An ideal spring hangs from the ceiling. A 1.95 kg mass is hung from the spring, stretching the spring a distance d=0.0865 m from its original length when it reaches equilibrium. The mass is then lifted up a distance L=0.0325 m from the equilibrium position and released. What is the kinetic energy of the mass at the instant it passes back through the equilibrium position?

Answers

Answer 1

Answer:

kinetic energy = 0.1168 J

Explanation:

From Hooke's law, we know that ;

F = kx

k = F/x

We are given ;

Mass; m = 1.95 kg

Spring stretch; d = x = 0.0865

So, Force = mg = 1.95 × 9.81

k = 1.95 × 9.81/0.0865 = 221.15 N/m

Now, initial energy is;

E1 = mgL + ½k(x - L)²

Also, final energy; E2 = ½kx² + ½mv²

From conservation of energy, E1 = E2

Thus;

mgL + ½k(x - L)² = ½kx² + ½mv²

Making the kinetic energy ½mv² the subject, we have;

½mv² = mgL + ½k(x - L)² - ½kx²

We are given L=0.0325 m

Plugging other relevant values, we have ;

½mv² = (1.95 × 9.81 × 0.0325) + (½ × 221.15(0.0865 - 0.0325)² - ½(221.15 × 0.0865²)

½mv² = 0.62170875 + 0.3224367 - 0.82734979375

½mv² = 0.1168 J


Related Questions

If during the submerged weighing procedure air bubbles were to adhere to the object, how would the experimental results be affected

Answers

Answer:

see from this analysis, the apparent weight of the body is lower due to the push created by the air brujuleas

Explanation:

We will propose this exercise using Archimedes' principle, which establishes that the thrust on a body is equal to the volume of the desalted liquid.

          B = ρ g V

The weight of a submerged body is the net force between the weight and the thrust

          F_net = W - B

we can write the weight as a function of the density

          ρ_body = m / V

         m =  ρ_body V

         W = mg

         W =  ρ _body g V

we substitute

         F_net= ( ρ_body -  ρ _fluid) g V

In general this force is directed downwards, we can call this value the apparent weight of the body. This is the weight of the submerged body.

          W_aparente = ( ρ_body -  ρ _fluid) g V

If some air bubbles formed in this body, the net force of these bubbles is

         F_net ’= #_bubbles ( ρ_fluido -  ρ_air) g V’

this force is directed upwards

whereby the measured force is

         F = W_aparente - F_air  

           

As we can see from this analysis, the apparent weight of the body is lower due to the push created by the air brujuleas

A nucleus of carbon 14 has 6 protons and 8 neutrons. The atomic number and mass number of carbon 14 are, respectively,
a) 6 and 8
b) 6 and 14
c) 8 and 14
d) 14 and 20
e) 14 and 22

Answers

Answer:

6 and 14 respectively

Explanation:

proton number = atomic number

mass number = proton number + neutron number

since

p.n = a.n = 6m.n = p.n + n.nm.n = 6 + 8 = 14m.n = 14

A 1.07 H inductor is connected in series with a fluorescent lamp to limit the current drawn by the lamp. If the combination is connected to a 28.9 Hz, 170 V line, and if the voltage across the lamp is to be 17.6 V, what is the current in the circuit

Answers

Answer:

0.784 A

Explanation:

From the question,

Note that the current in the circuit is the same as the current flowing through the inductor since they are both connected in series.

I = VL/XL....................... Equation 1

Where I = current flowing through the circuit, VL = Voltage drop across the inductor,  XL = reactance of the inductor.

XL = 2πfL................. Equation 2

Given: f = 28.9 Hz, L = 1.07 H, π = 3.143

XL = 2(3.143)(28.9)(1.07)

XL = 194.38 Ω.

VL = V-Vf

VL = 170-17.6

VL = 152.4 V

Substitute these values into equation 1

I = 152.4/194.38

I = 0.784 A

The current in the circuit when combination is connected  should be 0.784 A.

Calculation of the current:

SInce

we know that

I = VL/XL....................... Equation 1

Here,

I = current flowing through the circuit,

VL = Voltage drop across the inductor,  

XL = reactance of the inductor.

And,

XL = 2πfL................. Equation 2

Here

f = 28.9 Hz, L = 1.07 H, π = 3.143

So,

XL = 2(3.143)(28.9)(1.07)

XL = 194.38 Ω.

Now

VL = V-Vf

VL = 170-17.6

VL = 152.4 V

Now

I = 152.4/194.38

I = 0.784 A

hence, The current in the circuit when combination is connected  should be 0.784 A.

