 N of weight. If Charlie is 100 kg and Nate is 73 kg, what is the maximum upward...

The total force acting on ice is the sum of the forces with which Charlie and Nate push on ice. For both Charlie and Nate, the force with which each boy pushes on ice is equal in magnitude and opposite in direction to the normal force - the force with which the ice pushes back, according to the third Newton's Law.

For Nate, who is standing still, the normal force is equal to his weight:

`m_(Nate)g = 73*9.8 = 715.4 N`

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For Charlie, however, the normal force is different because he is jumping and experiences upward acceleration. According to the second Newton's Law, at the moment when Charlie is about to jump:

` ` `vecN + m_(Charlie)vec(g) = m_(Charlie)veca` .

The normal force and acceleration are directed upward, while the gravity force is downward, so

`N - m_(Charlie)g = m_(Charlie)a`

The normal force on Charlie, which equals in magnitude to the force with which Charlie pushes on ice, is therefore:

`N = m_(Charlie)g + m_(Charlie)a` .

The total force on the ice cannot exceed 3028 N, so this force plus Nate's weight found above cannot exceed 3028 N. The maximum acceleration is found from:

`m_(Charlie)g + m_(Charlie)a + m_(Nate)g = 3028 N`

980 + 100a + 715.4 = 3028

100a = 1332.6

a = 13.326 m/s^2

Charlie's maximum upward acceleration is 13.326 m/s^2.