How would you go about finding the force of this object?

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A wrench sliding off a tilted shelf experiences a force of 1.6N applied opposite to its motion, allowing it to move at a constant velocity. The work done by this applied force over a 1.2m distance is calculated as w = (1.6N)(1.2m), resulting in 1.92 J. However, the worksheet indicates that this calculation should also include a multiplication by cos 180 degrees due to the force acting in the opposite direction of the displacement. The use of cos 180 accounts for the negative work done against the motion. Thus, understanding the application of the cosine function is crucial for accurately determining the work done.
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A wrench slides off a tilted shelf, although if a force of 1.6N is applied opposite the wrench's motion the wrench will slide down the shelf with a constant velocity. If the shelf is 1.2m long, what is the work done by the applied force on the wrench?
This is what I did:
w=(1.6N)(1.2m)= and got 1.92 J
On the worksheet it said that I have to multiply it also by cos 180, but I'm not understanding where they got cos 180 from. Can someone please explain?
 
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The force is being applied in the opposite direction of the displacement for work. Therefore, you have to use 180 degrees instead of 0 degrees.
 
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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