Answer:
266.67 K
Explanation:
Recall the formula for ideal gasses:
P * V = n * R * T
from which a proportion can be obtained if the volume of the gas and its number of moles remain constant. This is:
T / P = constant and therefore T1 / P1 = T2/ P2
Then for our case:
300 / 36 = T2 / 32
solving for T2:
T2 = 300 * 32 / 36 = 266.67 K
A single coil of wire, with a radius of 0.13 m is rotated in a uniform magnetic field such that the angle between the field vector and the area vector obeys θ=ωt. If the strength of the field is 3.746 T, and the angular frequency is 524.7 rad/s, what is the induced emf in the loop at t=1.16 s?
The magnitude of emf induced in the single coil of wire rotated in the uniform magnetic field is 0.171 V.
The emf induced in the loop is determined by applying Faraday's law of electromagnetic induction.
emf = N(dФ/dt)
where;
N is number of turns of the wireФ is magnetic fluxФ = BA
where;
B is magnetic field strengthA is the area of the loopemf = NBA/t
A = πr²
A = π x (0.13)²
A = 0.053 m²
emf = NBA/t
emf = (1 x 3.746 x 0.053)/(1.16)
emf = 0.171 V
Thus, the magnitude of emf induced in the single coil of wire is 0.171 V.
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Two vehicles, a 3,650-kg car and a 9,850-kg truck, are parked in a lot 25.0 meters apart.
Calculate the gravitational force between these two vehicles.
500 kilograms of supplies are added to the truck. Explain whether the gravitational force increases, decreases, or stays the same between the two vehicles.
Remember to identify all data (givens and unknowns), list equations used, show all your work, include units and the proper number of significant digits, and write explanation in complete sentences to receive full credit.
1) The force is 3.8 * 10^-6 N
2) The force will increase since the force is proportional to the masses of the trucks
What is the gravitational force?Gravitational force is a fundamental force of nature that exists between any two objects that have mass or energy. It is the force of attraction that exists between any two objects in the universe, and is responsible for holding planets in their orbits, causing objects to fall towards the Earth, and keeping galaxies together.
Given;
F = Gm1m2/r^2
F = 6.6 * 10^-11 * 3,650 * 9,850/(25)^2
F = 3.8 * 10^-6 N
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A baseball pitcher throws a ball vertically upward and catches it at the same height 4.2 seconds later.
a) With what velocity did the pitcher throw the ball?
b) How high did the ball rise?
(a) The velocity of the ball is 41.16 m/s.
(b) The height reached by the ball is 86.44 m.
What is velocityVelocity is the rate of change of displacement.
(a) To calculate the velocity at which the pitcher throw the ball, we use the formula below
Formula:
v = u+gt...................... Equation 1Where:
v = Final velocityu = Initial velocityt = Timeg = Acceleration due to gravityFrom the question,
Given:
t = 4.2 secondsg = 9.8 m/s²u = 0 m/s from restSubstitute thee values into equation 1
v = 0+(4.2×9.8)v = 41.16 m/s(b) To calculate how high the ball rise, we use the formula
s = ut+gt²/2..................... Equation 2Where:
s = Height reached by the ballSubstitute into equation 2
s = (0×4.2)+(9.8×4.2²)/2s = 0+86.44s = 86.44 mLearn more about velocity here: https://brainly.com/question/24445340
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A point charge, Q1 = 12.0 C, is placed at the origin (0 cm, 0 cm) and a second charge, Q2, is placed at the coordinates (4.00 cm, 0 cm). A third charge, Q3 = 15.00 C, is placed at (5.0 cm, 0 cm). The force on Q3 is F⃑ = −20.0 N î. What is the value and sign of Q2?
Answer:
q₂ = -4.80 10⁻⁴ C = - 0.48 mC, charge is negative
Explanation:
Let's use coulomb's law
F = \(k \frac{q_1 q_2}{r^2}\)
and the sum of forces, remember that charges of the same sign repel and of different sign attract
∑ F = F₁₃ + F₂₃ (1)
Let's start by fixing a reference system located at charge 1 with the positive direction to the right. In the problem it indicates that the net force on charge 3 is F = - 20.0 N, the negative sign indicates that the force is towards the left
let's look for every force, the charge q₁ = 12 10-⁻³ C and q₃ = 15 10⁻³ C
F₁₃ =\(k \frac{q_1 q_3}{x_{13}^2}\)
F₁₃ = 9 10⁹ 12.0 15.0 10⁻⁶ / (5-0)²
F₁₃ = 64.8 10 3 N
This force is repulsive, that is, it is directed to the right
F₂₃ = k \frac{q_2 q_3}{x_{23}^2}
F₂₃ = 9 10⁹ q₂ 15.0 10⁻³ / (5-4)²
F₂₃ = 135 10⁶ q₂ N
we substitute in equation 1
-20.0 = 64.8 10³ + 135 10⁶ q₂
q₂ = (-20 - 64.8 10³) / 135 10⁶
q₂ = -4.80 10⁻⁴ C
the sign indicates that the charge is negative
Positive electric charges are always attracted to ________ charges.
