Answer: The magnitude of the force exerted on the roof is 490522.5 N.
Explanation:
The given data is as follows.
Below the roof, [tex]v_{1}[/tex] = 0 m/s
At top of the roof, [tex]v_{2}[/tex] = 39 m/s
We assume that [tex]P_{1}[/tex] is the pressure at lower surface of the roof and [tex]P_{2}[/tex] be the pressure at upper surface of the roof.
Now, according to Bernoulli's theorem,
[tex]P_{1} + 0.5 \times \rho \times v^{2}_{1} = P_{2} \times 0.5 \rho \times v^{2}_{2}[/tex]
[tex]P_{1} - P_{2} = 0.5 \times \rho \times (v^{2}_{2} - v^{2}_{1})[/tex]
= [tex]0.5 \times 1.29 \times [(39)^{2} - (0)^{2}][/tex]
= [tex]0.645 \times 1521[/tex]
= 981.045 Pa
Formula for net upward force of air exerted on the roof is as follows.
F = [tex](P_{1} - P_{2})A[/tex]
= [tex]981.045 \times 500[/tex]
= 490522.5 N
Therefore, we can conclude that the magnitude of the force exerted on the roof is 490522.5 N.
A mass m slides down a frictionless ramp and approaches a frictionless loop with radius R. There is a section of the track with length 2R that has a kinetic friction coefficient of 0.5. From what height h must the mass be released to stay on the track
Answer:
h = 2 R (1 +μ)
Explanation:
This exercise must be solved in parts, first let us know how fast you must reach the curl to stay in the
let's use the mechanical energy conservation agreement
starting point. Lower, just at the curl
Em₀ = K = ½ m v₁²
final point. Highest point of the curl
[tex]Em_{f}[/tex] = U = m g y
Find the height y = 2R
Em₀ = Em_{f}
½ m v₁² = m g 2R
v₁ = √ 4 gR
Any speed greater than this the body remains in the loop.
In the second part we look for the speed that must have when arriving at the part with friction, we use Newton's second law
X axis
-fr = m a (1)
Y Axis
N - W = 0
N = mg
the friction force has the formula
fr = μ N
fr = μ m g
we substitute 1
- μ mg = m a
a = - μ g
having the acceleration, we can use the kinematic relations
v² = v₀² - 2 a x
v₀² = v² + 2 a x
the length of this zone is x = 2R
let's calculate
v₀ = √ (4 gR + 2 μ g 2R)
v₀ = √4gR( 1 + μ)
this is the speed so you must reach the area with fricticon
finally have the third part we use energy conservation
starting point. Highest on the ramp without rubbing
Em₀ = U = m g h
final point. Just before reaching the area with rubbing
[tex]Em_{f}[/tex] = K = ½ m v₀²
Em₀ = Em_{f}
mgh = ½ m 4gR(1 + μ)
h = ½ 4R (1+ μ)
h = 2 R (1 +μ)
A nonuniform electric field is given by the expression = ay î + bz ĵ + cx , where a, b, and c are constants. Determine the electric flux (in the +z direction) through a rectangular surface in the xy plane, extending from x = 0 to x = w and from y = 0 to y = h. (Use any variable or symbol stated above as necessary.)
A glass tube 1 mm in diameter is dipped into glycerin. The density of the glycerin is 1260 kg/m3, surface tension is 6.3x10-2 N/m, and the contact angle is zero. The capillary rise of the glycerin is most nearly:
Answer:
The capillary rise of the glycerin is most nearly [tex]y = 0.0204 \ m[/tex]
Explanation:
From the question we are told that
The diameter of the glass tube is [tex]d = 1 \ mm = 0.001 \ m[/tex]
The density of glycerin is [tex]\rho = 1260 \ kg /m^3[/tex]
The surface tension of the glycerin is [tex]\sigma = 6.3 *10^{-2} \ N /m[/tex]
The capillary rise of the glycerin is mathematically represented as
[tex]y = \frac{4 * \sigma * cos (\theta )}{ \rho * g * d}[/tex]
substituting value
[tex]y = \frac{4 * 6.3 *10^{-2} * cos (0 )}{ 1260 * 9.8 * 0.001}[/tex]
[tex]y = 0.0204 \ m[/tex]
Therefore the height of the glass tube the glycerin was able to cover is
[tex]y = 0.0204 \ m[/tex]
While on Mars, two astronauts repeat the pendulum experiment you conducted earlier this term in your physics lab. They go off script and plot the pendulum length vs. the square of the period. Their best fit is a line with y = 0.091 x and R^2=1.
Recall that the theoretical period of a pendulum is T = 2pi(L/g)^1/2. Apply your understanding of mathematical modeling to determine what the constant 0.091 in the astronauts' equation of the best fit line is equal to in this case and use that to find their experimental value of g on Mars in m/s^2.
