Finding the force required to stop an object

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To find the force required to stop an object with a mass of 6.9*10^-3 kg and an initial velocity of 1300 m/s over a distance of 1 cm, the equation F = ma was used. The acceleration was calculated using the kinematic equation, resulting in a value of -8.45*10^8 m/s^2. However, the initial calculation mistakenly used 0.001 m instead of the correct 0.01 m for the stopping distance. After correcting this error, the force calculation would yield a different result. Simple mistakes in unit conversion can lead to significant errors in physics problems.
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Homework Statement


An object with mass 6.9*10^-3 kg and velocity 1300 m/s comes to a stop in 1cm. What force was applied to stop it?

Homework Equations


F = ma
v^2=v_o ^2+2a\Delta x

The Attempt at a Solution


v^2=v_o ^2+2a\Delta x
0=(1300)^2+2a(0.001)
a=-\frac{(1300)^2}{2(0.001)}=-8.45*10^8 \frac{m}{s^2}

F=ma
F=(6.9*10^{-3} kg)(-8.45*10^8 \frac{m}{s^2})= -5.83*10^6 N

Apparently that is not the correct answer. What did I do wrong?

Many thanks!
 
Last edited:
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1 cm = 0.01 m not 0.001 m.
 
Well now, I feel kind of silly :) At least it was a good mistake to make, being so simple to fix!

Thanks!
 
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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