Calculating Force: Solving a 10 kg Book and Wall Problem at a 30° Angle

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To calculate the force exerted while holding a 10 kg book against a wall at a 30° angle, the friction between the book and the wall is crucial. The force applied must counteract both the weight of the book and any horizontal forces due to the angle of application. If the wall is considered frictionless, the book would not stay in place, indicating that friction is necessary for stability. The calculation involves resolving the forces into components and applying Newton's laws. Ultimately, understanding the role of friction is essential for accurately determining the force applied.
TheShapeOfTime
If I am holding a 10.0 kg book against the wall with a 30 degree angle between the book and my arm (angle measured closest to my hand out), how can I find the force (in Newtons) that I'm pushing with?
 
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Is the wall frictionless??
 
Just to make sure we understand each other: I'm holding the book against the wall by leaning on it with my hand, applying a force at a 30 degree (measured as stated in my OP).

My understanding is that there has to be some friction against the wall otherwise I wouldn't be able to hold it there?
 
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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