Minimum Force to Prevent Slipping Down Plane

AI Thread Summary
A block weighing 75 N is on a 25-degree incline, and a force F is applied at a 40-degree angle to prevent it from slipping. The coefficient of static friction is 0.363, and the minimum force required to stop the block from sliding down is being calculated. The initial calculations yielded 7.3 N, but the correct answer is 8.05 N. Key considerations include the normal force and how the applied force affects it, as well as the direction of friction opposing the block's movement. Understanding these dynamics is crucial for accurately determining the minimum force needed.
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Homework Statement


A block weighing 75 N rests on a plane inclined at 25 degrees. A force F is applied to the object at 40 degrees to the horizontal, pushing it upward on the plane. Coefficient of static friction between block and plane is .363

EDIT: What is the minimum value of F that will prevent the block from slipping down the plane?

Homework Equations


Ff = uFn. F = ma, etc.

The Attempt at a Solution



So the free-body diagram has F and Ff in the same direction (diff angles) and F(parallel to surface) is in the other way.

Ff + Fcos(15) = Fgsin(25) (15 degrees because 45-20 = 15)
.363*75cos(25) + Fcos(15) = 75sin(25)

I solved for F and got 7.3 N while the answer is 8.05 N. Thank you for any hints/help
 
Last edited:
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If you have a block moving up a plane then it's kinetic friction (which will most likely be <= static friction) for starters... Also the friction force opposes the movement of the object you it should be

Fcos(15) = Fgsin(25) + Ff
 
Wow I forgot to put the actual question down, they're actually asking

What is the minimum value of F that will prevent the block from slipping down the plane?
 
Hint: What's the normal force? How does F affect the normal force?
 
got it thank you.
 
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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