## anonymous one year ago You drag a trunk of mass m across a level floor using a massless rope that makes an angle with the horizontal. Given a kinetic-friction coefficient (μ), Find the minimum force needed to move the trunk with constant speed. Do not answer in terms of theta; essentially, if you were allowed to vary the angle at which you pull the trunk, what is the minimum force required?

1. anonymous

Welches Thema ist das genau ?

2. Michele_Laino

your exercise can be represented by this drawing: |dw:1443890056456:dw|

3. Michele_Laino

now, your trunk will move by uniform rectilinear motion if and only if the subsequent condition holds: $\huge F\cos \theta = \mu \left( {mg - F\sin \theta } \right)$ where $$g=gravity$$, $$\mu$$ is the friction, and $$m$$ is the mass of trunk. Solving for $$F$$ we get: $\huge F = \frac{{\mu mg}}{{\cos \theta + \mu \sin \theta }}$ Next you can try to minimize that quantity, using calculus, namely you have to solve this equation: $\huge \frac{{\partial F}}{{\partial \theta }} = 0$

4. anonymous

thank you so much!

5. anonymous

although, I'm still not quite sure how to solve for the dF/dtheta