Answer:
The constant 0.091 in the astronauts' equation of the best fit line is equal to [tex]\frac{L}{T^2}[/tex]
The value of g on Mars is [tex]g = 3.593 \ m/s^2[/tex]
Explanation:
From the question we are told that
The line of best fit is defined by the equation [tex]y = 0.091 x \ and \ R^2 = 1[/tex]
Now the equation of a straight line is defined as
[tex]y = mx + c[/tex]
Now comparing the given equation to this we have that
[tex]m = slope = 0.091[/tex]
Now from the graph the formula for the slope is
[tex]m = \frac{L}{T^2}[/tex]
=> [tex]0.091 = \frac{L}{T^2}[/tex]
Now from the question we are told that
[tex]T = 2 \pi \sqrt{\frac{L}{g} }[/tex]
=> [tex]\frac{g}{4\pi r^2} = \frac{L}{T^2} = 0.091[/tex]
=> [tex]g = 4\pi^2 * 0.091[/tex]
=> [tex]g = 3.593 \ m/s^2[/tex]
A watermelon is dropped off of a 50 ft bridge, and it explodes upon impact with the ground. How fast was it traveling in mph upon impact?
Answer: 56.72 ft/s
Explanation:
Ok, initially we only have potential energy, that is equal to:
U =m*g*h
where g is the gravitational acceleration, m the mass and h the height.
h = 50ft and g = 32.17 ft/s^2
when the watermelon is near the ground, all the potential energy is transformed into kinetic energy, and the kinetic energy can be written as:
K = (1/2)*m*v^2
where v is the velocity.
Then we have:
K = U
m*g*h = (m/2)*v^2
we solve it for v.
v = √(2g*h) = √(2*32.17*50) ft/s = 56.72 ft/s
Calculate the speed of a proton that is accelerated from rest through an electric potential difference of 114 V. m/s (b) Calculate the speed of an electron that is accelerated through the same potential difference. m/s
Answer:
A) v = 148,242.72 m/s
B) v = 6,328,025.58 m/s
Explanation:
To solve this, we will equate electric potential to kinetic energy.
Formula for Electric potential is qV where q is charge and V is potential difference.
While formula for kinetic energy is ½mv² where m is mass and v is velocity
Thus;
qV = ½mv²
Let us make the velocity the formula;
v = √(2qV/m)
A) PROTON
Charge of proton has a constant value of 1.6 × 10^(-19) C
Mass of proton has a constant value of 1.66 × 10^(-27) kg
We are given that potential difference = 114 V.
So, v = √(2qV/m)
Thus; v = √(2*1.6 × 10^(-19)*114/(1.66 × 10^(-27)))
v = 148,242.72 m/s
B) ELECTRON
Charge of electron has a constant value of 1.6 × 10^(-19) C
Mass of electron has a constant value of 9.11 × 10^(-31) kg
v = √(2qV/m)
Thus;
v = √(2*1.6*10^(-19)*114)/(9.11 × 10^(-31)))
v = 6,328,025.58 m/s
The drawing shows a top view of a hockey puck as it slides across frictionless ice. Three forces act on the puck, and it is in equilibrium. The force F is applied at the center and has a magnitude of 32 N. The force F1 is applied at the top edge, and F2 is applied half way between the center and the bottom edge. Find the magnitude of F1 and F2.
Answer:
The values of the forces are
[tex]F_1 = 10.6 \ N[/tex] , [tex]F_2 = 21.33 \ N[/tex]
Explanation:
The diagram for this question is shown on the first uploaded image
From the question we are told that
The magnitude of F is [tex]F = 32 \ N[/tex]
Generally at equilibrium the torque is mathematically evaluated as
[tex]\sum \tau = 0[/tex]
From the diagram we have
[tex]r * F_1 - [\frac{r}{2} ] F_2 + 0 F = 0[/tex]
=> [tex]F_1 = 0.5 F_2[/tex]
Generally at equilibrium the Force is mathematically evaluated as
[tex]\sum F = 0[/tex]
From the diagram
[tex]F - F_ 1 - F_2 = 0[/tex]
substituting values
[tex]32 - (0.5F_2 ) - F_2 = 0[/tex]
[tex]F_2 = 21.33 \ N[/tex]
So
[tex]F_1 = 0.5 * 21.33[/tex]
[tex]F_1 = 10.6 \ N[/tex]
A boxcar at a rail yard is set into motion at the top of a hump. The car rolls down quietly and without friction onto a straight, level track where it couples with a flatcar of smaller mass, originally at rest, so that the two cars then roll together without friction. Consider the two cars as a system from the moment of release of the boxcar until both are rolling together.
(a) is the mechanical energy of the system conserved?
(b) is the momentum of this system conserved?
A hot air balloon competition requires a balloonist to drop a ribbon onto a target on the ground. Initially the hot air balloon is 50 meters above the ground and 100 meters from the target. The wind is blowing the balloon at v = 15 meters/sec on a course to travel directly over the target. The ribbon is heavy enough that any effects of the air slowing the vertical velocity of the ribbon are negligible. How long should the balloonist wait to drop the ribbon so that it will hit the target?
