A Question about Frictional Forces

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A horizontal force of 15 N is applied to a 0.50 kg book against a wall, with static and kinetic friction coefficients of 0.6 and 0.40, respectively. The discussion involves calculating the book's acceleration by analyzing forces acting on it, including static friction and gravitational force. The participant initially struggles with the calculations but realizes that the book does not move, indicating that static friction is sufficient to prevent motion. The maximum static friction force is determined by multiplying the coefficient of static friction by the normal force. Ultimately, the participant gains clarity on the problem and appreciates the assistance received.
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Homework Statement


A horizontal force of 15 N pushes a .50 kg book against a vertical wall. The book is initially at rest. If the coefficient of static friction= 0.6 and the coefficient of kinetic friction = 0.40, what is the acceleration of the book?


Homework Equations



F=ma
static friction= coefficient of static friction x normal force
kinetic friction= coefficient of kinetic friction x normal force


The Attempt at a Solution



First, I drew a free body diagram of a rectangle next to the wall. To the right, I had the force 15 N pointing towards the rectangle (the force exerted on the book). To the left, I had a force - 15 pointing towards the rectangle (the force exerted on the book by the wall). Pointing in the down direction, I had a vector mg. In the upward the direction the force is equal to the frictional force.

Thus, the force in the x direction equals 0.

Ff-MG= MAy
Thus, Ay= (Ff-MG)/M

Ff= coefficient of kinetic friction * normal force

For some reason, I'm not getting a good answer. Can someone tell me where I am going wrong? Thanks!
 
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The maximum static friction force at the point of pending motion is (coef. friction)*N. The actual static friction force may be different. Does the block move?
 
No it is not! I get it now! Thank you thank you 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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