From the change of GPE into KE. Conservation of energy tells us this.
Answer:
Deltoid Force, ![F_{d} = \frac {r_{a}mgsin\alpha_{a}}{r_{d}sin\alpha_{d}}](https://tex.z-dn.net/?f=F_%7Bd%7D%20%3D%20%5Cfrac%20%7Br_%7Ba%7Dmgsin%5Calpha_%7Ba%7D%7D%7Br_%7Bd%7Dsin%5Calpha_%7Bd%7D%7D)
Additional Information:
Some numerical information are missing from the question. However, I will derive the formula to calculate the force of the deltoid muscle. All you need to do is insert the necessary information and calculate.
Explanation:
The deltoid muscle is the one keeping the hand arm in position. We have two torques that apply to the rotating of the arm.
1. The torque about the point in the shoulder for the deltoid muscle,
2. The torque of the arm,
Assuming the arm is just being stretched and there is no rotation going on,
= 0
= 0
⇒ ![T_{Deltoid} = T_{arm}](https://tex.z-dn.net/?f=T_%7BDeltoid%7D%20%3D%20T_%7Barm%7D)
![r_{d}F_{d}sin\alpha_{d} = r_{a}F_{a}sin\alpha_{a}](https://tex.z-dn.net/?f=r_%7Bd%7DF_%7Bd%7Dsin%5Calpha_%7Bd%7D%20%3D%20r_%7Ba%7DF_%7Ba%7Dsin%5Calpha_%7Ba%7D)
Where,
is radius of the deltoid
is the force of the deltiod
is the angle of the deltiod
is the radius of the arm
is the force of the arm ,
which is the mass of the arm and acceleration due to gravity
is the angle of the arm
The force of the deltoid muscle is,
![F_{d} = \frac {r_{a}F_{a}sin\alpha_{a}}{r_{d}sin\alpha_{d}}](https://tex.z-dn.net/?f=F_%7Bd%7D%20%3D%20%5Cfrac%20%7Br_%7Ba%7DF_%7Ba%7Dsin%5Calpha_%7Ba%7D%7D%7Br_%7Bd%7Dsin%5Calpha_%7Bd%7D%7D)
but
,
∴ ![F_{d} = \frac {r_{a}mgsin\alpha_{a}}{r_{d}sin\alpha_{d}}](https://tex.z-dn.net/?f=F_%7Bd%7D%20%3D%20%5Cfrac%20%7Br_%7Ba%7Dmgsin%5Calpha_%7Ba%7D%7D%7Br_%7Bd%7Dsin%5Calpha_%7Bd%7D%7D)
Answer:
Latitude :
runs: east to west
measures : distances north and south of the equator
Longitude :
runs : north to south
measures : the distance east or west of the Prime Meridian
It's most likely the combination of a bucket and the wheel.
Explanation:
Make a table, listing the x and y coordinates of each square's center of gravity and its mass. Multiply the coordinates by the mass, add the results for each x and y, then divide by the total mass.
![\left\begin{array}{ccccc}x&y&m&xm&ym\\\frac{a}{2} &\frac{a}{2} &10&5a&5a\\\frac{3a}{2}&\frac{a}{2}&70&105a&35a\\\frac{a}{2}&\frac{3a}{2}&80&40a&120a\\\frac{3a}{2}&\frac{3a}{2}&50&75a&75a\\&\sum&210&225a&235a\\&&Avg&\frac{15a}{14}&\frac{47a}{42}\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5Cbegin%7Barray%7D%7Bccccc%7Dx%26y%26m%26xm%26ym%5C%5C%5Cfrac%7Ba%7D%7B2%7D%20%26%5Cfrac%7Ba%7D%7B2%7D%20%2610%265a%265a%5C%5C%5Cfrac%7B3a%7D%7B2%7D%26%5Cfrac%7Ba%7D%7B2%7D%2670%26105a%2635a%5C%5C%5Cfrac%7Ba%7D%7B2%7D%26%5Cfrac%7B3a%7D%7B2%7D%2680%2640a%26120a%5C%5C%5Cfrac%7B3a%7D%7B2%7D%26%5Cfrac%7B3a%7D%7B2%7D%2650%2675a%2675a%5C%5C%26%5Csum%26210%26225a%26235a%5C%5C%26%26Avg%26%5Cfrac%7B15a%7D%7B14%7D%26%5Cfrac%7B47a%7D%7B42%7D%5Cend%7Barray%7D%5Cright)
The x-coordinate of the center of gravity is 15/14 a.
The y-coordinate of the center of gravity is 47/42 a.