The energy required to heat 40.7 g of water (H2O) from -10°C to 70°C can be calculated as follows;Mass of water = 40.7 gTemperature change = 70 - (-10) = 80 °C Specific heat of ice = 2.06 J/g °CSpecific heat of water = 4.18 J/g °CHeat of fusion of water = 334 J/gAt first, we have to heat the ice from -10°C to 0°C using the formula;
q = mcΔTwhere m is the mass, c is the specific heat, and ΔT is the temperature change. For ice, c = 2.06 J/g °C, and the temperature change is 0 - (-10) = 10°C;
q1 = (40.7 g)(2.06 J/g °C)(10°C) = 839.42 J
This amount of heat energy is needed to bring the ice to its melting point. The amount of heat required to melt the ice at 0°C can be determined using the formula; q2 = mLfwhere Lf is the heat of fusion of ice, which is 334 J/g;
q2 = (40.7 g)(334 J/g) = 13590.8 J
Now, we have 40.7 g of water at 0°C.
To heat this water to 70°C, we use the formula;
q3 = mcΔT
where m is the mass, c is the specific heat, and ΔT is the temperature change. For water, c = 4.18 J/g °C, and the temperature change is 70 - 0 = 70°C;
q3 = (40.7 g)(4.18 J/g °C)(70°C) = 12123.94 J
The total energy required is;
\(q_total = q1 + q2 + q3 = 839.42 J + 13590.8 J + 12123.94 J = 26554.16 J\)
Thus, the energy required to heat 40.7 g of water (H2O) from −10∘C to \(70∘C is 2.66 x 10^4 J or 26.6 kJ\).
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Determine the acceleration of a car of mass 900 kg, when a net force of 2700 N acts on it.
Label the atmosphere layers of a star
Answer:
The layers of a star's atmosphere can include the photosphere, the chromosphere, and the corona. The photosphere is the layer of the star's atmosphere that is visible to us and is the source of the star's light. The chromosphere is the layer above the photosphere and is characterized by its reddish color. The corona is the outermost layer of the star's atmosphere and is characterized by its high temperatures.
Explanation:
5. What structure did Friedrich Kekule discover that allowed carbon atoms can bond
with up to four other atoms at the same time?
The figure shows a uniform, horizontal beam of length = 7 m and mass = 50 kg that ishanging by two cables as shown. If a person of mass = 60 kg stands at 3.6 m from the leftend, what are the tensions (T1 and T2) in the cables? Write only the answer to T2 incanvas (in newtons).T1T2
Given:
• Length of beam = 7 m
,• Mass of beam = 50 kg
,• Mass of person = 60 kg
,• Distance of the person from the left = 3.6 m
Let's find the tensions, T1 and T2.
First make a free body sketch:
Here, the net torque = 0.
To find the tension, T1, we have:
\(T_1*l-m_Pg*(l-l_1)-m_bg*\frac{l}{2}=0\)Where:
l = 7 m
mp = 60 kg
g is acceleration due to gravity = 9.8 m/s²
l1 = 3.6 m
mb = 50 kg
Thus, we have:
\(\begin{gathered} T_1*7-60*9.8*(7-3.6)-50*9.8*\frac{7}{2}=0 \\ \\ T_1*7-1999.2-1715=0 \\ \\ T_1=\frac{3714.2}{7} \\ \\ T_1=530.6\text{ N} \\ \end{gathered}\)Therefore, the tension T1 = 530.6 N.
To find the tension T2, we have:
\(\begin{gathered} T_2*7-60*9.8*3.6-50*9.8*3.5=0 \\ \\ T_2*7-2116.8-1715=0 \\ \\ T_2*7=2116.8+1715 \\ \\ T_2=\frac{2116.8+1715}{7} \\ T_2=547.4\text{ N} \\ \end{gathered}\)Thererfore the tension T2 = 547.5 N
• ANSWER:
T1 = 530.6 N
T2 = 547.4 N
why are unit of length mass and time independent with each other?
2. What is the power rating of an engine capable of lifting a 100 kg object 5 m vertically
in 4 seconds?
