Analyzing Force vs. Time graphs

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To determine mass from a Force vs. Time graph, one must understand that impulse, represented by the area under the graph, equates to the change in momentum. The relationship between force, mass, and acceleration (F=ma) is crucial, as mass can be calculated if acceleration is known. In scenarios involving circular motion, knowing the velocity and radius allows for acceleration calculation using v^2/r. If the object is in free fall, the acceleration is constant at 9.8 m/s², simplifying mass determination. Overall, the context of the problem, such as whether it involves collisions or free fall, significantly influences how mass can be derived.
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1. I REALLY need help here! I've been doing pretty good in physics so far this year, but a new quiz devastated me. Here's the problem:
I was given a Force vs. Time graph and a lot of the questions pertained to the mass of the object. How do I find the mass only given a F vs T graph?

Homework Equations


Is there any other data I can obtain from a Force/Time graph? (like acceleration, velocity, or something to do w/ friction)?
 
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A force time graph is all about impulse, and impulse is the change in momentum of an object.
 
Impulse is given by the area under an F-t graph.

As Kurdt said, impulse is the change in momentum of an object. ie. p2 - p1 or m(v2 - v1) [for constant mass].
 
If you're solely given the Force of an object over Time... I don't see how you could find the mass of the object unless you were somehow able to calculate the acceleration.

If the object was traveling around a circular path, and you were given the velocity or able to calculate the velocity and the radius of the circle, then you could substitute (v^2)/r as the acceleration...

But I believe, as in introductory physics, the equation F=ma has to come into play here.
(or F=(mv^2)/r)

NOW, you might have been told that this was a free-falling object, or a nuance similar. In which case, that gives you the acceleration (9.8 m/s^2)- so it may be tricky.
 
If it is analysing a collision, which F-t graphs are so often used for, and you know the initial and final velocities, then the mass can be found from the relationship in my last post.
 
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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