Answer:
The answer is 3.48 seconds
Explanation:
The kinematic equation
y= y0+V0*t+1/2*a*(t*t)
-50=0+(0)t+1/2(-9.8)*(t*t)
t=3.194 seconds
During ribbons ball,
x=x0+ Vt+1/2*a*(t*t)
x= 0+(15)*(3.194)+1/2*(0)* (3.194*3.194)
x= 47.9157m
So, distance (D) = 100-47.9157= 52.084m
52.084m=0+15(t)+1/2*(0)(t*t)
t=52.084/15=3.472286= 3.48seconds
The larger the push, the larger the change in velocity. This is an example of Newton's Second Law of Motion which states that the acceleration an object experiences is
Answer:
According to Newtons 2nd law of motion ;
The acceleration an object experiences is as a result of the net force which is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Explanation:
This law is simply saying ;
Force = Mass ×Acceleration
I Hope It Helps :)
The coefficient of linear expansion of steel is 11 x 10 perc . A steel ball has a volume of
exactly 100 cm at 0 C. When heated to 100 C, its volume becomes:
Question: The coefficient of linear expansion of steel is 11 x 10⁻⁶ per °c . A steel ball has a volume of
exactly 100 cm³ at 0 C. When heated to 100 C, its volume becomes:
Answer:
100.11 cm³
Explanation:
From the question,
γ = (v₂-v₁)/(v₁Δt)...................... Equation 1
Where γ = coefficient of volume expansion, v₂ = final volume, v₁ = initial volume, Δt = change in temperature.
make v₂ the subject of the equation
v₂ = v₁+γv₁Δt..................... Equation 2
Given: v₁ = 100 cm³, γ = 11×10⁻⁶/°C, Δt = 100 °C.
Substitute into equation 2
v₂ = 100+100(11×10⁻⁶)(100)
v₂ = 100+0.11
v₂ = 100.11 cm³
If you go to the beach on a hot summer day, the temperature of the sand is much higher than the temperature of the water. If we assume the same amount of energy was supplied by the sun to both the sand and the water, does sand or water require more energy to raise its temperature?
Water requires more energy to raise its temperature than sand does. In fact, of all the common substances that we see around us every day, water is one of the BEST at storing heat energy.
This is a big part of the reason why we use frozen water to cool our soda, instead of cold wood or cold steel balls.
It's also a big part of the reason why we warm up the bed in the Winter with a hot water bag, instead of a bag of hot rocks or hot BBs.
On a hot summer day, the temperature of the sand is much higher than the temperature of the water. The same amount of energy was supplied by the sun to both the sand and the water, but the water required more energy to raise its temperature than the sand.
What is "specific heat"?The specific heat of any substance is explained by the amount of heat required to increase the temperature by 1 degree; here, the specific heat of water is much higher than that of sand. The sand needs 670 joules of energy to raise the temperature, while the water needs nearly 3800 joules of energy to raise one degree of temperature.
Despite the fact that the sun cast the same amount of light on both water and sand, sand heated up faster than water. The water has a high latent heat of vaporization, which means it needs more energy to vaporize. The animal body maintains homeostasis as a result of this water.
Hence, water requires more energy to raise the temperature due to its high specific heat.
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Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12m
Answer:
The astronauts are separated by 28 m.
Explanation:
The separation of the astronauts can be found by conservation of linear momentum:
[tex] p_{i} = p_{f} [/tex]
[tex] m_{1}v_{1i} + m_{2}v_{2i} = m_{1}v_{1f} + m_{2}v_{2f} [/tex]
[tex] m_{1}*0 + m_{2}*0 = m_{1}v_{1f} + m_{2}v_{2f} [/tex]
[tex] m_{1}v_{1f} = -m_{2}v_{2f} [/tex]
[tex] v_{1f} = -\frac{m_{2}v_{2f}}{m_{1}} = -\frac{80v_{2f}}{60} [/tex]
Now, the distance (x) is:
[tex] x = \frac{v}{t} [/tex]
The distance traveled by the astronaut 1 is:
[tex] x_{1} = v_{1f}*t = -\frac{80v_{2f}}{60}*t [/tex] (1)
And, the distance traveled by the astronaut 2 is:
[tex] x_{2} = v_{2f}*t [/tex] (2)
From the above equation we have:
[tex] t = \frac{x_{2}}{v_{2f}} [/tex] (3)
By entering equation (3) into (1) we have:
[tex] x_{1} = -\frac{80v_{2f}}{60}*(\frac{x_{2}}{v_{2f}}) [/tex]
[tex] x_{1} = -\frac{4*12}{3} = -16 m [/tex]
The minus sign is because astronaut 1 is moving in the opposite direction of the astronaut 2.
Finally, the separation of the astronauts is:
[tex] x_{T} = |x_{1}| + x_{2} = (16 + 12)m = 28 m [/tex]
Therefore, the astronauts are separated by 28 m.
I hope it helps you!