Given values are:
Force,
f = 100Time,
t = 4 secondsNow,
→ \(Work \ done= f\times d\)
\(= 100\times 50\)
\(= 500\)
hence,
The power will be:
= \(\frac{Work}{time}\)
= \(\frac{500}{4}\)
= \(125 \ watt\)
Thus the response above is right.
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Two objects collide. One of the objects deforms upon collision. What type of collision is this?
Select one:
A: Elastic collision, because energy is used to defom the object.
B: Inelastic collision, because energy is conserved.
C: Inelastic collision, because kinetic energy was lost when the object was deformed.
D: Elastic collision, because momentum is conserved.
Answer:
D Elastic collision because momentum is conserved
Explanation:
this is the answer may i be marked brainliest?
what is the greatest distance (in degrees) that a star can be from polaris and still be circumpolar as seen from philadelphia pa (latitude 40.0 °)
A star is considered circumpolar if it remains above the horizon throughout the entire night. The greatest distance that a star can be from Polaris, the North Star, and still be circumpolar is 50°.
Circumpolar stars are those that do not set below the horizon but instead appear to revolve around the celestial pole. In the northern hemisphere, Polaris serves as the North Star, located very close to the celestial north pole.
For a star to be circumpolar as seen from Philadelphia (latitude 40.0°), it must remain above the horizon at all times during the night.
The distance between Polaris and the celestial pole is equivalent to the observer's latitude. In this case, since the latitude of Philadelphia is 40.0°, any star within 40.0° of Polaris will be circumpolar.
Therefore, the greatest distance a star can be from Polaris and still be circumpolar is 40.0° + 10.0° (as the North Star is approximately 10.0° away from the celestial pole), giving a total of 50.0°.
Any star within this range, up to 50.0° from Polaris, will never dip below the horizon and will remain visible throughout the entire night as a circumpolar star.
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18. Which would be the most reliable source of information to use for a history report? (2 points)
O An encyclopedia
O A magazine article
O A newspaper
A TV show
Answer:
encyclopedia most reliable I think
Calculate What is the change in speed of the P
wave as it goes from the mesosphere to the outer
core? From the outer core to the inner core?
lithc
asthenosphere
What are fossil fuels made from?
A. Radioactive Material
B. Harmful Poisons
C. Organic Material
D. Non-Organic Material
Answer:
organic material
Explanation:
two windmills stand on a field 456 feet apart. a cow is in the field, 320 feet from one windmill and 210 feet from the other. what is the measure of theta?
The cosine rule is used to determine the values of unknown aides and angles in a triangle
The measure of θ is approximately 117.2°
Reason:
Given parameters are;
The distance between the two windmills, a = 456 feet
The distance between the cow and one of the windmills, b = 320 feet
Distance between the cow and the other windmills, c = 210 feet
Required, the angle θ between b, and c direction
Solution;
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(θ)
\(cos (\theta) = \dfrac{b^2 + c^2 - a^2}{2 \cdot b \cdot c }\)Which gives;
\(cos (\theta) = \dfrac{320^2 + 210^2 - 456^2}{2 \times 320 \times 210 }\)
\(\theta = arcos \left(\dfrac{320^2 + 210^2 - 456^2}{2 \times 320 \times 210 }\right) \approx 117.2 ^{\circ}\)The measure of θ ≈ 117.2°
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A wheel is being turned to open a valve on a compressor. The resistance that is applied to the axle of the valve is 235 lb. The diameter of the wheel that is being turned is 20in and an effort force of 45 lb is being applied to the wheel. What is the required diameter of the axle to overcome the resistance force
Answer:
3.8 in
Explanation:
A wheel and axle machine is a machine in which the wheel rotates around the rod (axle). They rotate together thereby transferring force among each other.
The formula for a wheel and axle is:
Fr * Rr = Fe * Re
Where Fr is the resistance force, Rr is the radius of the resistance force, Fe is the effort force and Re is the radius of the resistance force.
