Problem

(II) ($a$) If $m_A=$ 13.0 kg and mB= 5.0 kg in Fi…

04:55

Problem 32 Medium Difficulty

(II) A pair of fuzzy dice is hanging by a string from your rearview mirror. While you are accelerating from a
stoplight to $28 \mathrm{~m} / \mathrm{s}$ in $6.0 \mathrm{~s},$ what angle $\theta$ does the string make
with the vertical? See Fig. $4-50$.

Answer

(a) See the free-body diagrams included.
b)$a=g \frac{m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}} \quad F_{\mathrm{T}}=m_{\mathrm{A}} a=g \frac{m_{\mathrm{A}} m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}$

July 26, 2020

How come in the video the answer is shown to be 'a= (mB*g)/(mA-mB)' but in the answer section on the page it says 'a= (mB*g)/(mA+mB)'?

Sharieleen A.

October 23, 2020

That was not easy, glad this was able to help

Catherine A.

October 27, 2020

Kathleen T., thanks this was super helpful.

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Video Transcript

haider. So in this problem we need to determine the angle that the strings make with the vertical. So in here we have a dice. And the first thing that we need to do is to draw all the forces that are acting on the dies. And then appliance need to second law we can obtain equations for the Y. And the X. Company. So doing that we find that we have attention that we call team that is due to this string. And we also have the weight of the dice that we call. W. We also note that the system has an acceleration because the dice is inside of a car and it axillary res from from velocity in six seconds. That velocity is that we call final velocity Is equal to 28 m/s in a time of six seconds. So um we first are going to find the equations of for the dynamics of this. So some of the forces in the X company we have that this is detention sign of tita because the angle is with respect to the vertical and this because the car is moving in the horizontal way it is moving in the ads access. So dad we will have an acceleration in this company. So this is mm which is the mask of the dice times the acceleration for the white company of the forces. We will have two forces which are T casino tita in the positive part of wine and minus their weight in this case the dice is not moving in In this company. So it is equal to zero. Now from this we obtained that the tension times the cosine of theta is equal to the weight. We know that the weight is equal to the mass times the acceleration due to gravity. With these two equations, we're going to call this one in these two we are going to determine the angle tita and what we can do is to eliminate detention in the other equation so that we can divide want over to Yeah, Equation 1/2. So that we could see that these will give us deal sign data over T of consign of tita and for the right hand side we will have and A times A. M. Of G. So we have that. We can eliminate this too. And we also eliminate the tension so that we know that sign of tita. Over a dozen of teacher is the tangent of tita. And then we will have a over T. So to obtain the angle tita, we take the inverse function of the tangent function for both of the size of these equations. So we won't have Tangent of -1. All of the acceleration over the acceleration due to gravity. We know the acceleration due to gravity because this is the value of 9.8 m/s. But we don't know the acceleration of the dies or the car in which the diet is in it. Sm So we need to determine the acceleration but we know from the beginning that we are given a velocity and the time. So you think any memories? Yes. In key markets we can solve this by using the following equation. We know that the final velocity is equal to the initial velocity plus the acceleration times at time T. And we know that the initial velocity is zero and the final velocity is the one that we are given. So solving for a, we know that this is the final velocity over the time. We know that the final velocity is 28 meters per second and the time is six seconds. So from here we obtain about you off. Yeah. Mhm. For 0.6, see seven meters per second is square. So now we know the body of the acceleration. So we just simply need to substitute that value into the equation for tita. And then we can obtain the value for the angle tita. So it does regions substitute those values. The acceleration is 4.66 m/s square and the acceleration due to gravity is 99.8 m/s square. So good in this, plugging this into the calculator, we obtain about you. Yeah, 25 point 48 degrees. And this is the angle the district make with the particle

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