Answer:
Negative electric charges
The diagram below shows four layers of Earth.
The picture shows the internal structure of Earth. The central region is labeled 'A.' The layer around the central region is labeled 'B.' The outermost layer is labeled 'D.' The layer inside Earth which is just after layer D is labeled 'C.'
In which of these layers does hot material move upwards and cool material sink downwards?
Layer A
Layer B
Layer C
Layer D
Answer:
Layer C
Explanation:
Hope this helps!
-Liyah<3
A ball is thrown vertically upwards with a velocity of 10 m /s from the balcony of a tall building.
The balcony is 15m above the ground and gravitational acceleration is 10m/s^2.
Calculate the time taken for the ball to reach maximum height.
The time taken for the ball to reach its maximum height is 1 second.
To calculate the time taken for the ball to reach its maximum height, we can use the kinematic equation for vertical motion. The equation is:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the ball is thrown vertically upwards, so the initial velocity (u) is 10 m/s (considering upwards as positive) and the acceleration (a) is -10 m/s² (negative because it opposes the motion).
The final velocity (v) at the maximum height will be zero because the ball momentarily comes to a stop before reversing its direction. Therefore, we can rewrite the equation as:
0 = 10 - 10t
Simplifying the equation, we get:
10t = 10
Dividing both sides by 10, we find:
t = 1 second
Therefore, the time taken for the ball to reach its maximum height is 1 second.
During this time, the ball covers the distance required to reach the maximum height, overcoming the gravitational acceleration. After reaching the maximum height, it will start to descend towards the ground due to the gravitational pull.
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An m = 6.11 g bullet is fired into a 365 g block that is initially at rest at the edge of a table of h = 1.08 m height as shown in the figure.
1. The bullet remains in the block, and after the impact the block lands d = 1.84 m from the bottom of the table. How much time does it take the block to reach the ground once it flies off the edge of the table?
2. What is the initial horizontal velocity of the block as it flies off the table?
3. Determine the initial speed of the bullet.
(a) The time taken the block to reach the ground once it flies off the edge of the table is 0.47 s.
(b) The initial horizontal velocity of the block as it flies off the table is 3.91 m/s.
(c) The initial speed of the bullet is 237.5 m/s.
Time of motion of the blockThe time of motion of the block is calculated as follows;
h = ¹/₂gt²
where;
h is height of the tablet is time of motiont = √(2h/g)
t = √( (2 x 1.08) / 9.8)
t = 0.47 s
Initial horizontal velocity of the blockx = vt
v = x/t
v = (1.84)/(0.47)
v = 3.91 m/s
Initial speed of the bulletm1u1 + m2u2 = v(m1 + m2)
where;
m1 is mass of bulletm2 is mass of blocku1 is initial velocity of the bulletu2 is the initial velocity of the blockv is initial horizontal velocity of the block as it flies off the table0.00611(u1) + 0.365(0) = 3.91(0.00611 + 0.365)
0.00611u1 = 1.451
u1 = 1.451/0.00611
u1 = 237.5 m/s
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A constant net force of 345 N is applied to slide a heavy stationary
couch across the floor. If the force is contact with the couch for 1.5 seconds,
then what is the change in momentum of the couch
Answer:
P = 517.5 [kg*m/s]
Explanation:
We must remember that momentum is defined as the product of force by the time of force duration.
\(P=F*t\)
where:
P = momentum [kg*m/s]
F = force [N]
t = time [s]
\(P=345*1.5\\P=517.5[kg*m/s]\)
A loudspeaker of mass 15.0 kg is suspended a distance of h = 1.00 m below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 2.70 m .
1. What is the tension T in each of the cables?
Use 9.80 m/s2 for the magnitude of the free-fall acceleration.
Answer:
To solve the problem, we use the equations of equilibrium to find the tension in each cable holding up the loudspeaker. Since the loudspeaker is in equilibrium, the sum of the forces acting on it is zero. The weight of the loudspeaker is calculated first, and then we use trigonometry to find the horizontal and vertical components of the tension in one of the cables. We then apply the equation of equilibrium in the y direction to find the tension in each cable. The final answer is that the tension in each cable is approximately 81.1 N, which balances the weight of the loudspeaker.