Given that: Fr = 235 lb, Fe = 45 lb, Re = 20 in / 2 = 10 in. Hence:
235 * Rr = 45 * 10
Rr = 45 * 10 / 235
Rr= 1.9 in
Diameter of axle = 2 * 1.9 = 3.8 in
Problem 11.14 A woman of mass m stands at the edge of a solid cylindrical platform of mass M and radius R. At t 0, the platform is rotating with negligible friction at angular velocity wo about a vertical axis through its center, and the woman begins walking with speed v (relative to the platform) toward the center of the platform
This can be expressed as,T2 = (M + m)aT1 = Mg/2where,T2−T1= (M + m)a − Mg/2 Solving the above equations will give the value of α and then we can find out the final velocity of the platform.
Here's the solution to the given problem: Let the origin of our coordinate system be located at the center of the platform. We can assume that there is no friction between the platform and the ground. If v Rw, the woman will collide with the center of the platform after the platform stops moving because it is not able to move with the required speed to reach the center of the platform before it stops. The net torque about the origin, assuming that the angular momentum is conserved, is Iα = τ, or, assuming that the angular momentum is conserved,T2−T1=IwoR2wR2+mr2αT2 = Mg/2 + Mv/RT1 = (M + m)g/2Let a be the speed of the platform just after the woman reaches the center, which is given by a = v + αr. This can be expressed as,T2 = (M + m)aT1 = Mg/2where,T2−T1= (M + m)a − Mg/2Solving the above equations will give the value of α and then we can find out the final velocity of the platform.
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A loop of wire is in the shape of two concentric semicircles as shown. (Figure 1) The inner circle has radius a; the outer circle has radius b. A current I flows clockwise through the outer wire and counterclockwise through the inner wire. Part A What is the magnitude, B, of the magnetic field at the center of the semicircles? Express B in terms of any or all of the following: I, a, b, and mu_0.
Answer:
vote me brainliest
Explanation:
The magnitude B of the magnetic field at the center of the semicircles is given by these expression B = (μ₀(I(outer) - I(inner)))/(π(a + b)). The B in terms of the asked variable.
In this case, we have two concentric semicircles, each carrying current in opposite directions. Let's consider a circular loop with radius r, where a < r < b. The magnetic field at the center of this loop will be the sum of the magnetic fields produced by the two semicircles.
For the outer semicircle (radius b), the magnetic field at the center can be calculated as follows:
∮ B · dl = μ₀I(outer)
For the inner semicircle (radius a), the magnetic field at the center has the opposite direction, so the equation becomes:
∮ B · dl = -μ₀I(inner)
Since the circular loop with radius r contains both the inner and outer semicircles, we can add these equations together:
∮ B · dl = μ₀(I(outer) - I(inner))
The line integral ∮ dl represents the circumference of the circular loop, which is 2πr:
B(2πr) = μ₀(I(outer) - I(inner))
B = (μ₀(I(outer) - I(inner)))/(2πr)
In this case, as we are interested in the magnetic field at the center of the semicircles, the radius r would be the average radius between a and b, given by:
r = (a + b)/2
Substituting this value into the equation, we get the final expression for the magnitude B of the magnetic field at the center of the semicircles:
B = (μ₀(I(outer) - I(inner)))/(2π((a + b)/2))
B = (μ₀(I(outer) - I(inner)))/(π(a + b))
Therefore, the magnitude B of the magnetic field at the center of the semicircles is given by B = (μ₀(I(outer) - I(inner)))/(π(a + b)).
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Q.7. For a system with a transfer function of G(s)=- co² s² +2a+w² if the natural frequency is 0.5 and the damping ratio is 1.3, which of the following statements is correct regarding the unit step response of the system?
O A) Damped
O B) Undamped
O C) Underdamped
O D) Crittically Damped
O E) Overdamped
The system described by the transfer function G(s) = -co² s² + 2a + w², with a damping ratio of 1.3 and a natural frequency of 0.5, has an overdamped unit step response. So, the correct option is (E)
The transfer function of the system is given as G(s) = -co² s² + 2a + w², where co represents the damping ratio, a represents an arbitrary constant, and w represents the natural frequency of the system. We are given that the natural frequency is 0.5 and the damping ratio is 1.3.
To determine the type of unit step response, we need to analyze the damping ratio (co) in relation to the critical damping value (co_critical).
The critical damping ratio (co_critical) is defined as the value where the system is on the threshold between being overdamped and underdamped. It is given by the formula co_critical = 2 * sqrt(a * w²).
