The concept of this question can be well understood by listing out the parameters given.
The mass of the block = 51 g = 51 × 10⁻³ kgThe distance of the block from the table = 30 cmLength of the spring = 30 cmThe purpose is to determine the spring constant.
Let us assume that the two blocks are Block A and Block B.
At point A on block A, the initial velocity on the block is zero
i.e. u = 0
We want to determine the time it requires for Block A to reach the table. The can be achieved by using the second equation of motion which can be expressed by using the formula.
[tex]\mathsf{S = ut + \dfrac{1}{2}gt^2}[/tex]
From the above formula,
The distance (S) = 30 cm; we need to convert the unit to meter (m).
Since 1 cm = 0.01 mThen, 30cm = 0.3 mThe acceleration (g) due to gravity = 9.8 m/s²
∴
inputting the values into the equation above, we have;
[tex]\mathsf{0.3 = (0)t + \dfrac{1}{2}*(9.80)*(t^2)}[/tex]
[tex]\mathsf{0.3 = \dfrac{1}{2}*(9.80)*(t^2)}[/tex]
[tex]\mathsf{0.3 =4.9*(t^2)}[/tex]
By dividing both sides by 4.9, we have:
[tex]\mathsf{t^2 = \dfrac{0.3}{4.9}}[/tex]
[tex]\mathsf{t^2 = 0.0612}[/tex]
[tex]\mathsf{t = \sqrt{0.0612}}[/tex]
[tex]\mathbf{t =0.247 \ seconds}[/tex]
However, block B comes to an instantaneous rest on point C. This is achieved by the dropping of the block on the spring. During this process, the spring is compressed and it bounces back to oscillate in that manner. The required time needed to get to this point C is half the period, this will eventually lead to the bouncing back of the block with another half of the period, thereby completing a movement of one period.
By applying the equation of the time period of a simple harmonic motion.
[tex]\mathbf{T = 2 \pi \sqrt{\dfrac{m}{k}}}[/tex]
where the relation between time (t) and period (T) is:
[tex]\mathsf{t = \dfrac{T}{2}}[/tex]
T = 2t
T = 2(0.247)
T = 0.494 seconds
[tex]\mathbf{T = 2 \pi \sqrt{\dfrac{m}{k}}}[/tex]
By making the spring constant (k) the subject of the formula:
[tex]\mathbf{\dfrac{T}{2 \pi } = \sqrt{ \dfrac{m}{k}}}[/tex]
[tex]\Big(\dfrac{T}{2 \pi }\Big)^2 = { \dfrac{m}{k}[/tex]
[tex]\dfrac{T^2}{(2 \pi)^2 }= { \dfrac{m}{k}[/tex]
[tex]\mathsf{ T^2 *k = 2 \pi^2*m} \\ \\ \mathsf{ k = \dfrac{2 \pi^2*m}{T^2}}[/tex]
[tex]\mathsf{ k =\Big( \dfrac{(2 \pi)^2*(51 \times 10^{-3})}{(0.494)^2} \Big) N/m}[/tex]
[tex]\mathbf{ k =8.25 \ N/m}[/tex]
Therefore, we can conclude that the spring constant between the two 51 g blocks held at a distance 30 cm above a table as a result of instantaneous rest caused by the compression of the spring is 8.25 N/m.
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Suppose a 60-turn coil lies in the plane of the page in a uniform magnetic field that is directed out of the page. The coil originally has an area of 0.325 m2. It is stretched to have no area in 0.100 s. What is the magnitude (in V) and direction (as seen from above) of the average induced emf if the uniform magnetic field has a strength of 1.60 T
Answer:
emf = 312 V
Explanation:
In this exercise the electromotive force is asked, for which we must use Faraday's law
emf = [tex]- N \frac{d \Phi }{dt}[/tex]- N dfi / dt
Ф = B. A = B A cos θ
bold type indicates vectors.
