1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
anastassius [24]
3 years ago
6

Let v1, , vk be vectors, and suppose that a point mass of m1, , mk is located at the tip of each vector. The center of mass for

this set of point masses is equal to v = m1v1 + + mkvk m where m = m1 + + mk. Determine the center of mass for the vectors u1 = (−1, 0, 2) (mass 3 kg), u2 = (2, 1, −3) (mass 1 kg), u3 = (0, 4, 3) (mass 2 kg), and u4 = (5, 2, 0) (mass 5 kg).
Physics
1 answer:
g100num [7]3 years ago
6 0

Answer:

Explanation:

Center of mass is give as

Xcm = (Σmi•xi) / M

Where i= 1,2,3,4.....

M = m1+m2+m3 +....

x is the position of the mass (x, y)

Now,

Given that,

u1 = (−1, 0, 2) (mass 3 kg),

m1 = 3kg and it position x1 = (-1,0,2)

u2 = (2, 1, −3) (mass 1 kg),

m2 = 1kg and it position x2 = (2,1,-3)

u3 = (0, 4, 3) (mass 2 kg),

m3 = 2kg and it position x3 = (0,4,3)

u4 = (5, 2, 0) (mass 5 kg)

m4 = 5kg and it position x4 = (5,2,0)

Now, applying center of mass formula

Xcm = (Σmi•xi) / M

Xcm = (m1•x1+m2•x2+m3•x3+m4•x4) / (m1+m2+m3+m4)

Xcm = [3(-1, 0, 2) +1(2, 1, -3)+2(0, 4, 3)+ 5(5, 2, 0)]/(3 + 1 + 2 + 5)

Xcm = [(-3, 0, 6)+(2, 1, -3)+(0, 8, 6)+(25, 10, 0)] / 11

Xcm = (-3+2+0+25, 0+1+8+10, 6-3+6+0) / 11

Xcm = (24, 19, 9) / 11

Xcm = (2.2, 1.7, 0.8) m

This is the required center of mass

You might be interested in
What work is done by the electric force when the charge moves a distance of 2.70 m at an angle of 45.0∘ downward from the horizo
Andreyy89

Incomplete question as many data is missing.I have assumed value of charge and electric field.The complete question is here

A charge of 28 nC is placed in a uniform electric field that is directed vertically upward and that has a magnitude of 5.00×10⁴ V/m.

What work is done by the electric force when the charge moves a distance of 2.70 m at an angle of 45.0 degrees  downward from the horizontal?

Answer:

W_{work}=2.67*10^{-3}J

Explanation:

Given data

Charge q=28 nC

Electric field E=5.00×10⁴ V/m.

Distance d=2.70 m

Angle α=45°

To find

Work done by electric force

Solution

W_{work}=F_{force}*D_{distance}Cos\alpha  \\where\\F_{force}=q_{charge}*E_{Electric-Field}\\So\\W_{work}=qE*D*Cos\alpha \\W_{work}=(28*10^{-9}C )(5.00*10^{4}V/m )(2.70m)Cos(45)\\W_{work}=2.67*10^{-3}J

8 0
3 years ago
How can we produce energy by turning a turbine?​
maw [93]
Wind turbines work on a simple principle: instead of using electricity to make wind—like a fan—wind turbines use wind to make electricity. Wind turns the propeller-like blades of a turbine around a rotor, which spins a generator, which creates electricity.
7 0
3 years ago
How will the solubility of a gas solute change if the pressure above the solution is reduced?
Hoochie [10]
If the pressure above a solution containing a gas solute is reduced, the limit of the gas's solubility will decrease.
6 0
3 years ago
Read 2 more answers
Categorize these resources as either renewable or Non-renewable
valentinak56 [21]

renewable: water, plants, animals

nonrenewable: rocks, soil

i hope this helps :)

5 0
3 years ago
Show that the effective force constant of a series combination is given by 1keff=1k1+1k2. (Hint: For a given force, the total di
S_A_V [24]

Answer:

1keff=1k1+1k2

see further explanation

Explanation:for clarification

Show that the effective force constant of a series combination is given by 1keff=1k1+1k2. (Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination. Also, each spring must exert the same force. Do you see why?

From Hooke's law , we know that the force exerted on an elastic object is directly proportional to the extension provided that the elastic limit is not exceeded.

Now the spring is in series combination

F\alphae

F=ke

k=f/e.........*

where k is the force constant or the constant of proportionality

k=f/e

f_{eff} =f_{1} +f_{2}............................1

also for effective force constant

divide all through by extension

1) Total force is

Ft=F1+F2

Ft=k1e1+k2e2

F = k(e1+e2) 2)

Since force on the 2 springs is the same, so

k1e1=k2e2

e1=F/k1 and e2=F/k2,

and e1+e2=F/keq

Substituting e1 and e2, you get

1/keq=1/k1+1/k2

Hint: For a given force, the total distance stretched by the equivalent single spring is the sum of the distances stretched by the springs in combination.

4 0
3 years ago
Other questions:
  • How is power defined
    5·2 answers
  • When a physical change occurs, the mass of the substance is conserved. This means that the total mass of the substance remains t
    5·1 answer
  • A man weighing 490N on earth weighs 81.7N on the moon.His mass on the moon is kg
    15·2 answers
  • 4. A football player has a mass of 75 kg, and he is running with a velocity of 18 m/s. What is his momentum? Answer:​
    5·1 answer
  • The mass of a hot-air balloon and its occupants is 381 kg (excluding the hot air inside the balloon). The air outside the balloo
    5·1 answer
  • The diagram shows changes of state between solid, liquid, and gas. The atoms of a substance gain energy during a change of state
    13·2 answers
  • Ke...
    10·1 answer
  • Four examples of second class levers​
    8·1 answer
  • Which is the most accurate description of how the coolant works in an engine?
    6·1 answer
  • the most likely places where stars and planetary systems are forming in the universe are- the most likely places where stars and
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!