In our case, the natural frequency (w) is 0.5, so we can calculate co_critical as follows: co_critical = 2 * sqrt(a * 0.5²).
Since the damping ratio (co) is given as 1.3, we can compare it with co_critical to determine the type of unit step response.
If co > co_critical, the system is considered overdamped (Option E).
If co = co_critical, the system is considered critically damped (Option D).
If co < co_critical, the system is considered underdamped (Option C).
Based on the given values, we can determine that the system is overdamped (Option E) because the damping ratio (1.3) is greater than the critical damping ratio.
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A 12 V battery is connected to a resistor, a light bulb, and a buzzer. What are the energy conversions that occur in the circuit?
The energy conservation that occurred in the circuit when a 12 V battery is connected to a resistor, a light bulb, and a buzzer is light energy (light bulb) and to sound energy (buzzer).
What is energy conservation?The principle of energy conservation states that energy can neither be created nor destroyed but can be transferred from one form to another.
When a 12 V battery is connected to a resistor, a light bulb, and a buzzer, the energy conservation that occur in the circuit is light energy (light bulb) and to sound energy (buzzer).
Thus, the energy conservation that occurred in the circuit when a 12 V battery is connected to a resistor, a light bulb, and a buzzer is light energy (light bulb) and to sound energy (buzzer).
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Consider a three-dimensional harmonic oscillator, whose state vector ) is: |) = |az)|a₂) |az) where lar), lay) and laz) are quasi-classical states (cf. Complement Gy) for one- dimensional harmonic oscillators moving along Ox, Oy and Oz, respectively. Let L = Rx P be the orbital angular momentum of the three-dimensional oscillator. a. Prove: (L₂) = iħ (aza-aαv) AL₂ = √/la1² + |a₂|² and the analogous expressions for the components of L along Or and Oy. b. We now assume that: {Lz) = (Ly) =0, (L₂) = Ali> 0 Show that a must be zero. We then fix the value of A. Show that, in order to minimize ALT + ALy, we must choose: ag = -iαy = eivo V₂ (where po is an arbitrary real number). Do the expressions AL.AL, and (AL)²+ (AL)2 in this case have minimum values compatible with the inequalities obtained in question b. of the preceding exercise? c. Show that the state of a system for which the preceding conditions are satisfied is necessarily of the form: |v) = cx (ar) |xnr=k, n₁=0, n₂=0) k with: (a + iat) k |Xn,=k, n=0,1 ,n₁=0, n₂ =0) |4n₂=0, n₁=0, n₂ =0) √2kk! ak Ck (α) e-la/²/2 = √k! ; ar = ¹0 √ (the results of Complement Gy and of § 4 of Complement Dyi can be used). Show that the angular dependence of Xn, k, n=0, n.-0) is (sin ei)k. L2 is measured on a system in the state ). Show that the probabilities of the various possible results are given by a Poisson distribution. What results can be obtained in a measurement of Lz that follows a measurement of L2 whose result was 1(1+1)ħ²? =
This is a multi-part question involving a three-dimensional harmonic oscillator and its angular momentum.
a. The orbital angular momentum operator `L` can be written in terms of the position and momentum operators as `L = r x p`. The squared magnitude of the angular momentum is given by `L^2 = Lx^2 + Ly^2 + Lz^2`. The `z` component of the angular momentum can be written as `Lz = xp_y - yp_x`, where `p_x` and `p_y` are the momentum operators along the `x` and `y` directions, respectively.
Since the state vector `|ψ⟩` is given as a product of quasi-classical states for one-dimensional harmonic oscillators along each axis, we can use the ladder operator formalism to evaluate the action of `Lz` on `|ψ⟩`. The ladder operators for a one-dimensional harmonic oscillator are defined as `a = (x + ip) / √2` and `a† = (x - ip) / √2`, where `x` and `p` are the position and momentum operators, respectively.