They indicate that the magnetic field is constant, the angle between the normal to the area and the magnetic field is parallel by local cosine values 1
It also indicates that the area is reduced from a₀ = 0.325 me² to a_f = 0 in a time interval of ΔT = 0.100 s, suppose that this reduction is linear
emf = -N B [tex]\frac{dA}{dT}[/tex]
emf = - N B (A_f - A₀) / Dt
we calculate
emf = - 60 1.60 (0 - 0.325) /0.100
emf = 312 V
The direction of this voltage is exiting the page
A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of the momentum change of the lighter fragment is A) 25 times as great as the momentum change of the heavier fragment. B) The same as the momentum change of the heavier fragment. C) 1/25 as great as the momentum change of the heavier fragment. D) 5 times as great as the momentum change of the heavier fragment. E) 1/4 as great as the momentum change of the heavier fragment.
Answer:
B) The same as the momentum change of the heavier fragment.
Explanation:
Since the initial momentum of the system is zero, we have
0 = p + p' where p = momentum of lighter fragment = mv where m = mass of lighter fragment, v = velocity of lighter fragment, and p' = momentum of heavier fragment = m'v' where m = mass of heavier fragment = 25m and v = velocity of heavier fragment.
0 = p + p'
p = -p'
Since the initial momentum of each fragment is zero, the momentum change of lighter fragment Δp = final momentum - initial momentum = p - 0 = p
The momentum change of heavier fragment Δp' = final momentum - initial momentum = p' - 0 = p' - 0 = p'
Since p = -p' and Δp = p and Δp' = -p = p ⇒ Δp = Δp'
So, the magnitude of the momentum change of the lighter fragment is the same as that of the heavier fragment.
So, option B is the answer
Two loudspeakers are placed 1.8 m apart. They play tones of equal frequency. If you stand 3.0 m in front of the speakers, and exactly between them, you hear a minimum of intensity. As you walk parallel to the plane of the speakers, staying 3.0 m away, the sound intensity increases until reaching a maximum when you are directly in front of one of the speakers. The speed of sound
The question is incomplete. The complete question is :
Two loudspeakers are placed 1.8 m apart. They play tones of equal frequency. If you stand 3.0 m in front of the speakers, and exactly between them, you hear a minimum of intensity. As you walk parallel to the plane of the speakers, staying 3.0 m away, the sound intensity increases until reaching a maximum when you are directly in front of one of the speakers. The speed of sound in the room is 340 m/s.
What is the frequency of the sound?
Solution :
Given :
The distance between the two loud speakers, [tex]d = 1.8 \ m[/tex]
The speaker are in phase and so the path difference is zero constructive interference occurs.
At the point [tex]D[/tex], the speakers are out of phase and so the path difference is [tex]$=\frac{\lambda}{2}$[/tex]
Therefore,
[tex]$AD-BD = \frac{\lambda}{2}[/tex]
[tex]$\sqrt{(1.8)^2+(3)^2-3} =\frac{\lambda}{2}$[/tex]
[tex]$\lambda = 2 \times 0.4985$[/tex]
[tex]$\lambda = 0.99714 \ m$[/tex]
Thus the frequency is :
[tex]$f=\frac{v}{\lambda}$[/tex]
[tex]$f=\frac{340}{0.99714}$[/tex]
[tex]f=340.9744[/tex] Hz
Choose the appropriate explanation how such a low value is possible given Saturn's large mass - 100 times that of Earth.
a. This low value is possible because the magnetic field of Saturn is so strong.
b. This low value is possible because the magnetic field of Saturn is so weak.
c. This low value is possible because the density of Saturn is so high.
d. This low value is possible because the density of Saturn is so low.
Answer:
Explanation:
That is an amazing fact.
The minus sign is what you have to pay attention to. The earth has a mass of 100 times that of Saturn. As someone on here once noted, Saturn has such a low density that it would float in water.
The answer is D
A kind of variable that a researcher purposely changes in investigation is
Answer:
independent variable
Explanation:
27. The part of the Earth where life exists .
Mesosphere
Stratosphere
Troposphere
Biosphere
Answer:
Biosphere is the part of the earth where life exists.
