Impulse and Force-Time Graph Problem

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The problem involves calculating the maximum force (Fmax) that results in an impulse of 7.1 Ns using a force-time graph. The impulse is determined by the area under the graph, which is represented as a triangle with the formula 0.5 * Fmax * time. Initially, Fmax was calculated as 1.775 N using an incorrect time value. The error was identified as a misunderstanding of the time axis, which is in milliseconds, leading to the need for a revised calculation. Correctly interpreting the time units is crucial for accurate impulse calculations.
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Homework Statement


09.EX05.jpg

In the figure , what value of Fmax gives an impulse of 7.1 Ns


Homework Equations


1832c91daa867136732d31cc7c988eb0.png



The Attempt at a Solution


Impulse is the integral of force with respect to time which is the same the area under the force-time graph which is given by the area of the triangle: 0.5*Fmax*8s

7.1 Ns = 4s * Fmax
Fmax = 1.775 N

However that's not the right answer. Where did I go wrong? Thanks!
 
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The time axis is in milliseconds.
 
Haha thanks! I never would've noticed that.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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