Convert the measurement.<br> 56.8 grams= ounces

The 6-lb particle is subjected to the action of its weight and forces F1 = 52i + 6j - 2tk6 lb, F2 = 5t 2 i - 4tj - 1k6 lb, and F

olga2289 [7]

Answer:

r=294.9m

Step-by-step explanation:

The forces on the particle are

$W=mg\hat{j}\\F_{1}=52\hat{i}+6\hat{j}-2t\hat{k}\\F_{2}=5t^{2}\hat{i}-4t\hat{j}-1\hat{k}\\F_{3}=(5-2t)\hat{i}$

Now , we sum all these forces to get the net force

$F_{T}=W+F_{1}+F_{2}+F_{3}\\F_{T}=(52+5t^{2}+5-2t)\hat{i}+((6+6-4t)\hat{j}+(-2t-1)\hat{k}\\F_{T}=(57-2t+5t^{2})\hat{i}+(12-4t)\hat{j}+(-2t-1)\hat{k}\\$

we can use the fact F=m*a and integrate the acceleration

$a(t)=\frac{1}{m}F(t)\\\\v(t)=\int a(t)dt=\frac{1}{m}\int{F_{T}}dt\\\\v(t)=\frac{1}{m}[(57t-t^{2}+\frac{5}{3}t^{3})\hat{i}+(12t-2t^{2})\hat{j}+(-t^{2}-t)\hat{k}]\\\\r(t)=\int v(t)dt=\frac{1}{m}[(\frac{57}{2}t^{2}-\frac{1}{3}t^{3}}+\frac{5}{4}t^{4})\hat{i}+(6t^{2}-\frac{2}{3}t^{3})\hat{j}+(-\frac{1}{3}t^{3}-\frac{1}{2}t^{2})]$

and we evaluate in r(2) an we take the norm to obtain the distance

$r(2)=\frac{1}{m}[\frac{394}{3}\hat{i}+\frac{56}{3}\hat{j}-\frac{14}{3}\hat{k}]\\|r(2)|=\frac{1}{m}\sqrt{[(\frac{394}{3})^{2}+(\frac{56}{3})^{2}+(\frac{14}{3})^{2}]}\\|r(2)|=\frac{132.73}{0.45}=294.9m$

I hope this is useful for you

regards

8 0

4 years ago

True or False: All statements of equality below are correct. Please help!!

koban [17]

Answer:

True?

Step-by-step explanation:

8 0

3 years ago

8.4.49 A cow is tethered to one corner of a square barn, 19 feet by 19 feet, with a rope 160 feet long. (See the illustration

SashulF [63]

Answer:

$20096 ft^2$

Step-by-step explanation:

We are given that

Length of rope=l=160 feet

Radius of quadrant of circle=r=160 feet

We have to find the maximum grazing area of the cow.

We know that

Area of quadrant of circle= $\frac{1}{4}\pi r^2$

Where $\pi=3.14$

Using the formula

Area grazed by cow= $\frac{1}{4}\times 3.14(160)^2$

Area grazed by cow= $20096 ft^2$

4 0

4 years ago

A linear sequence starts a + 2b, a + 6b, a+10b

Trava [24]

Answer:

a = -12

b = 3

Step-by-step explanation:

second term = a + 6b

to find the 5th term, notice the pattern (since this is a linear equation, each term increases by the same amount) and each term increases by 4b: 2b -> 6b -> 10b.

therefore, the 4th term would be a+14b and the 5th would be a+18b

so a + 6b = 8

and a + 18b = 44

u now have two simultaneous equations, which can be solved through substitution or elimination. I'm gonna use elimination because it's quicker in this case:

$a + 6b = 8\\- (a + 18b = 44)\\ -12b = -36\\b = 3$

steps: (since the a would cancel out by subtracting, subtract then solve for b. divide by -12 on both sides to isolate the b)

now that u know the value of b, substitute it into an equation to solve for a:

a + 6b = 8

a + 6(3) = 8

a + 24 = 8

a = 8 - 24

a = -16

hope this helps!

6 0

3 years ago

The length of a rectangle is 8cm more than 3 times it’s width. The perimeter of the rectangle is 64cm

FinnZ [79.3K]

Answer:

<em>The length is 26 cm, and the width is 6 cm.</em>

Step-by-step explanation:

The width is unknown. Let w = width.

The length is 8 cm more than 3 times the width.

length = 3w + 8

The perimeter is 64 cm.

P = length + length + width + width

3w + 8 + 3w + 8 + w + w = 64

8w + 16 = 64

8w = 48

w = 6

The width is 6 cm.

length = 3w + 8 = 3(6) + 8 = 18 + 8 = 26

The length is 26 cm

7 0

4 years ago

Convert the measurement. 56.8 grams= ounces