Using these definitions, we can write the position and momentum operators in terms of the ladder operators as `x = (a + a†) / √2` and `p = (a - a†) / i√2`. Substituting these expressions into the definition of `Lz`, we get:
`Lz = (xp_y - yp_x) = ((a_x + a_x†) / √2)((a_y - a_y†) / i√2) - ((a_y + a_y†) / √2)((a_x - a_x†) / i√2)`
` = (1/2i)(a_xa_y† - a_x†a_y - a_ya_x† + a_y†a_x)`
` = iħ(a_xa_y† - a_x†a_y)`
where we have used the commutation relation `[a, a†] = 1`.
The action of this operator on the state vector `|ψ⟩` is given by:
`(Lz)|ψ⟩ = iħ(a_xa_y† - a_x†a_y)|αx⟩|αy⟩|αz⟩`
`= iħ(αxa_y† - αya_x†)|αx⟩|αy⟩|αz⟩`
`= iħ(αx - αy)Lz|αx⟩|αy⟩|αz⟩`
where we have used the fact that the ladder operators act on quasi-classical states as `a|α⟩ = α|α⟩` and `a†|α⟩ = d/dα|α⟩`.
Since `(Lz)|ψ⟩ = iħ(αx - αy)Lz|ψ⟩`, it follows that `(Lz)^2|ψ⟩ = ħ^2(αx - αy)^2(Lz)^2|ψ⟩`. Therefore, we have:
`(L^2)|ψ⟩ = (Lx^2 + Ly^2 + Lz^2)|ψ⟩`
`= ħ^2(αx^2 + αy^2 + (αx - αy)^2)(L^2)|ψ⟩`
`= ħ^2(αx^2 + αy^2 + αx^2 - 2αxαy + αy^2)(L^2)|ψ⟩`
`= ħ^2(3αx^2 + 3αy^2 - 4αxαy)(L^2)|ψ⟩`
This shows that `(L^2)|ψ⟩` is proportional to `(L^2)|ψ⟩`, which means that `(L^2)` is an eigenvalue of the operator `(L^2)` with eigenstate `|ψ⟩`. The eigenvalue is given by `(L^2) = ħ^2(3αx^2 + 3αy^2 - 4αxαy)`.
b. If we assume that `(Lz)|ψ⟩ = (Ly)|ψ> = 0`, then from part (a) above it follows that `(Ly)^2|ψ> = ħ^2(3ay^3-4axay+3az²)(Ly)^²|ψ>` and `(Lz)^2|ψ> = ħ^2(3az^3-4axaz+3ay²)(Lz)^²|ψ>`. Since `(Ly)^2|ψ> = (Lz)^2|ψ> = 0`, it follows that `3ay^3-4axay+3az² = 0` and `3az^3-4axaz+3ay² = 0`. Solving these equations simultaneously, we find that `ax = ay = az = 0`.
If we fix the value of `(L^2)`, then from part (a) above it follows that `(L^2) = ħ^2(3αx^2 + 3αy^2 - 4αxαy)`. Since `ax = ay = az = 0`, this equation reduces to `(L^2) = 0`.
To minimize `(Lx)^2 + (Ly)^2`, we must choose `αx` and `αy` such that the expression `3αx^2 + 3αy^2 - 4αxαy` is minimized. This can be achieved by setting `αx = -iαy`, where `αy` is an arbitrary complex number. In this case, the expression becomes `3αx^2 + 3αy^2 - 4αxαy = 6|αy|^2`, which has a minimum value of `0` when `αy = 0`.
c. If the conditions in part (b) are satisfied, then the state vector `|ψ⟩` can be written as a linear combination of eigenstates of the operator `(Lz)^2`. These eigenstates are of the form `|n⟩|m⟩|k⟩`, where `n`, `m`, and `k` are non-negative integers and `|n⟩`, `|m⟩`, and `|k⟩` are eigenstates of the number operator for the one-dimensional harmonic oscillator along each axis.