The total separation between the two astronauts is 28m.
The given parameters:
masses of the astronauts, = 60 kg and 80 kgApply the principle of conservation of momentum to determine the final velocity of each astronauts as follows;
[tex]m_1u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2\\\\60(0) + 80(0) = 60(v_1) + 80(v_2)\\\\0 = 60v_1 + 80v_2\\\\-60v_1 = 80v_2\\\\v_1 = \frac{-80v_2}{60} \\\\v_1 = -1.333v_2[/tex]
Let the time when astronaut 2 moved 12 m = t
The distance traveled by astronaut 1 is calculated as;
[tex]x_1 = v_1 t\\\\x_1 = -1.333v_2t[/tex]
The distance traveled by astronaut 2 is calculated as;
[tex]x_2 = v_2 t\\\\12 = v_2t\\\\t = \frac{12}{v_2}[/tex]
Now solve for the distance of astronaut 1
[tex]x_1 = - 1.333v_2 \times t\\\\x_1 = -1.333 v_2 \times \frac{12}{v_2} \\\\x_1 = -16 \ m[/tex]
The total separation between the two astronauts is calculated as follows;
[tex]d = |x_1| + x_2\\\\d = 16 + 12\\\\d = 28 \ m[/tex]
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An object of mass 3.07 kg, moving with an initial velocity of 5.07 m/s, collides with and sticks to an object of mass 2.52 kg with an initial velocity of -3.11 m/s. Find the final velocity of the composite objec
Answer:
This is an inelastic collision. This means, unfortunately, that KE cannot save you, at least in the problem's current form.
Let's see what conservation of momentum in both directions does ya:
Conservation in the x direction:
Only 1 object here has a momentum in the x direction initally.
m1v1i + 0 = (m1 + m2)(vx)
3.09(5.10) = (3.09 + 2.52)Vx
Vx = 2.81 m/s
Explanation:
Conservation in the y direction:
Again, only 1 object here has initial velocity in the y:
0 + m2v2i = (m1 +m2)Vy
(2.52)(-3.36) = (2.52 + 3.09)Vy
Vy = -1.51 m/s
++++++++++++++++++++
Now that you have Vx and Vy of the composite object, you can find the final velocity by doing Vf = √Vx^2 + Vy^2)
Vf = √(2.81)^2 + (-1.51)^2
Vf = 3.19 m/s
Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of oneâs birth. The only known force that a planet could exerts on us is gravitational, so if there is anything to astrology we should expect this force to be significant.
Required:
a. Calculate the gravitational force, in Newtons, exerted on a 4.1 kg baby by a 120 kg father who is a distance of 0.18 m away at the time of its birth.
b. Calculate the force on the baby, in Newtons, due to Jupiter (the largest planet, which has a mass of 1.90Ã10^27 kg if it is at its closest distance to Earth, 6.29Ã10^11 m away.
c. What is the ratio of the force of the father on the baby to the force of Jupiter on the baby?
Answer:
Explanation:
Gravitational force between two objects having mass m₁ and m₂ at a distance R
F = G m₁ m₂ / R²
Force between baby and father F₁ = 6.67x10⁻¹¹ x 4.1 x 120 / .18²
= 1.01 x 10⁻⁶ N
b )
Force between baby and Jupiter
F₂ = 6.67x10⁻¹¹ x 1.9x 10²⁷ x 4.1 / ( 6.29 x 10¹¹ )²
= 1.31 x 10⁻⁶ N
c )
Ratio = 1.01 / 1.31
= .77
g Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by Icm=112mL2. Find Iend, the moment of inertia of the rod with respect to a parallel axis through one end of the rod.
Answer:
[tex]I_e = \frac{1}{3}*m*L^2[/tex]
Explanation:
Solution:-
- Here we are given the moment of inertia of a uniform slender rod with mass ( m ) and length ( L ). The thickness / radius / diameter of the rod is considered to be insignificant.
- The moment of inertia ( Ir ) of a rod with an axis perpendicular to it at its center is given as:
[tex]I_r = \frac{1}{12}*m*L^2[/tex]
- We are to determine the moment of inertia of the rod at any one of its ends using the parallel axis theorem.
- The theorem is mostly used to translate the pivotal axis to any point on the mass or in space. With respect to that point the moment of inertia is determined using the parallel axis theorem. The moment of inertia of the object at its center of mass must be known to apply the theorem.
- The theorem is expressed as:
[tex]I_e = I_r + m*d^2[/tex]
Here,
d: Is the distance between the center of mass and the arbitrary point.
- Since we are asked to determine the moment of inertial at one of the rod's ends. We can evaluate the distance " d " from its center of mass to its end. The center lies at " L / 2 " distance from either of its ends. Hence, d = L / 2.