Learn more about current here: https://brainly.com/question/11311946

What does a constant velocity look like on a displacement vs time graph?

Answers

Answer:

A line with slope equal to the velocity.

Explanation:

If one is in the presence of constant velocity, that means that at the quotient between displacement and time elapsed is a constant value, therefore one can write the following equation:

[tex]\frac{displacement}{time} =constant[/tex]

therefore, solving for displacement we get:

[tex]displacement= constant \,*\, time[/tex]

which if plotted with displacement (D) on the vertical axis  and time (t) on the horizontal axis, renders a line with slope equal to the constant value of the velocity (v):

[tex]D=v\,*\,t[/tex]

A 2MeV proton is moving perpendicular to a uniform magnetic field of 2.5 T.the force on a proton is

Answers

Answer:

7.8x10-12N

Explanation:

We know that

Magnetic force = F = qVB

And

Also Kinetic energy K.E is

E = (1/2)mV²

So making v subject

V = √(2E / m)

And

E = KE = 2MeV

= 2 × 106 eV

= 2 × 106 × 1.6 × 10–19 J

= 3.2 × 10–13 J

And then

V= √2x3.2E-13/1.6E-27

1.9E7m/s

Given that

mass of proton = 1.6 × 10–27 kg,

Magnetic field strength B = 2.5 T.

So F= qBv sinစ

=

So F = 1.6 × 10–19 × 2.5 × 1.9 x10^7 x sin 90°

= 7.8 x 10^-12N

Answer:

8*10^-12

Explanation:

Given that

Energy of proton, K = 2 MeV = 2 * 1.6*10^-19 *10^6 = 3.2*10^-13

magnetic field strength, B = 2.5 T

mass of proton, m = 1.67*10^-27 kg

K = ½mv², making v² the subject of formula by rearranging, we have

v² = 2k/m

v² = (2 * 3.2*10^-13) / 1.67*10^-27

v² = 6.4*10^-13 / 1.6*10^-27

v² = 4*10^14

v = √4*10^14

v = 2*10^7 m/s

f = qvbsinθ, where

θ = 90

v = 2*10^7 m/s

b = 2.5 T

q = 1.6*10^-19

f = 1.6*10^-19 * 2*10^7 * 2.5 sin 90

f = 8*10^-12 N

thus, the force on the proton is 8*10^-12

In an experiment you measure a first-order red line for Hydrogen at an angle difference of ΔΘ = 22.78o. The diffraction grating you are using has 5900 lines per cm.

a) What is the wavelength of this light?

b) What is the value of Rydberg's constant for this measurement?

Answers

Answer:

a) wavelength = 656.3 nm

b)  the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹

Explanation:

Given that;

angle of diffraction Θₓ = 22.78°

incident angle Θ₁ = 0

slit separation d  = 5900 lines per cm = 1/5900 cm = 10⁻²/5900 m = 0.01/5900 m

order of diffraction n = 1

wavelength λ = ?

to find the wavelength, we use the expression

λ = d (sinΘ₁ + sinΘₓ) / n

To find the wavelength λ;

λ = 0.01/5900 × (sin0 + sin22.78° )

λ = 6.5626 × 10⁻⁷ m

λ = 656.3 x 10⁻⁹ m

∴ λ = 656.3 nm

b)

According Balnur's  series spectral lines; n₁ = 3, n₂ = 2 and

λ = R [ 1/n₂² - 1/n₁²]

where  R is Rydberg's constant

from λ = R [ 1/n₂² - 1/n₁²]

R = 1/λ [n₂²n₁² / n₁² - n₂²]

R = 10⁹/ 656.3 [ 9 × 4 / 9 - 4 ]

R = 1.097 × 10⁷ m⁻¹

Therefore the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹

a 5-ton bus stopped on a ramp at a 30-degree angle. What is the friction force with the ground, in newtons, to keep it from sliding down the slope?

Answers

Answer:

2500 N

Explanation:

Draw a free body diagram of the bus.  There are three forces:

Weight force mg pulling down,

Normal force N pushing perpendicular to the ramp,

and friction force F pushing parallel to the ramp.

Sum of forces in the parallel direction:

∑F = ma

F − mg sin θ = 0

F = mg sin θ

F = (5000 N) (sin 30°)

F = 2500 N

The atomic mass number of copper is A=64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the atoms left behind are in a cubic crystal lattice. What is the smallest distance between two copper atoms?