The action of the ladder operators on these states is given by:
`a_x|n⟩|m⟩|k⟩ = √n|n-1⟩|m⟩|k⟩`
`a_x†|n⟩|m⟩|k⟩ = √(n+1)|n+1⟩|m⟩|k⟩`
`a_y|n⟩|m⟩|k⟩ = √m|n⟩|m-1⟩|k⟩`
`a_y†|n⟩|m⟩|k⟩ = √(m+1)|n⟩|m+1⟩|k⟩`
`a_z|n⟩|m⟩|k⟩ = √k|n⟩|m⟩|k-1⟩`
`a_z†|n⟩|m⟩|k⟩ = √(k+1)|n⟩|m⟩|k+1⟩`
Since we have assumed that `(Lz)|ψ> = (Ly)|ψ> = 0`, it follows that:
`(Lz)|ψ> = iħ(a_xa_y† - a_x†a_y)|ψ> = iħ(∑_n,m,k c_nmk(a_xa_y† - a_x†a_y)|n>|m>|k>)`
`= iħ(∑_n,m,k c_nmk(√n√(m+1)|n-1>|m+1>|k> - √(n+1)√m |n+1>|m-1>|k>))`
`= iħ(∑_n,m,k (c_(n+1)(m+1)k√(n+1)√(m+1) - c_n(m-1)k√n√m)|n>|m>|k>)`
`= 0`
This implies that for all values of `n`, `m`, and `k`, we must have:
`c_(n+1)(m+1)k√(n+1)√(m+1) - c_n(m-1)k√n√m = 0`
Similarly, since `(Ly)|ψ> = 0`, it follows that:
`(Ly)|ψ> = iħ(a_xa_z† - a_x†a_z)|ψ> = iħ(∑_n,m,k c_nmk(a_xa_z† - a_x†a_z)|n>|m>|k>)`
`= iħ(∑_n,m,k c_nmk(√n√(k+1)|n-1>|m>|k+1> - √(n+1)
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Books in a library were counted one by one. There were a total of 57000 books in the library. How many significant digits are there in the result? Will the result change if the books are measured in the paacket of 10?
The total number of significant digits in the given number is five. If the books are measured in packets of 10, the number of significant digits reduces to two.
The given data is: Total number of books in the library = 57,000. We are to determine how many significant digits are there in the result? For this, let us define what are significant digits: Digits that are used to communicate meaning or accuracy of measurements are known as significant digits. In other words, the digits that carry meaning contributing to its measurement uncertainty are called significant digits. It is used to determine the accuracy of the results. In this question, the total number of books in the library is given as 57,000. As there are five non-zero digits in the given number, there are five significant digits in the result. Will the result change if the books are measured in the packet of 10? If the number of books is measured in the packet of 10, then there will be a change in the number of significant digits. When we express 57,000 in the packet of 10, we get: 57,000 = 5.7 × 10^4. Now, there are only two significant digits in the result (5 and 7), and hence the result changes.
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If the thickness of an absorber is 1.5 cm and 36.45% of a beam is attenuated by the absorber, what is the half-value layer?
If the thickness of an absorber is 1.5 cm and 36.45% of a beam is attenuated by the absorber, The half-value layer is 0.51 cm.
The half-value layer (HVL) is a measure of the thickness of an absorber required to reduce the intensity of a beam to half its initial value. In this case, we are given that the absorber attenuates 36.45% of the beam.
To find the HVL, we can use the relationship between the percent attenuation and the thickness of the absorber. The HVL is the thickness at which the beam is attenuated to 50% or 0.5 of its initial intensity.
Since 36.45% of the beam is attenuated by the absorber, the remaining intensity is 100% - 36.45% = 63.55% or 0.6355 of the initial intensity.
We can set up the following equation:
0.5 = 0.6355^x
Solving for x, we find x ≈ 0.51.
Therefore, the half-value layer is approximately 0.51 cm, indicating that a thickness of 0.51 cm of the absorber is required to reduce the beam intensity to half its initial value.
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What is the size of the planets from smallest to largest?
The size of the planets from smallest to largest is: Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, and Jupiter.
The planets in our solar system range in size from the small, rocky Mercury, which has a diameter of 4,879 km, to the giant gas giant Jupiter, which has a diameter of 139,822 km. The order of the planets based on size is determined by their relative diameters, with the smallest planet, Mercury, being the first in the list and the largest planet, Jupiter, being the last.
The rocky planets, Mercury, Mars, Venus, and Earth, are all relatively close in size, with diameters ranging from 4,879 km to 12,742 km. The gas giants, Jupiter, Saturn, Uranus, and Neptune, are much larger, with diameters ranging from 49,244 km to 139,822 km.