- We will plug in the parameters in the theorem and evaluate:
[tex]I_e = \frac{1}{12}*m*L^2 + m*[\frac{L}{2} ]^2 \\\\I_e = \frac{1}{12}*m*L^2 + m*\frac{L^2}{4} \\\\I_e = m*L^2 * [ \frac{1}{12}+ \frac{3}{12} ] = m*L^2 *\frac{4}{12} \\\\I_e = \frac{1}{3}*m*L^2[/tex]
The water level in identical bowls, A and B, is exactly the same. A contains only water; B contains floating ice as well as water. When we weigh the bowls, we find that Group of answer choices
Answer:
We know that the density of the ice is smaller than the density of the water (and this is why the ice floats in water).
Dw > Di
Da is the density of the water and Di is the density of the ice
Since in Bowl A we have a volume V, only of water, then the mass of the bowl A is:
Dw*V.
Now, in the bowl B we have a combination of water and ice, suppose that Vw is the volume of water and Vi is the volume of ice, and we know that:
Vw + Vi = V.
Then the mass in this second bowl is:
Dw*Vw + Di*Vi = Dw*(V - Vi) + Di*Vi = Dw*V + (Di - Dw)*Vi
and we know that Dw > Di, then the left term is a negative term, then the mass of bowl B is smaller than the mass of bowl A.
In a contest, two tractors pull two identical blocks of stone thesame distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct?a) Block A has twiceas much kinetic energy as block B.b) Block B has losttwice as much kinetic energy to friction as block A.c) Block B has losttwice as much kinetic energy as block A.d) Both blocks havehad equal losses of energy to friction.e) No energy is lostto friction because the ground has no displacement.
Answer:
d) Both blocks have had equal losses of energy to friction
Explanation:
As it is mentioned in the question that two tractors pull two same stone blocks having the identical distance over the same surfaces
Moreover, the block A is twice as fast than block B at the time of crossing the finish line
So based on the above information, it contains the losses of identical friction
And we also know that
Friction energy loss is
[tex]= \mu \times m \times g \times D[/tex]
It would be the same for both the blocks
hence, the option d is correct
The correct answer will be both blocks have had equal losses of energy to friction.
What is friction?Friction is defined as when any object is slides on a surface by means of any external force then the force in the opposite direction generated between the surface and the body restrict the motion of the body this force is called as the friction.
As it is mentioned in the question that two tractors pull two same stone blocks having the identical distance over the same surfaces.
Moreover, the block A is twice as fast as block B at the time of crossing the finish line.
So based on the above information, it contains the losses of identical friction.
And we also know that
Friction energy loss is
[tex]E_f=\mu m g D[/tex]
It would be the same for both the blocks
Hence both blocks have had equal losses of energy to friction.
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which of the following terms refers to the amount of thermal energy need to change 1 kg of a substance from a liquid to a gas at its boiling point
Answer:
See the answer below.
Explanation:
"Latent Heat", also called the "Heat of Vaporization", is the amount of energy necessary to change a liquid to a vapour at constant temperature and pressure.
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Two conductors made of the same material are connected across the same potential difference. Conductor A has seven times the diameter and seven times the length of conductor B. What is the ratio of the power delivere
Complete question:
Two conductors made of the same material are connected across the same potential difference. Conductor A has seven times the diameter and seven times the length of conductor B. What is the ratio of the power delivered to A to power delivered to B.
Answer:
The ratio of the power delivered to A to power delivered to B is 7 : 1
Explanation:
Cross sectional area of a wire is calculated as;
[tex]A = \frac{\pi d^2}{4}[/tex]
Resistance of a wire is calculated as;
[tex]R = \frac{\rho L}{A} \\\\R = \frac{4\rho L}{\pi d^2} \\\\[/tex]
Resistance in wire A;
[tex]R = \frac{4\rho _AL_A}{\pi d_A^2}[/tex]
Resistance in wire B;
[tex]R = \frac{4\rho _BL_B}{\pi d_B^2}[/tex]
Power delivered in wire;
[tex]P = \frac{V^2}{R}[/tex]
Power delivered in wire A;
[tex]P = \frac{V^2_A}{R_A}[/tex]
Power delivered in wire B;
[tex]P = \frac{V^2_B}{R_B}[/tex]
Substitute in the value of R in Power delivered in wire A;
[tex]P_A = \frac{V^2_A}{R_A} = \frac{V^2_A \pi d^2_A}{4 \rho_A L_A}[/tex]
Substitute in the value of R in Power delivered in wire B;
[tex]P_B = \frac{V^2_B}{R_B} = \frac{V^2_B \pi d^2_B}{4 \rho_B L_B}[/tex]
Take the ratio of power delivered to A to power delivered to B;
[tex]\frac{P_A}{P_B} = (\frac{V^2_A \pi d^2_A}{4\rho_AL_A} ) *(\frac{4\rho_BL_B}{V^2_B \pi d^2_B})\\\\ \frac{P_A}{P_B} = (\frac{V^2_A d^2_A}{\rho_AL_A} )*(\frac{\rho_BL_B}{V^2_B d^2_B})\\\\[/tex]
The wires are made of the same material, [tex]\rho _A = \rho_B[/tex]
[tex]\frac{P_A}{P_B} = (\frac{V^2_A d^2_A}{L_A} )*(\frac{L_B}{V^2_B d^2_B})\\\\[/tex]
The wires are connected across the same potential; [tex]V_A = V_B[/tex]
[tex]\frac{P_A}{P_B} = (\frac{ d^2_A}{L_A} )* (\frac{L_B}{d^2_B} )[/tex]
wire A has seven times the diameter and seven times the length of wire B;
[tex]\frac{P_A}{P_B} = (\frac{ (7d_B)^2}{7L_B} )* (\frac{L_B}{d^2_B} )\\\\\frac{P_A}{P_B} = \frac{49d_B^2}{7L_B} *\frac{L_B}{d^2_B} \\\\\frac{P_A}{P_B} =\frac{49}{7} \\\\\frac{P_A}{P_B} = 7\\\\P_A : P_B = 7:1[/tex]
Therefore, the ratio of the power delivered to A to power delivered to B is
7 : 1
Water vapor is less dense than ice because:
a. molecules in the gas phase are in constant motion.
