Calculating Work Done by Gravity on a 21N Book Falling and Moving on a Shelf

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The work done by gravity on a 21N book falling 3 meters to the floor is calculated as 63 Joules, since the force and displacement are in the same direction. When the book is picked up to the shelf, the work done by gravity is -63 Joules, as the displacement is upward against the force of gravity. For the horizontal sliding of the book along the shelf, the work done by gravity is 0 Joules, since there is no vertical displacement. Understanding the relationship between force direction and displacement is key to calculating work. The final answers are 63 J for falling, -63 J for lifting, and 0 J for sliding.
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Homework Statement



- A book has a weight of 21N. It falls off the shelf on to the floor, 3 m below. The work done by the force of gravity is what?

- A book has a weight of 21N. You pick it up off the floor, and return it to the shelf, 3 m above. The work done by the force of gravity is what?

- A book has a weight of 21N. You slide it horizontally along the shelf, a distance of 3 m. The work done by the force of gravity is what?


Homework Equations



Work = Force x Distance



The Attempt at a Solution



I don't get the differences, please help!
 
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Hello, Well you understand that Work=Force*distance. well let's look at this problem in this way, If a force is applied to an object, and that object slides in the direction of the displacement then the work is positive. so the first one should be W=63 Joules downward. because 21N*3m. Since the displacement (downward) is in the same direction as the force (gravity downward) then work is positive. The person picking up the book is different because the work is the same however since the displacement (upward) is in the opposite direction as the force (gravity downward) then work is negative. One important thing about work is that if there is no component of force in the direction of displacement then the Work is zero. So for the work of the guy sliding the book horizontally is zero. Hope that helps
 
Thanks so much, that's much more clear. So basically the answer for the first question is 63 J, the answer for the second is -63 J and the answer for the last one is 0?
 
Yessir! Glad it makes sense
 
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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