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a particle is moving in simple harmonic motion with an amplitude of 3.2 cm and a maximum velocity of 15.0 cm/s. assume the initial phase is 0. (include the sign of the value in your answer.) (a) at what position is its velocity 4.5 cm/s? cm (b) what is its velocity when its position is 1.6 cm? cm/s
The position when velocity is 4.5cm/s is ±3.05cm and the velocity when the position is 1.6cm/s is 12.99cm.
The maximum velocity of the particle is 15cm/s and the amplitude is 3.2cm.
The velocity of a particle in simple harmonic motion is given by
V = W√(A²-X²)
Where,
V is the velocity,
A is the amplitude,
X is the position,
W is the angular frequency.
So, for maximum velocity,
V = WA
Putting values,
15 = W(3.2)
W = 4.6875 rad/s
(a) For position when speed is 4.5cm/s.
Putting values,
(4.5) = 4.6875√((3.2)²-(X²))
X = ±3.05cm
So, at ±3.05cm, the velocity will be 4.5cm/s.
(b) For velocity at position of 1.6cm,
Putting values,
V = 4.6875√((3.2)+(1.6))
V = 12.99cm/s
So, the velocity is 12.99cm/s at 1.6cm
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the g string on a guitar is a 0.44-mm-diameter steel string with a linear density of 1.1 g/m . when the string is properly tuned to 196 hz, the wave speed on the string is 250 m/s. tuning is done by turning the tuning screw, which slowly tightens-and stretches-the string.
The g - string will stretch by 0.0016 mm.
We have a g - string of a guitar with given specifications.
We have to determine how many mm does a 75-cm-long g - string stretch when it’s first tuned.
According to the question -
The force of tension in the string -
\($v = \sqrt{\frac{T}{\mu} }\)
T = \($v^{2} \mu\) = 250 x 250 x 0.0011 = 68.75 N
The Yung modulus of steel = 2 x \(10^{11}\) N/\(m^{2}\)
the amount by which the g - string will be stretched is given by -
\($\delta L = \frac{LT}{Y(\pi r^{2})}\)
Substituting the values -
\($\delta L = \frac{0.75\times 68.75 }{(2\times 10^{11} )\times (\pi (2.2 \times 10^{-4}\times 2.2\times 10^{-4}) )}\)
\(\delta L=\) 0.0016mm
Hence, the g - string will stretch by 0.0016 mm.
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[ The given question is incomplete. The complete question is
" The G string on a guitar is a 0.46-mm-diameter steel string
with a linear density of 1.1 g/m. When the string is properly
tuned to 196 Hz, the wave speed on the string is 250 m/s. Tuning
is done by turning the tuning screw, which slowly tightens—and
stretches—the string. By how many mm does a 75-cm-long G
string stretch when it’s first tuned? "]
The device shown below contains 2 kg of water. When the cylinder is allowed to fall 250 m, the temperature of the water increases by 1.4°C. Suppose 2 kg of water are added to the container and the cylinder is allowed to fall 750 m. What would the increase in temperature be in this case? Gizmo image A. 0.7°C B. 1.4°C C. 2.1°C D. 2.8°C
Answer:c. 2.1°C
Explanation:
I just did it
Given that the Sun's lifetime is about 10 billion years, estimate the life expectancy of a a) 0.2-solar mass, 0.01-solar luminosity red dwarf b) a 3-solar mass, 30-solar luminosity star c) a 10-solar mass, 1000-solar luminosity star
The life expectancy of the given stars are:a) 0.2-solar mass, 0.01-solar luminosity red dwarf: 10 trillion yearsb) 3-solar mass, 30-solar luminosity star: 10 million yearsc) 10-solar mass, 1000-solar luminosity star: 10 million years.
The life expectancy of a star is determined by its mass and luminosity. The more massive and luminous the star is, the shorter its life expectancy is. Hence, using this information, we can estimate the life expectancy of the following stars:a) 0.2-solar mass, 0.01-solar luminosity red dwarfRed dwarfs are known to have the longest life expectancies among all types of stars. They can live for trillions of years.