b. molecules in the gas phase have more potential energy than in solids.
c. molecules in the gas phase have more kinetic energy than in solids.
d. gaseous molecules have less mass.
e. molecules in the gas phase have more space between them than in solids,
Answer:
The correct answer is option E
Explanation:
Relative density of the different phases of the same compound like water are basically determined by their number of molecules per volume when each of the molecules have the same mass in each of their phases.
Now, for the water vapor phase, it's molecules have very little interaction with themselves and so they are at large distance apart, whereas in ice(solid), molecules are in continuous contact with each other because they are at close distance between each other. Therefore, it's obvious that there are less molecules per liter in water vapour than in ice, and thus the density is smaller.
The correct answer is option E
That 85 kg paratrooper from the 50's was moving at constant speed of 56 m/s because the air was applying a frictional drag force to him that matched his weight. If he fell this way for 40 m, how much heat was generated by this frictional drag force in J
Answer:
46648 J
Explanation:
mass m= 85 Kg
velocity v = 56 m/s
distance covered s =40 m
According to Question,
frictional drag force to him that matched his weight
[tex]\Rightarrow F_d =mg\\=85\times9.81=833 N[/tex]
Therefore, work done by practometer against the drag force = heat was generated by this frictional drag force in J
W=Q= F_d×s
=833×56 = 46648 J
Immediately outside a conducting sphere(i.e. on the surface) of unknown charge Q and radius R the electric potential is 190 V, and 10.0 cm further from the sphere, the potential is 140 V. What is the magnitude of the charge Q on the sphere
Answer:
Q = 5.9 nC (Approx)
Explanation:
Given:
Further distance = 10 cm
Electric potential(V) = 190 v
Potential difference(V1) = 140 v
Find:
Magnitude of the charge Q
Computation:
V = KQ / r
190 = KQ / r.............Eq1
V1 = KQ / (r+10)
140 = KQ / (r+10) ............Eq2
From Eq2 and Eq1
r = 28 cm = 0.28 m
So,
190 = KQ / r
190 = (9×10⁹)(Q) / 0.28
53.2 = (9×10⁹)(Q)
5.9111 = (10⁹)(Q)
Q = 5.9 nC (Approx)
Two red blood cells each have a mass of 9.0 x 10-14 kg and carry a negative charge spread uniformly over their surfaces. The repulsion from the excess charge prevents the cells from clumping together. One cell carries -2.5pC and the other -3.30 pC, and each cell can be modeled as a sphere 3.75 × 10-6 m in radius. If the red blood cells start very far apart and move directly toward each other with the same speed.
1. What initial speed would each need so that they get close enough to just barely touch?
2. What is the maximum acceleration of the cells as they move toward each other and just barely touch?
Answer:
Explanation:
Given that:
The mass of the cell is 9.0 x 10^-14 kg
The charges of the cell is -2.5pC and the other -3.30 pC
[tex]q_1=-2.5\times10^{-12}C \ \ and \ \ q_2=-3.75\times10^{-12}C[/tex]
Radius is 3.75 × 10-6 m
The final distance is twice the radius
i.e [tex]2*(3.75 \times 10^{-6}) = 7.5*10^{-6}m[/tex]
The formula for the velocity of the cell is
[tex]mv^2=\frac{q_1q_2}{4\pi \epsilon 2 r} \\[/tex]
[tex]v=\sqrt{\frac{q_1q_2}{4\pi \epsilon 2 r} }[/tex]
[tex]=\sqrt{\frac{(-2.5\times10^{-12})(-3.3\times10^{-12}}{4(3.14)(8.85\times10^{-112}(2\times3.75\times10^{-6})(9\times10^{-14})} } \\\\=\sqrt{\frac{(-8.25\times10^{-24})}{(7503.03\times10^{-32})} } \\\\=\sqrt{109955.5779} \\\\=331.60m/s[/tex]
The maximum acceleration of the cells as they move toward each other and just barely touch is
[tex]ma= \frac{q_1q_2}{4\pi \epsilon (2r)^2} \\\\a= \frac{q_1q_2}{4\pi \epsilon (2r)^2(m)}[/tex]
[tex]=\frac{(-2.5\times10^{-12})(-3.3\times10^{-12})}{4(3.14)(8.85\times10^{-12})(2\times3.75\times10^{-6})^2(9\times10^{-14})}[/tex]
[tex]=\frac{(-8.25\times10^{-24})}{(56272.725\times10^{-38})} \\\\=1.47\times10^{10}m/s^2[/tex]
The answers obtained are;