What is the name of the compound br8P4
Answer:
Octabromine tetraphosphide
Explanation:
This compound has in its formula:
- Eight bromines
- Four phosphorous
8 → octa prefix
4 → tetra prefix
Right answer is Octabromine tetraphosphide
A student of mass 50kg takes 15seconds to run up a flight of 50 steps. If each step is 20cm, calculate the potential energy of the student at the maximum height
Answer:
the answer is 49000 joules at the maximum height
Explanation:
we know the mass (50kg)
we know the acceleration due to gravity(9.8m/s²)
we know the height too(maximum height meaning the 50th step so we multiply 50 with 20cm as each step is 20 cm and we get 1000 cm, convert to m it is 100 m
the formula is potential energy=mgh
m for mass
g for acceleration due to gravity
h for height
multiply them
50x9.8x100
we get 49000
the unit of potential energy is joules so the answer is
49000 joules
Answer:
49000 joules
Explanation:
hope it helpss
A force of 200 N, acting at 60° to the horizontal, accelerates a block of mass 50 kg along a horizontal plane. Calculate the component of the 200N force that accelerates the block horizontally
Answer:
Explanation:
a) Fx = F cos (θ)
= (200) cos(60)
= 100 N
b) FR = ma
Fx + Ff = ma
100 + Ff = (50)(1,5)
Ff = 75 - 100
= -25 N
c) Fy = F sin θ
= (200) sin(60)
= 173,2 N
Two loudspeakers, 5.5 m apart and facing each other, play identical sounds of the same frequency. You stand halfway between them, where there is a maximum of sound intensity. Moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.25 m . Assume the speed of sound is 340 m/s.
Required:
a. What is the frequency of the sound?
b. If the frequency is then increased while you remain 0.21 m from the center, what is the first frequency for which that location will be a maximum of sound intensity?
c.
Solution :
Let [tex]$d_1=\frac{5.5}{2}[/tex]
= 2.75 m
[tex]d_2 = 0.21 \ m[/tex]
And [tex]$d=|d_1-d_2|$[/tex]
[tex]$d=(d_1+d_2) - (d_1-d_2)$[/tex]
[tex]$d=(2.75+0.21) - (2.75-0.21)$[/tex]
[tex]$d = 2.96-2.54$[/tex]
[tex]d = 0.42 \ m[/tex]
a). At minimum,
[tex]$d=\frac{\lambda}{2}$[/tex]
[tex]$\lambda = 2d$[/tex]
= 2 x 0.42
= 0.84 m
Frequency, [tex]$\nu = \frac{v}{\lambda}$[/tex]
[tex]$=\frac{340}{0.84}$[/tex]
= 404.76 Hz
Therefore, the frequency of he sound, [tex]$\nu$[/tex] = 404.76 Hz
b). At maximum, λ = d = 0.42 m
Therefore, the frequency, [tex]$\nu = \frac{v}{\lambda}[/tex]
[tex]$=\frac{350}{0.42}$[/tex]
= 809.52 Hz
A smooth circular hoop with a radius of 0.400 m is placed flat on the floor. A 0.325-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 8.50 m/s. After one revolution, its speed has dropped to 5.50 m/s because of friction with the floor.
(a) Find the energy transformed from mechanical to internal in the particle "hoop" floor system as a result of friction in one revolution.
(b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.
Answer:
a) W = - 6.825 J, b) θ = 1.72 revolution
Explanation:
a) In this exercise the work of the friction force is negative and is equal to the variation of the kinetic energy of the particle
W = ΔK
W = K_f - K₀
W = ½ m v_f² - ½ m v₀²
W = ½ 0.325 (5.5² - 8.5²)
W = - 6.825 J
b) find us the coefficient of friction
Let's use Newton's second law
fr = μ N
y-axis (vertical) N-W = 0
fr = μ W
work is defined by
W = F d
the distance traveled in a revolution is
d₀ = 2π r
W = μ mg d₀ = -6.825
μ = [tex]\frac{ -6.825}{d_o \ mg}[/tex]
The total work as the object stops the final velocity is zero v_f = 0
W = 0 - ½ m v₀²
W = - ½ 0.325 8.5²
W = - 11.74 J
μ mg d = -11.74
we subtitle the friction coefficient value
( [tex]\frac{-6.8525 }{d_o mg}[/tex]) m g d = -11.74
6.825 [tex]\frac{d}{d_o}[/tex] = 11.74
d = 11.74/6.825 d₀
d = 1.7201 2π 0.400
d = 4.32 m
this is the total distance traveled, the distance and the angle are related
θ = d / r
θ = 4.32 / 0.40
θ = 10.808 rad
we reduce to revolutions
θ = 10.808 rad (1rev / 2π rad)
θ = 1.72 revolution
As a roller coaster car crosses the top of a 40-m-diameter loop-the-loop, its apparent weight (the normal force) is the same magnitude as the car's weight. What is the car's speed at the top?
