I've been trying to solve a physics problem, and I'm not sure how exactly to do it.
Body $A$ in Fig. $6-33$ weighs $102N$, and body $B$ weighs $32N$. The coefficients of friction between $A$ and the incline are $\mu_s=.56$ and $\mu_k=.25$. Angle $θ$ is $40°$. Let the positive direction of an $x$ axis be up the incline. In unit-vector notation, what is the acceleration of $A$ if $A$ is initially $(a)$ at rest, $(b)$ moving up the incline, and $(c)$ moving down the incline?
What I don't understand is how I'm supposed to find the acceleration when it's going up and down; wouldn't that require an outside force? I do know that the acceleration is $0\ ms^{-2}$ at rest. So far I've found the normal force $(F_n = 102\cos(40^\circ) = 78.14N)$ and the kinetic friction $(F_k = 78.14*\frac14 = 19.54N)$, but I'm not sure where to go from there.
Best Answer
As others mentioned, solving the equations isn't the issue. Writing them down correctly for each case is key, and that's a physics thing.
But, this can be treated as a one-dimensional problem. Write down the forces on $A$, and then take the components parallel to the plane. You'll consider the weight of $A$ (gravity), the appropriate frictional force (it's not the same for each case), the normal force exerted by the plane on $A$, and the tension in the string. For $B$, you'll consider the weight of $B$ and the tension in the string.
The blocks will have the same magnitude of acceleration (assuming that the string doesn't stretch). The tension in the string will be a constant (so the tension force considering $A$ will equal that of $B$).
This allows you to calculate the net force on $A$, which gives the acceleration. That will work for parts (b) and (c). For (a) it might be a tad trickier to solve things and you have to look at what's happening to see the answer, since block $A$ may not move at all in that case.