The <em>estimated</em> displacement of the center of mass of the olive is
.
<h3>Procedure - Estimation of the displacement of the center of mass of the olive</h3>
In this question we should apply the definition of center of mass and difference between the coordinates for <em>dynamic</em> (
) and <em>static</em> conditions (
) to estimate the displacement of the center of mass of the olive (
):
(1)
Where:
- x-Coordinate of the i-th element of the system, in meters.
- y-Coordinate of the i-th element of the system, in meters.
- x-Component of the net force applied on the i-th element, in newtons.
- y-Component of the net force applied on the i-th element, in newtons.
- Mass of the i-th element, in kilograms.
- Gravitational acceleration, in meters per square second.
If we know that
,
,
,
,
,
and
, then the displacement of the center of mass of the olive is:
<h3>Dynamic condition
![\vec{r} = \left[\frac{(0)\cdot (0.50)\cdot (9.807)+(0)\cdot (0) + (1)\cdot (1.50)\cdot (9.807) + (1)\cdot (-3)}{(0.50)\cdot (9.807) + 0 + (1.50)\cdot (9.807)+(-3)}, \frac{(0)\cdot (0.50)\cdot (9.807) + (0)\cdot (3) + (2)\cdot (1.50)\cdot (9.807) +(2) \cdot (-2)}{(0.50)\cdot (9.807) + (3)+(1.50)\cdot (9.807)+(-2)} \right]](https://tex.z-dn.net/?f=%5Cvec%7Br%7D%20%3D%20%5Cleft%5B%5Cfrac%7B%280%29%5Ccdot%20%280.50%29%5Ccdot%20%289.807%29%2B%280%29%5Ccdot%20%280%29%20%2B%20%281%29%5Ccdot%20%281.50%29%5Ccdot%20%289.807%29%20%2B%20%281%29%5Ccdot%20%28-3%29%7D%7B%280.50%29%5Ccdot%20%289.807%29%20%2B%200%20%2B%20%281.50%29%5Ccdot%20%289.807%29%2B%28-3%29%7D%2C%20%5Cfrac%7B%280%29%5Ccdot%20%280.50%29%5Ccdot%20%289.807%29%20%2B%20%280%29%5Ccdot%20%283%29%20%2B%20%282%29%5Ccdot%20%281.50%29%5Ccdot%20%289.807%29%20%2B%282%29%20%5Ccdot%20%28-2%29%7D%7B%280.50%29%5Ccdot%20%289.807%29%20%2B%20%283%29%2B%281.50%29%5Ccdot%20%289.807%29%2B%28-2%29%7D%20%20%5Cright%5D)
![\vec r = (0,704, 1.233)\,[m]](https://tex.z-dn.net/?f=%5Cvec%20r%20%3D%20%280%2C704%2C%201.233%29%5C%2C%5Bm%5D)
</h3>
<h3>Static condition</h3><h3>
![\vec{r}_{o} = \left[\frac{(0)\cdot (0.50)\cdot (9.807) + (1)\cdot (1.50)\cdot (9.807)}{(0.50)\cdot (9.807) + (1.50)\cdot (9.807)}, \frac{(0)\cdot (0.50)\cdot (9.807) + (2)\cdot (1.50)\cdot (9.807)}{(0.50)\cdot (9.807)+(1.50)\cdot (9.807)} \right]](https://tex.z-dn.net/?f=%5Cvec%7Br%7D_%7Bo%7D%20%3D%20%5Cleft%5B%5Cfrac%7B%280%29%5Ccdot%20%280.50%29%5Ccdot%20%289.807%29%20%2B%20%281%29%5Ccdot%20%281.50%29%5Ccdot%20%289.807%29%7D%7B%280.50%29%5Ccdot%20%289.807%29%20%2B%20%281.50%29%5Ccdot%20%289.807%29%7D%2C%20%5Cfrac%7B%280%29%5Ccdot%20%280.50%29%5Ccdot%20%289.807%29%20%2B%20%282%29%5Ccdot%20%281.50%29%5Ccdot%20%289.807%29%7D%7B%280.50%29%5Ccdot%20%289.807%29%2B%281.50%29%5Ccdot%20%289.807%29%7D%20%20%5Cright%5D)
</h3><h3>
![\vec r_{o} = \left(0.75, 1.50)\,[m]](https://tex.z-dn.net/?f=%5Cvec%20r_%7Bo%7D%20%3D%20%5Cleft%280.75%2C%201.50%29%5C%2C%5Bm%5D)
</h3><h3 /><h3>Displacement of the center of mass of the olive</h3>

![\overrightarrow{\Delta r} = (0.704-0.75, 1.233-1.50)\,[m]](https://tex.z-dn.net/?f=%5Coverrightarrow%7B%5CDelta%20r%7D%20%3D%20%280.704-0.75%2C%201.233-1.50%29%5C%2C%5Bm%5D)
![\overrightarrow{\Delta r} = (-0.046, -0.267)\,[m]](https://tex.z-dn.net/?f=%5Coverrightarrow%7B%5CDelta%20r%7D%20%3D%20%28-0.046%2C%20-0.267%29%5C%2C%5Bm%5D)
The <em>estimated</em> displacement of the center of mass of the olive is
. 
To learn more on center of mass, we kindly invite to check this verified question: brainly.com/question/8662931
Answer:
option A
Explanation:
given,
Force = F
angle = θ
weight on suitcase = mg
distance = d
constant velocity so, acceleration a = 0
coefficient of friction = µ
Work done = ?
Work done is equal to force into displacement.
Friction act opposite to the force acting so, work done by frictional force will be negative.
frictional force will act into horizontal direction opposite to force.
here displacement is equal to d
now,
W = -F d cos θ
Hence,the correct answer is option A
It's D. By "net" they mean the overall force the object experiences, so sum all the force vectors, those in a negative direction (eg friction) should be subtracted.
Answer:
See below
Explanation:
At point A the PE = mgh = 2 * 10 * 1 = 20 J
at point B, all of the PE , 20 J , is converted to Kinetic Energy
KE = 1/2 m v^2
20 = 1/2 (2)(v^2 )
20 = v^2 v = sqrt 20 = 4.47 m/s
for the friction part
vf = vo t + 1/2 a t^2 vf = final velocity = 0 (stopped)
vo = original velocity = 4.47 m/s
a = -1 m/s^2
0 = 4.47 t + 1/2 (-1) t^2
- .5t^2 + 4.47 t = 0
t ( -.5t+ 4.47) = 0 shows t = 4.47/.5 = 8.9 seconds