Answer:
40 because if it is the same weight then there is no weight to make the ride slower so it 40
Explanation:
Paramagnetism is closely associated with: A. the tendency of electron dipole moments to align with an applied magnetic field B. the force exerted by electron dipole moments on each other C. the exchange force between electrons D. the tendency of electron dipole moments to align opposite to an applied magnetic field
Answer:
the tendency of electron dipole moments to align with an applied magnetic field
Explanation:
Paramagnetism has to do with possession of unpaired electrons. Substances that possess unpaired electrons are said to be paramagnetic.
When an external magnetic field is applied to a paramagnetic substance, the magnetic field causes the electrons spins of the paramagnetic substance to align parallel to the field,which leads to a net attraction.
Hence, paramagnetism is closely associated with the tendency of electron dipole moments to align with an applied magnetic field.
Convert 385k to temperature of
Answer:
233.33°F
Explanation:
(385K - 273.15) * 9/5 + 32 = 233.33°F
A 5.85-mm-high firefly sits on the axis of, and 13.7 cm in front of, the thin lens A, whose focal length is 5.01 cm. Behind lens A there is another thin lens, lens B, with focal length 25.9 cm. The two lenses share a common axis and are 62.5 cm apart. 1. Is the image of the firefly that lens B forms real or virtual?
a. Real
b. Vrtual
2. How far from lens B is this image located (expressed as a positive number)?
3. What is the height of this image (as a positive number)?
4. Is this image upright or inverted with respect to the firefly?
a. Upright
b. Inverted
Answer:
1. The image is real
2. 5.85
3. h' = 3.05 mm
4. The image is upright
Explanation:
1. Start with the first lens and apply 1/f = 1/p + 1/q
1/5.01 = 1/13.7 + 1/q
q = 7.90 cm
Since that distance is behind the first lens, and the second lens is 62.5 cm behind the first lens, that distance is 62.5 - 7.90 = 54.6 cm in front of the second lens, and becomes the object for that lens, thus,
1/25.9 = 1/54.6 + 1/q
q = 49.3 cm behind the second lens
Using that information, since q is positive, the image is real
2. Also, using that information, you have the second answer, which is 49.3 cm
The height can be found from the two magnifications.
m = -q/p
m1 = -7.9/13.7 = -.577
m2 = -49.3/54.6 = -.903
Net m = (-.577)(-.903) = .521
Then, m = h'/h
.521 = h'/5.85
3. h' = 3.05 mm
4. For the fourth answer, since the overall magnification is positive, the final image is upright
what is science ? what qualities do we deal in deal in physic ?
science is all about the world around us
As the speed of a particle approaches the speed of light, the momentum of the particle Group of answer choices approaches zero. decreases. approaches infinity. remains the same. increases.
Answer:
approaches infinity
Explanation:
There are two momentums, the classical momentum which is equal to the product of mass and velocity, and the relativistic momentum, the one we should look at when we work with high speeds, and this happens because massive objects have a speed limit, in this case, we are approaching the speed of light, so we need to work with the relativistic momentum instead of the classical momentum.
The relativistic momentum can be written as:
[tex]p = \frac{1}{\sqrt{1 - \frac{u^2}{c^2} } } *m*u[/tex]
where
u = speed of the object relative to the observer, in this case we have that u tends to c, the speed of light.
m = mass of the object
c = speed of light.
So, as u tends to c, we will have:
[tex]\lim_{u \to c} p = \frac{1}{\sqrt{1 - \frac{u^2}{c^2} } } *m*u[/tex]
Notice that when u tends to c, the denominator on the first term tends to zero, thus, the relativistic momentum of the object will tend to infinity.