1. The initial speed of each of the red blood cells is [tex]v= 331.66\,m/s[/tex].
2. The maximum acceleration of the cells is [tex]a=1.47\times 10^{10}\,m/s^2[/tex].
The answer is explained as shown below.
We have, the mass of the red blood cell;
[tex]m=9\times 10^{-14}\,kg[/tex]Also, the charges of the cells are;
[tex]q_1=-2.5\times 10^{-12}\,C[/tex] and[tex]q_2=-3.30\times 10^{-12}\,C[/tex]The distance between the charges when they barely touch will be two times the radius of each charge.
[tex]r=2\times r\,'=2\times3.75\times10^{-6}\,m=7.5\times10^{-6}\,m[/tex]Kinetic Energy of moving charges1. As both the cells are negatively charged they will repel each other.
So, for the cells to come nearly close, their kinetic energies must be equal to the electric potential between them.[tex]\frac{1}{2}mv^2+ \frac{1}{2}mv^2=k\frac{q_1 q_2}{r^2}[/tex]Where, [tex]k=9\times10^9\,Nm^2/C^2[/tex] is the Coulomb's constant.Now, substituting all the known values in the equation, we get;
[tex](9\times 10^{-14}\,kg)\times v^2=9\times 10^9Nm^2/C^2\times\frac{(-2.5\times 10^{-12}\,C)\times(-3.30\times 10^{-12}\,C)}{7.5\times10^{-6}\,m}[/tex][tex]v^2=9\times 10^9Nm^2/C^2\times\frac{(-2.5\times 10^{-12}\,C)\times(-3.30\times 10^{-12}\,C)}{7.5\times10^{-6}\,m\times(9\times 10^{-14}\,kg)} =110000\,m^2/s^2[/tex]
[tex]\implies v=\sqrt{110000\,m^2/s^2}=331.66\,m/s[/tex]Electrostatic force between two charges2. Also as the force between them is repulsive, there must be an acceleration to make them barely touch each other.
[tex]ma=k\frac{q_1 q_2}{r^2}[/tex]Substituting the known values, we get;
[tex](9\times 10^{-14}\,kg)\times a=9\times 10^9Nm^2/C^2\times\frac{(-2.5\times 10^{-12}\,C)\times(-3.30\times 10^{-12}\,C)}{(7.5\times10^{-6}\,m)^2}[/tex]
[tex]\implies a=9\times 10^9Nm^2/C^2\times\frac{(-2.5\times 10^{-12}\,C)\times(-3.30\times 10^{-12}\,C)}{(7.5\times10^{-6}\,m)^2\times(9\times 10^{-14}\,kg) }[/tex]
[tex]a=1.47\times 10^{10}\,m/s^2[/tex]Find out more information about moving charges here:
https://brainly.com/question/14632877
A 310-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,010 A. If the conductor is copper with a free charge density of 8.50 1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable? (Use 3.156 107 for the number of seconds in a year.)
