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
If during the submerged weighing procedure air bubbles were to adhere to the object, how would the experimental results be affected
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
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 = 14A 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
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?
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
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?
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?
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?
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
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
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 questionSince 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
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
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?
Explanation:
43 holits × (5 gorfs / 3 holits) × (2 queets / 7 gorfs) ≈ 20.5 queets