Then the correct option is infinity, as the particle speed approaches the speed of light, the relativistic momentum of the particle tends to infinity.
basic source of magnetism is a) charged particles alone b)Movement of charged particles c) Magnetic dipoles d)magnetic domains
Answer:
C . Magnetic dipoles is the correct
Answer:
b). movement of charged particles.
Explanation:
These charges create the nagnetic dipoles.
Calculate the electric field at point A, located at coordinates (0 m, 12.0 m ). Give the x and y components of the electric field as an ordered pair. Express your answer in newtons per coulomb to three significant figures.
Answer:
The correct answer is "[tex](0,300\times 10^{-3} \ N/C)[/tex]".
Explanation:
The given problem seems to be incomplete. Please find the attachment of the complete query.
According to the question,
At point A, we have
⇒ [tex]E_x = \frac{k q_1}{d_1^2} Cos \theta_1 - \frac{k q_2}{d_2^2} Cos \theta_2[/tex]
or,
⇒ [tex]E_x = 9\times 10^9\times [\frac{6\times 10^{-9}}{15^2}\times \frac{9}{15}-\frac{8\times 10^{-9}}{20^2}\times \frac{16}{20} ][/tex]
[tex]=0[/tex]
and,
⇒ [tex]E_y = \frac{kq_1}{d_1^2}Sin \theta_1 +\frac{kq_2}{d_2^2}Sin \theta_2[/tex]
or,
⇒ [tex]E_y = 9\times 10^9\times [\frac{6\times 10^{-9}\times 12}{15^2\times 15}+ \frac{8\times 10^{-9}\times 12}{20^2\times 20} ][/tex]
[tex]=0.3 \ N/C[/tex]
Which term defines seeking some way of achieving a goal by overcoming obstacles or finding an answer to a question?
Answer:
Problem solving
hope this helps :)
What computer measures physical quantities?
Answer:
Three Types of Computer The Computer are classified into three main types:: • Analog Computers • Digital Computers • Hybrid Computers (Analog + Digital) Analog Computers:: Analog Computer measures “Physical Quantities” for example Temperature, Voltage, Pressure, and Electric Current.
Thorium-232 goes through multiple types of decay in order to reach a stable isotope. What isotope is created after the first two decays if it first goes through an alpha decay and then a beta decay?
A)uranium-236
B)protactinium-232
C)radon-224
D)Astinium-228
Answer:
The answer would be D), if the decay is beta negative.
Explanation:
Thorium-232 goes through alpha decay:
Thorium-232 --> Helium-4 + Radium-228
Radium-228 then can undergo beta positive or beta negative decay:
Beta positive = Radium-228 --> Electron + Francium-228
Beta negative = Radium-228 --> Positron + Actinium-228
Therefore, the isotope that is created is Actinium-228
if a projectile travels in the air for 6 seconds when does the projectile reach its highest point
This question deals with projectile motion, which is a motion on both the x-axis and y-axis, simultaneously. The total time of flight of the projectile trajectory is given, while the time to reach the highest point of the projectile is required to be found.
The projectile will reach the highest point in "3 seconds".
The total time of flight of a projectile is the time during which the projectile remains in the air. For a projectile motion that ends up on the same horizontal level, from where it started, the time to reach the highest point, is equal to half of the total time of flight.
In other words, the projectile motion takes the same time, to go from the starting level to the highest point (i.e upward motion), as the time taken to reach the starting level from the highest point (i.e downward motion).
[tex]t = \frac{1}{2}T[/tex]
where,
t = time to reach the highest point = ?
T = total time of flight = 6 seconds
Therefore,
[tex]t - \frac{1}{2}(6\ seconds)[/tex]
t = 3 seconds
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A ring with an 18mm diameter falls off a scientist's finger into the solenoid in the lab. The solenoid is 25 cm long, 5.0 cm in diameter and has 1500 turns. When turned on, the current in the solenoid is increases linearly to 20 A in 1 second. What is the induced emf in the ring?
a) 2.0 x 10-5 v
b) 3.8 x 10-5 v
c) 1.2 x 10-3 v
d) 1.9 x 10-4 v
Answer:
the answer should be b) 3.8 x 10-5 v
A mountain biker takes a jump in a race and goes airborne. The mountain bike is travelling at 10.0 m/s before it goes airborne. If the mass of the front wheel on the bike is 750 g and has radius 35 cm, what is the angular momentum of the spinning wheel in the air the moment the bike leaves the ground?
