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
krok68 [10]
3 years ago
12

Determine the location of the center of mass of a "L" whose thin vertical and horizontal members have the same length L and the

same mass M. Use the formal definition to find the x and y coordinates, and check your result by doing the calculation with respect to two different origins, one in the lower left corner at the intersection of the horizontal and vertical members and one at the top of the vertical member.
(a) Origin at the lower left

x = ?

y = ?

(b) Origin at the top of the vertical member

x = ?

y = ?
Physics
1 answer:
Vladimir79 [104]3 years ago
6 0

Answer:

a)  x_{cm} = L / 2 , y_{cm}= L/2, b) x_{cm} = L / 2 , y_{cm}= L/2

Explanation:

The center of mass of a body is the point where all external forces are applied, it is defined by

      x_{cm} = 1 / M ∑  x_{i} m_{i} = 1 /M ∫ x dm

      y_{cm} = 1 / M ∑ y_{i}  m_{i} = 1 / M ∫ y dm

where M is the total body mass

Let's calculate the center of mass of our L-shaped body, as formed by two rods one on the x axis and the other on the y axis

a) let's start with the reference zero at the left end of the horizontal rod

let's use the concept of linear density

    λ = M / L = dm / dl

since the rod is on the x axis

     dl = dx

    dm = λ dx

let's calculate

      x_{cm} = M ∫ x λ dx = λ / M ∫ x dx

      x_{cm} = λ / M x² / 2

we evaluate between the lower integration limits x = 0 and upper x = L

      x_{cm} = λ / M (L² / 2 - 0)

  we introduce the value of the density that is cosntnate

     x_{cm} = (M / L) L² / 2M

     x_{cm} = L / 2

We repeat the calculation for verilla verilla

     λ = M / L = dm / dy

     y_{cm} = 1 / M ∫ y λ dy

     y_{cm} = λ M y² / 2

     y_{cm} = M/L  1/M (L² - 0)

     y_{cm}= L/2

b) we repeat the calculation for the origin the reference system is top of the vertical rod

     horizontal rod

        x_{cm} = 1 / M ∫λ x dx = λ/M   x² / 2

we evaluate between the lower limits x = 0 and the upper limit x = -L

      x_{cm} = λ / M [(-L)²/2 - 0] = (M / L) L² / 2M

      x_{cm} = L / 2

vertical rod

      y_{cm} = 1 / M ∫y dm

      y_{cm} = λ / M ∫y dy

      y_{cm} = λ / M y2 / 2

we evaluate between the integration limits x = 0 and higher x = -L

      y_{cm} = (M / L) 1 / M ((-L)²/2 -0)

      y_{cm} = L / 2

You might be interested in
A student wearing a frictionless roller skates on a horizontal is pushed by a friend with a constant force of 55N. How far must
umka21 [38]

Answer:

6.58m

Explanation:

The kinetic energy = Workdone on the roller

Workdone = Force * distance

Given

KE = Workdone = 362J

Force = 55N

Required

Distance

Substitute into the formula;

Workdone = Force * distance

362 = 55d

d = 362/55

d = 6.58m

Hence the student must push at a distance of 6.58m

3 0
3 years ago
What is the mass of a child in a wagon that has a velocity of 10 m/s and a Momentum of 30 KG* M/S
LenKa [72]

Explanation:

sinces : Momentum = velocity × mass

then : 30 = 10 × m and m = 30 ÷ 10 = 3 kg

3 0
2 years ago
he triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2.00 1
meriva

Answer:

Moment of inertia = 0.3862kg-m²

Explanation:

2.00x10³

2.80cm

145 rad

r = r⊥ x F

F is an applied force

r⊥ is the distance between the applied force and axis

Force exerted = 2.00x10³

r⊥ = 2.8cm = 0.028m

Alpha = 145rad/s²

r = 0.028m x 2.00x10³

r = 56.0N-m

To get the moment of inertia

56.0N-m² = (145rad/s²) x I

The I would be:

I = (56.0N-m²)/(145rad/s²)

I = 56/145

= 0.3862Kg-m²

This is the moment of inertia.

Thank you!

5 0
3 years ago
Need help with this plz
Lisa [10]

Answer:

1 - amplification

3- actinide

5 - radioactive decay ( im not really sure on this one )

7- alternating current

Explanation:

7 0
3 years ago
What type on msd causes inflammation of the tendons that correct bones to muscles
svp [43]

I believe it would be Tendonitis

8 0
3 years ago
Other questions:
  • How do you know about Black Holes?
    11·2 answers
  • How many significant figures are there in : (a) 0.000054 (b) 3.001 x 10^5 (c) 5.600
    7·1 answer
  • BRAINLIEST ANSWER!!!!!!!!!!!!!!!!!!!
    10·2 answers
  • Define mechanics and describe its three major divisions
    9·1 answer
  • In which of the following situations would be the government had been most likely to become involved in union protests?
    6·1 answer
  • A diver jumps up off a pier at an angle of 25° with an initial velocity of 3.2 m/s. How far from the pier will the diver hit the
    9·2 answers
  • What is air masses? And 5 effect of it​
    14·1 answer
  • Convert 47 meters to gigameters
    5·1 answer
  • All changes in the state of matter of a substance requires a change in
    12·2 answers
  • Brainliest brainliest help help help mememememememme
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!