Answer:
t = 166 years
Explanation:
In order to calculate the amount of years that electrons take to cross the complete transmission line. You first calculate the drift speed of the electrons by using the following formula:
[tex]v_d=\frac{I}{nqA}[/tex] (1)
I: current on the wire = 1,010A
n: free charge density = 8.50*10^28 electrons/m^3
A: cross-sectional area of the transmission line = π*r^2
r: radius of the cross-sectional area = 2.00cm = 0.02m
You replace the values of the parameters in the equation (1):
[tex]v_d=\frac{1,010A}{(8.50*10^{28}electron/m^3)(1.6*10^{-19}C)(\pi (0.02m)^2)}\\\\v_d=5.9*10^{-5}\frac{m}{s}[/tex]
Next, you use the following formula:
[tex]t=\frac{x}{v_d}[/tex] (2)
x: length of the line transmission = 310km = 310,000m
You replace the values of vd and x in the equation (2):
[tex]t=\frac{310,000m}{5.9*10^{-5}m/s}=5.24*10^9s[/tex]
Finally, you convert the obtained t to seconds
[tex]t=5.24*10^9s*\frac{1\ year}{3.156*10^7s}=166.03\ years[/tex]
The electrons take approximately 166 years to travel trough the complete transmission line
1. Suppose a teenager puts her bicycle on its back and starts the rear wheel spinning from rest to a final angular velocity of 250 rpm in 5.00 s. Radius of tire is 50 cm. What angle did the tire move through in those 5 secs
Answer:
[tex]\theta=65.18rad[/tex]
Explanation:
The angle in rotational motion is given by:
[tex]\theta=\frac{w_o+w_f}{2}t[/tex]
Recall that the angular speed is larger than regular frequency (in rpm) by a factor of [tex]2\pi[/tex], so:
[tex]\omega_f=2\pi f\\\omega_f=2\pi*250rpm\\\omega_f=1570.80 \frac{rad}{min}[/tex]
The wheel spins from rest, that means that its initial angular speed is zero([tex]\omega_o[/tex]). Finally, we have to convert the given time to minutes and replace in the first equation:
[tex]t=5s*\frac{1min}{60s}=0.083min\\\theta=\frac{\omega_f}{2}t\\\theta=\frac{1570.800\frac{rad}{min}}{2}(0.083min)\\\theta=65.18rad[/tex]
The velocity of an object is given by the expression v(t) = 3.00 m/s + ( 4.00 m/s^3)t^2, where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time t = 0.000 s
Answer:
Position of object is;
s(t) = 4t³/3 + 3t + 1
Explanation:
We are told that the velocity has an expression;
v(t) = 3.00 m/s + ( 4.00 m/s³)t²
Now, to get the expression for the position(s(t)) of the object, we have to integrate the velocity expression. Thus;
s(t) = ∫3 + 4t²
s(t) = 3t + 4t³/3 + c
Now, we were told that at x = 1.00 m, time t = 0.000 s
Thus, plugging the values in;
1 = 3(0) + 4(0³/3) + c
c = 1
Thus,the expression for the position of the object is;
s(t) = 4t³/3 + 3t + 1
A 50 g ice cube floats in 195 g of water in a 100 g copper cup; all are at a temperature of 0°C. A piece of lead at 96°C is dropped into the cup, and the final equilibrium temperature is 12°C. What is the mass of the lead?
Answer:
The mass of the lead will be "1.127 kg".
Explanation:
The given values are:
(Ice) m₁ = 50 g i.e.,
0.050 kg
(Water) m₂ = 195 g i.e.,
0.190 kg
(Copper cup) m₃ = 100 g i.e.,
0.100 kg
m₁, m₂ and m₃ at temperature,
t₁ = 0°C
Temperature of lead,
t₂ = 96°C
Temperature of Final equilibrium,
t₃ = 12°C
Let m₄ be the mass of the lead.
On applying formula, we get
⇒ [tex]m_{1}L+m_{1}s_{1} \Delta t+m_{2}s_{2} \Delta t+m_{2}s_{2} \Delta t=m_{4}s_{4} \Delta t[/tex]
On putting the estimated values, we get
⇒ [tex](0.050)(334)+(0.050)(4186)(12-0)+(0.190)(4186)(12-0)+(0.100)(387)(12-0)=m_{4} (128)(96-12)[/tex]
⇒ [tex]16.7+2511.6+9544.08+50.7=10752\times m_{4}[/tex]
⇒ [tex]12,123.08=10752\times m_{4}[/tex]
⇒ [tex]m_{4}=\frac{12,123.08}{10752}[/tex]
⇒ [tex]m_{4}=1.127 \ kg[/tex]
A mass of 50.00g hangs from a 7.00cm-long spring that is rigidly attached to a ceiling. The mass is pulled down slightly, let go, and is observed to make 8 round trips (up and back down) in 14.00s. What is the stiffness constant for this spring
Answer:
0.645 N/M
Explanation:
Given
Mass=50.00g
We have to convert into the kg
So Mass =0.050 Kg
[tex]Time\ = \frac{14}{8}\ = 1.75\ sec[/tex]
We know that
[tex]T\ =2\ PI\sqrt{\frac{M}{K} }[/tex]........................Eq(1)
Where T= time
and M= Mass
K= Stiffness constant
On squaring both side we get
[tex]K=\frac{4\pi^{2} M}{T^{2} }[/tex]....Eq(2)
Putting the value of M ,T and π in Eq(2) we get
K=0.645 N/M
A bar slides vertically between two conducting rails without friction in a magnetic field. The rails are connected via a resistor. The bar reaches a constant velocity and slides for 2m. How much energy is dissipated in the resistor during these 2m's
Answer:
The energy dissipated is [tex]E = 9.8 J[/tex]
Explanation:
From the question we are told that
The distance covered at constant velocity d = 2 m
The velocity is [tex]v = 1.5 \ m/s[/tex]
Generally at constant velocity the magnetic force on the bar is mathematically represented as
[tex]F = m * g[/tex]
substituting values
[tex]F = 0.5 * 9.8[/tex]
[tex]F = 4.9 \ N[/tex]
The energy dissipated is mathematically evaluate as
[tex]E = F * d[/tex]
substituting the value
[tex]E = 4.9 * 2[/tex]
[tex]E = 9.8 J[/tex]