Answer:
Explanation:
The formula for angular momentum is
L = mvr where L is the angular momentum, m is the mass of the object, v is the velocity of the object, and r is the radius of the object. The problem we have that prevents us from just throwing those numbers in there is that mass has to be in kg and it's not, and radius has to be in meters and it's not.
Changing the mass to kg:
750 g = .750 kg
Changing the radius to m:
35 cm = .35 m
Now we can fill in the variables with their respective values:
L = .750(10.0)(.35) gives us
[tex]L=2.625\frac{kg*m^2}{s}[/tex]
Physics question plz help ASAP
What improvements were made in measuring system with the introduction of standard units?
Answer:
Standard units are commonly used units of measurement, which help us measure length, height, weight, temperature, mass and more. These units are standardised, which means that everyone gets the same understanding of the size, weight and other properties of objects and things.
Explanation:
In order to test an intentionally weak adhesive, the bottom of the small 0.15-lb block is coated with adhesive and then the block is pressed onto the turntable with a known force. The turntable starts from rest at t = 0 and uniformly accelerates with a = 2 rad/s^2. If the adhesive fails at exactly t = 3 s, then determine:
a. the magnitude of the ultimate shear force that the adhesive supports
b. the angular displacement of the turntable at the time of failure
Answer:
answer
Explanation:
it is the answer which was presented in the year
Two resistances, R1 and R2, are connected in series across a 12-V battery. The current increases by 0.500 A when R2 is removed, leaving R1 connected across the battery. However, the current increases by just 0.250 A when R1 is removed, leaving R2 connected across the battery.
(a) Find R1.
Ω
(b) Find R2.
Ω
Answer:
a) R₁ = 14.1 Ω, b) R₂ = 19.9 Ω
Explanation:
For this exercise we must use ohm's law remembering that in a series circuit the equivalent resistance is the sum of the resistances
all resistors connected
V = i (R₁ + R₂)
with R₁ connected
V = (i + 0.5) R₁
with R₂ connected
V = (i + 0.25) R₂
We have a system of three equations with three unknowns for which we can solve it
We substitute the last two equations in the first
V = i ( [tex]\frac{V}{ i+0.5} + \frac{V}{i+0.25}[/tex] )
1 = i ( [tex]\frac{1}{i+0.5} + \frac{1}{i+0.25}[/tex] )
1 = i ( [tex]\frac{i+0.5+i+0.25}{(i+0.5) \ ( i+0.25) }[/tex] ) = [tex]\frac{i^2 + 0.75i}{i^2 + 0.75 i + 0.125}[/tex]
i² + 0.75 i + 0.125 = 2i² + 0.75 i
i² - 0.125 = 0
i = √0.125
i = 0.35355 A
with the second equation we look for R1
R₁ = [tex]\frac{V}{i+0.5}[/tex]
R₁ = 12 /( 0.35355 +0.5)
R₁ = 14.1 Ω
with the third equation we look for R2
R₂ = [tex]\frac{V}{i+0.25}[/tex]
R₂ =[tex]\frac{12}{0.35355+0.25}[/tex]
R₂ = 19.9 Ω
the lamp cord is 85cm long and comprises cupper wire. Calculate the wire‘s resistance?
radius of a wire is 1.8mmm,Use value of resistivity for Cu as 1.75 × 10-8Ωm.
Answer:
R = 0.0015Ω
Explanation:
The formula for calculating the resistivity of a material is expressed as;
ρ = RA/l
R is the resistance
ρ is the resistivity
A is the area of the wire
l is the length of the wire
Given
l = 85cm = 0.85m
A = πr²
A = 3.14*0.0018²
A = 0.0000101736m²
ρ = 1.75 × 10-8Ωm.
Substitute into the formula
1.75 × 10-8 = 0.0000101736R/0.85
1.4875× 10-8 = 0.0000101736R
R = 1.4875× 10-8/0.0000101736
R = 0.0015Ω