A horizontal force of $100 \mathrm{~N}$ pushes a 12-kg block up a frictionless incline that makes an angle of $25^{\circ}$ with the horizontal.

$(b)$ What is the magnitude of acceleration of the block?

A box is held in position on a frictionless incline by a cable (Figure 4-46).

$(b)$ Find the tension as a function of $\theta$ and $m$, and check your result for plausibility in the special cases of $\theta=0^{\circ}$ and $\theta=90^{\circ}$.

A box is held in position on a frictionless incline by a cable (Figure 4-46).

$(a)$ If $\theta=60^{\circ}$ and $m=50 \mathrm{~kg}$, find the tension in the cable and the normal force exerted by the incline.

In Figure 4-45, the objects are attached to spring scales calibrated in newtons. Give the reading(s) of the balance(s) in each case, assuming that both the scales and the strings are massless.

The system shown in Figure 4-42 is in equilibrium and the incline is frictionless. It follows that the mass $m$ is (a) $3.5 \mathrm{~kg}$, (b) $3.5 \sin 40^{\circ} \mathrm{kg}$, (c) $3.5 \tan 40^{\circ} \mathrm{kg}$, (d) none of these answers. FIGURE 4-42 Problem 57

A $20.0 \mathrm{~kg}$ box rests on a frictionless ramp with a $15.0^{\circ}$ slope. The mover pulls on a rope attached to the box to pull it up the incline (Figure 4-44). If the rope makes an angle of $40.0^{\circ}$ with the horizontal, what is the smallest force $F$ the mover will have to exert to move the box up the ramp?