Problem about Force, Work, and Energy

AI Thread Summary
The discussion revolves around a physics problem involving MJ's fall from a height, focusing on the relationship between force, work, and energy. The initial conditions include heights and forces measured by a scale at different points during the fall. The equations used to solve for the height at h3 are questioned, particularly regarding the interpretation of forces and the scale's readings. Clarification is sought on whether the scale measures normal force and how the heights are defined in relation to MJ's posture. The conversation highlights the complexities in applying energy conservation principles in this context.
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Homework Statement



MJ is falling from the highest point in his jump.
h1(the highest point) = 2m, and the scale reads 0N,
h2 = 1m, and the scale reads 2500N,
and h3=?m, and the scale reads 800N.
MJ is at rest at h3

Homework Equations



E1+W of point2-3= E3

The Attempt at a Solution



mgh1+FN(h2-h3)+Fg(h2-h3)= mgh3, because there is no KE1 or KE3,
80(10)(2)+2500-2500h3-800+800h3= 800h3,
3300= 2500h3, h3 = 1.32m (obviously incorrect as h3 is higher than h2)
 
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What 'scale' is this - what is it measuring? Should the 800m be 800N?
 
Sorry, the question is talking about a scale as in a bathroom scale, which measures FN in Newtons
 
Then my next question is how exactly the heights are defined. At h2, he must be in contact with the scales, so the height is not being measured from scales to feet. If it's from scales to anything higher than the ankle it will depend on posture - maybe he's crouching at h2, and the heights are measured to the head. But a reasonable guess is that he's upright in each case and the heights are measured to c of g.
I don't see how you can write the equations you have in your attempt. They imply e.g. that the scales supplied an upward force of 2500N for the entire distance as he descended from h3 to h2.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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