Answers

Answer:

0.228 nm

Explanation:

Atomic mass number of copper = 64

but an atomic mass unit = 1.66 x 10^-27 kg

therefore, the mass of the copper atom m = 64 x 1.66 x 10^-27 kg = 1.06 x 10^-25 kg

The number of atoms in this mass n = ρ/m

where ρ is the density of copper = 8.96 x 10^3 kg/m^3

==> n = (8.96 x 10^3)/(1.06 x 10^-25) = 8.45 x 10^28 atoms/m^3

We know that the volume occupied by this amount of atoms n = [tex]a^{3}[/tex]

where a is the lattice constant

equating, we have

8.45 x 10^28 = [tex]a^{3}[/tex]

a = 4.389 x 10^9

we also know that

d =  1/a

where d is the smallest distance between the two copper atom.

d = 1/(4.389 x 10^9) = 2.28 x 10^-10 m

==> 0.228 nm

An electron and a 0.033 0-kg bullet each have a velocity of magnitude 495 m/s, accurate to within 0.010 0%. Within what lower limit could we determine the position of each object along the direction of the velocity

Answers

Answer:

1.170*10^-3 m

3.23*10^-32 m

Explanation:

To solve this, we apply Heisenberg's uncertainty principle.

the principle states that, "if we know everything about where a particle is located, then we know nothing about its momentum, and vice versa." it also can be interpreted as "if the uncertainty of the position is small, then the uncertainty of the momentum is large, and vice versa"

Δp * Δx = h/4π

m(e).Δv * Δx = h/4π

If we make Δx the subject of formula, by rearranging, we have

Δx = h / 4π * m(e).Δv

on substituting the values, we have

for the electron

Δx = (6.63*10^-34) / 4 * 3.142 * 9.11*10^-31 * 4.95*10^-2

Δx = 6.63*10^-34 / 5.67*10^-31

Δx = 1.170*10^-3 m

for the bullet

Δx = (6.63*10^-34) / 4 * 3.142 * 0.033*10^-31 * 4.95*10^-2

Δx = 6.63*10^-34 / 0.021

Δx = 3.23*10^-32 m

therefore, we can say that the lower limits are 1.170*10^-3 m for the electron and 3.23*10^-32 for the bullet

Two identical resistors were connected in parallel and their equivalent resistance was
4 ohm. If the two resistors were connected in series, then their equivalent resistance
(in ohm) would be:
Select one:
a. 30
b.4
c. 16
d. 8
O e. 2
Å

Answers

Answer:

C

Explanation:

Rt= total resistance

we know that 1/Rt=1/R1+1/R2(from ohm's law)

Since, Rt=4 and R1=R2

we will get,

1/4=2/R2

R2=8

when in series Rt=R1+R2,

So, Rt=8+8=16 ohm's

If the two resistors are connected in series, then their equivalent resistance (in ohm) will be 16 ohms

The correct answer to the question is Option C. 16 ohms

Fact from the question

Since the two resistors are identical, then

R₁ = R₂

Determination of the two resistors

•Equivalent resistance (Rₜ) = 4 Ohms

Resistor 1 (R₁) = Resistor 2 (R₂) =?

In parallel connection,

Rₜ = (R₁ × R₂) / (R₁ + R₂)

4 = (R₁ × R₁) / (R₁ + R₁)

4 = R₁² / 2R₁

4 = R₁ / 2

Cross multiply

R₁ = 4 × 2

R₁ = 8 Ohms

Thus,

R₂ = R₁ = 8 Ohms

Determination of the equivalent resistance in series

•Resistor 1 (R₁) = 8 Ohms

•Resistor 2 (R₂) = 8 Ohms

•Equivalent resistance (Rₜ) =?

In series connection,

Rₜ = R₁ + R₂

Rₜ = 8 + 8

Rₜ = 16 Ohms

Thus, the correct answer to the question is Option C. 16 ohms

Learn more about arrangement of resistors:

https://brainly.com/question/9476617

g If the momentum of an electron doubles, by what factor would its de Broglie wavelength be multiplied

Answers

Explanation:

The de broglie wavelength is given by :

[tex]\lambda=\dfrac{h}{p}[/tex]

Here,

h is Planck's constant

p is momentum

Momentum and De-Broglie wavelength has inverse relationship. If momentum of an electron double, its wavelength gets half.

Which is one physical property that all stars have

Answers

Answer:

Star characteristics consider physical characteristics such as stellar mass, size, surface temperature, and luminosity .

Answer:

They are made of gases.

Explanation:

Edg 2020

3 holits = 5 gorfs
7 gorfs = 2 queets
How many queets are there in 43 holits?

Answers

Explanation:

43 holits × (5 gorfs / 3 holits) × (2 queets / 7 gorfs) ≈ 20.5 queets

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