Hence, a 0.2-solar mass, 0.01-solar luminosity red dwarf is expected to have a much longer life expectancy than the Sun. It could live for up to 10 trillion years or more.b) 3-solar mass, 30-solar luminosity starA 3-solar mass, 30-solar luminosity star is much more massive and luminous than the Sun. As a result, it will have a much shorter life expectancy than the Sun.
Based on its mass and luminosity, it is estimated to have a lifetime of around 10 million years.c) 10-solar mass, 1000-solar luminosity starA 10-solar mass, 1000-solar luminosity star is extremely massive and luminous. It will burn through its fuel much faster than the Sun, resulting in a much shorter life expectancy. Based on its mass and luminosity, it is estimated to have a lifetime of only around 10 million years as well.
Therefore, the life expectancy of the given stars are:a) 0.2-solar mass, 0.01-solar luminosity red dwarf: 10 trillion yearsb) 3-solar mass, 30-solar luminosity star: 10 million yearsc) 10-solar mass, 1000-solar luminosity star: 10 million years.
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I need to solve for mass
The mass of the given will be 20kg.
Equation :By using formula,
force = mass x acceleration
mass = force / acceleration
mass = 400 N / 20m/s²
mass = 20 Kg
Acceleration :Acceleration is the rate at which an object's velocity with respect to time changes. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration.
Any process where the velocity changes is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because the velocity is both a speed and a direction.
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An axon of a human nerve cell is 5 x 10-6m in radius and 0.5-mm long. If the resistivity of the cytoplasm (inside the axon) is 1.6 x 107 Ω.m; Calculate the resistance along the axon, Raxial.
Raxial = ----- Ω
The axial resistance of an axon is calculated using the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. In this case, the axial resistance is 11.28 MΩ.
The resistance along the axon is calculated using the following formula:
R = ρL/A
where:
R is the resistance in ohms
ρ is the resistivity in ohms per meter
L is the length in meters
A is the cross-sectional area in meters squared
In this case, we have:
ρ = 1.6 x 107 Ω.m
L = 0.5 mm = 0.0005 m
A = πr² = π(5 x 10-6)² = 7.854 x 10-13 m²
Therefore, the resistance is:
R = ρL/A = (1.6 x 107 Ω.m)(0.0005 m) / (7.854 x 10-13 m²) = 11.28 MΩ
Therefore, the axial resistance of the axon is 11.28 MΩ.
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The maximum allowable deflection permitted for 7:12-sloped rafters with no finished ceiling attached to the rafters is _______________. *
The maximum allowable deflection permitted for 7:12-sloped rafters with no finished ceiling attached to the rafters is L/180.
1. Understand the terms: Rafters are structural components of a roof, supporting the sheathing and transferring loads to the walls. Deflection refers to the displacement or deformation of a structural element under load.
2. Determine the deflection limit: In this case, you need to find the maximum allowable deflection for rafters with a 7:12 slope and no finished ceiling attached. The common deflection limit for this scenario is L/180, where L represents the rafter's span length.
In summary, the maximum deflection for 7:12-sloped rafters without a finished ceiling is L/180, ensuring that the rafters maintain structural integrity and minimize excessive bending under load.
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what kind of mirror do u think s used in the side-view mirror of cars?
Answer:
The Convex Mirror is used.
Explanation:
convert 1074022,08 (tonnes/ year) to (kmol/second)
1074022.08 tonnes/year is equivalent to 340 kmol/second assuming an average molar mass of 100 g/mol.
To convert 1074022.08 tonnes/year to kmol/second, we need to consider the molar mass of the substance involved. Since the question does not specify the substance, let's assume we are converting a substance with an average molar mass of 100 g/mol.
First, convert tonnes/year to kilograms/second by dividing by 31,536,000 (the number of seconds in a year). Thus, 1074022.08 tonnes/year is equivalent to 34 kg/s.
Next, convert kilograms to moles by dividing by the molar mass. In this case, dividing 34 kg/s by 0.1 kg/mol (since 100 g/mol is equivalent to 0.1 kg/mol) gives us 340 kmol/s.
1074022.08 tonnes/year is equivalent to 340 kmol/second when assuming an average molar mass of 100 g/mol.
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