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
WARRIOR [948]
3 years ago
11

Consider two massless springs connected in series. Spring 1 has a spring constant k1, and spring 2 has a spring constant k2. A c

onstant force of magnitude F is being applied to the right. When the two springs are connected in this way, they form a system equivalent to a single spring of spring constant k.
Part A

What is the effective spring constant k of the two-spring system? Express the effective spring constant in terms of k1 and k2.

Part B

Now consider three springs set up in series as shown. (Figure 2) The spring constants are k1, k2, and k3, and the force acting to the right again has magnitude F. Find the spring constant k′ of the three-spring system. Express your answer in terms of k1, k2, and k3.
Physics
2 answers:
Andru [333]3 years ago
8 0

Answer:

a. k = (1/k₁ + 1/k₂)⁻¹ b. k = (1/k₁ + 1/k₂ + 1/k₃)⁻¹

Explanation:

Since only one force F acts, the force on spring with spring constant k₁ is F = k₁x₁ where x₁ is its extension

the force on spring with spring constant k₂ is F = k₂x₂ where x₁ is its extension

Let F = kx be the force on the equivalent spring with spring constant k and extension x.

The total extension , x = x₁ + x₂

x = F/k = F/k₁ + F/k₂

1/k = 1/k₁ + 1/k₂

k = (1/k₁ + 1/k₂)⁻¹

B

The force on spring with spring constant k₃ is F = k₃x₃ where x₃ is its extension

Let F = kx be the force on the equivalent spring with spring constant k and extension x.

The total extension , x = x₁ + x₂ + x₃

x = F/k = F/k₁ + F/k₂ + F/k₃

1/k = 1/k₁ + 1/k₂ + 1/k₃

k = (1/k₁ + 1/k₂ + 1/k₃)⁻¹

vesna_86 [32]3 years ago
5 0

Answer:

a) K = k1k2/k2+k1

b) k1k2k3/(k2k3+k1k3+k1k2)

Explanation:

Hooke's law states that the extension of an elastic material is directly proportional to the applied force provided the elastic limit is not exceeded. Mathematically;

F = ke where;

F is the applied force

k is the elastic constant

e is the extension

If we consider 2 springs 1 an 2 with spring constant k1 and k2 connected in series to each other, their respective spring constant according to hooke's law will be expressed as;

k1 = F/e1 and k2 = F/e2 where F is a constant force.

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

The equivalent extension e = F/K

Since the two spring are in series, the effective spring constant K of the two-spring system is expressed as follows;

Since the total extension of the string

e = e1+e2

F/K = F/k1+F/k2

F(1/K) = F(1/k1)+F(1/k2)

1/K = 1/k1+1/k2

1/K = (k2+k1)/k1k2

Reciprocating both sides gives

K = k1k2/k2+k1

b) Similarly if there are 3 springs connected in series to each other with spring constant k1, k2 and k3, their individual extension will be expressed as;

e1 = F/k1

e2 = F/k2

e3 = F/ke

Their equivalent extension e in series will be expressed as e = F/K

Writing their equivalent extension in terms of their individual extension will give;

e = e1+e2+e3

F/K = F/k1+F/k2+F/k3

1/K = 1/k1+1/k2+1/k3

1/K = (k2k3+k1k3+k1k2)/k1k2k3

Taking the reciprocal of both sides to get K

K = k1k2k3/(k2k3+k1k3+k1k2)

You might be interested in
Air "breaks down" when the electric field strength reaches 3×106n/c, causing a spark. a parallel-plate capacitor is made from tw
aalyn [17]
Ok, I think this is right but I am not sure:
 Q = ϵ
 0AE
A= π π
 r^2

=(8.85x10^-12 C^2/Nm^2)
( π π (0.02m)^2)
(3x10^6 N/C) =3.3x10^-8 C = 33nC N = Q/e = (3.3x10^-8 C)/(1.60x10^-19 C/electron) = 2.1x10^11 electrons


4 0
3 years ago
Which statement is true? Which statement is true? An orbital that penetrates into the region occupied by core electrons is more
masya89 [10]

Hey there!:

Here the Statement - D is correct.  

Because Orbitals containing the core electrons are more attracted towards nuclear charge and hence less shilded from nuclear charge than an orbital that doesn't penetrate.  Also due to more attraction between the orbital containing core electron and nucleus, it will have less energy.

Hope this helps!

6 0
3 years ago
A snail and an inchworm are in a race. Their race track heads north for a distance of 2 m. If the inchworm comes to the end of t
olga2289 [7]
Well the basic equation for velocity is v=d/t where d is distance and t is time. So v=2m/50s and the answer is v=0.04meter/second.
7 0
3 years ago
Electric Circuits Homework
nirvana33 [79]
<h2>Sorry, But I don't know!!</h2>
3 0
2 years ago
You are on a sled at the top of a hemispherical, snowy hill of radius 13 m. You begin to slide down the hill. How fast are you m
8_murik_8 [283]

Answer:

Explanation:

There will be loss of potential energy due to loss of height and gain of kinetic energy .

loss of height = R - R cos 14 ,    R is radius of hemisphere .

R ( 1 - cos 12 )

= 13 ( 1 - .978 )

h = .286 m

loss of potential energy

= mgh

= m x 9.8 x .286

= 2.8 m

gain of kinetic energy

1/2 m v ² = mgh

v² = 2 g h

v²  = 2 x 9.8 x 2.8

v = 7.40 m /s

4 0
3 years ago
Read 2 more answers
Other questions:
  • I'm in  my lab, writing an essay about the properties of Bose Einstein Condensate. I forgot the formula of producing the condens
    13·1 answer
  • A flat surface of area 3.20 m2 is rotated in a uniform electric field of magnitude e = 6.20 x 105 n/c. determine the electric fl
    6·1 answer
  • A pair of slits in a double slit experiment are illuminated with monochromatic light of wavelength 480 nm. The slits are separat
    10·1 answer
  • Who created a steel plow
    12·2 answers
  • You are a member of a citizen's committee investigating safety in the high school sports program. You are interested in knee dam
    6·1 answer
  • Calculate the speed for a car that went a distance of 125 kilometers in 2 hours​
    8·1 answer
  • Which refers to the rate of change in velocity?
    13·1 answer
  • Suppose that a particular artillery piece has a range R = 9880 yards . Find its range in miles. Use the facts that 1mile=5280ft
    7·1 answer
  • Using the graph, predict how many paper clips a 7.5 V battery would pick up for both the 25-coil electromagnet and the 50-coil e
    13·1 answer
  • What sport does not require a high level of fitness
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!