Question

A machine at a post office sends packages out a chute and down a ramp to be loaded into delivery vehicles. (a) Calculate the acceleration of a box heading down a 10 deg slope, assuming the coefficient of friction for a parcel on waxed wood is 0.100. (b) Find the angle of the slope down which this box could move at a constant velocity. You can neglect air resistance in both parts.

Answer 1

Answer:

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Answer 2

Given:

$\begin{array}{l}\mu_{k}=0.10 \\\theta=10^{\circ}\end{array}$

We have to find

$\text { a) } a\\\text { b) } \theta_{\max }$

$\text { a) According to Newton's second law the net force acting on the body is given by }\\\\F_{\text {net }}=m \times a \quad \rightarrow(1)\\Also\\F_{n e t}=m \cdot g \cdot \sin (10)-f =>(2)\\\\\text { From (1) and (2) we get }\\a=g\left(\sin \theta-\mu_{k} \cos \theta\right) =>(3)\\\\\text { By substitution in (3) we get}\\\\a=9.8(\sin 10-.1 \cos 10)=.74 \mathrm{~m} \cdot \mathrm{s}^{-2}$

$\text { b) To get } \theta_{\max } \text { the acceleration must be } 0 \text { as well as the net force }\\\\F_{n e t}=0\\\\\sin \theta-\mu_{k} \cos \theta=0\\\tan \theta=\mu_{k} =>(4)\\\\\text { By substitution in }(4) \text { we get }\\\theta=\arctan .1=5.7^{\circ}$

Hence,

$\text { a) } a=.74 \mathrm{~m} \cdot \mathrm{s}^{-2}\\\text { b) } \theta=5.7^{\circ}$