___
Given:
Mass of loudspeaker (m) = 15.0 kg
Distance from ceiling (h) = 1.00 m
Length of cable (l) = 2.70 m
Acceleration due to gravity (g) = 9.80 m/s^2
Weight of loudspeaker:
Fg = mg
Fg = (15.0 kg)(9.80 m/s^2)
Fg = 147 N
Horizontal and vertical components of tension in one cable:
sinθ = h/l
sinθ = 1.00 m / 2.70 m
θ = sin^(-1)(1.00/2.70)
θ ≈ 21.6°
T_x = T sinθ
T_y = T cosθ
where T is the tension in the cable.
Equation of equilibrium in y direction:
ΣF_y = 2T cosθ - Fg = 0
Solving for T:
2T cosθ = Fg
T = Fg / (2 cosθ)
Plugging in the values:
T = (147 N) / (2 cos(21.6°))
T ≈ 81.1 N
State four factors affecting thermal conductivity
Answer:
∙ Temperature
∙ Concentration of electrolyte
∙ Nature of the electrolyte added
∙ Nature of solvent and its viscosity
Explanation:
Uuse Lenz's law to explore what happens when an electromagnet is activated a short distance from a wire loop. You will need to use the right-hand rule to find the direction of the induced current.
Answer:
Explanation:
According to the Fleming's right hand rule, if we spread our right hand such that the thumb, fore finger and the middle finger are mutually perpendicular to each other, then the thumb indicates the direction of force, fore finger indicates the direction of magnetic field, then the middle finger indicates the direction of induced current.
According to the Lenz's law, the direction of induced emf is such that it always opposes the cause due to which it is produced.
A crate with a mass of 35.0 kg is pushed with a horizontal force of 150 N. The crate moves at a constant speed across a level, rough surface a distance of 5.85 m
(a) The work done by the 150 N force is 877.5 Joules.
(b) The coefficient of kinetic friction between the crate and the surface is approximately 0.437.
To answer this problem, we must take into account the work done by the applied force as well as the work done by friction.
(a) The applied force's work may be estimated using the following formula:
Work = Force * Distance * cos(theta)
where the force is 150 N and the distance is 5.85 m. Since the force is applied horizontally and the displacement is also horizontal, the angle theta between them is 0 degrees, and the cosine of 0 degrees is 1.
As a result, the applied force's work is:
Work = 150 N * 5.85 m * cos(0) = 877.5 J
So, the work done by the 150 N force is 877.5 Joules.
(b) Frictional work is equal to the force of friction multiplied by the distance. The work done by friction is identical in amount but opposite in direction to the work done by the applied force since the crate travels at a constant speed.
The frictional work may be estimated using the following formula:
Work = Force of Friction * Distance * cos(theta)
The net force applied on the crate is zero since it is travelling at a constant pace. As a result, the friction force must be equal to the applied force, which is 150 N.
Thus, the work done by friction is:
Work = 150 N * 5.85 m * cos(180) = -877.5 J
Since the work done by friction is negative, it indicates that the direction of the frictional force is opposite to the direction of motion.
The coefficient of kinetic friction may be calculated using the following equation:
Friction Force = Kinetic Friction Coefficient * Normal Force
The normal force equals the crate's weight, which may be computed as:
Normal Force = mass * gravity
where the mass is 35.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2.
Normal Force = 35.0 kg * 9.8 m/s^2 = 343 N
Now, we can rearrange the equation for the force of friction to solve for the coefficient of kinetic friction:
Force of Friction = coefficient of kinetic friction * Normal Force
150 N = coefficient of kinetic friction * 343 N
coefficient of kinetic friction = 150 N / 343 N ≈ 0.437
As a result, the kinetic friction coefficient between the container and the surface is roughly 0.437.
In summary, the work done by the 150 N force is 877.5 Joules, and the coefficient of kinetic friction between the crate and the surface is approximately 0.437.
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The equipotential surfaces associated with a point charge are
The equipotential surfaces associated with a point charge are concentric shells.
What is an electric charge?Charged material experiences a force when it is exposed to an electromagnetic field due to the physical property of electric charge. You can have a positive or negative electric charge.
The equipotential surface is the region where all points with the same potential are located. On the equipotential surface, a charge can be moved from one point to another without exerting any effort.
Thus,a point charge's related equipotential surfaces are concentric shells.
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What does it mean that a theory or model is workable?
PLEASEEEEEEEE HELP ME FAST
Answer:
model is viable if the assumptions that answer it are in accordance with the fundamental principles or laws of physics and if it gives conclusions that can be tested with experiments.
Explanation:
A model in physics must be verified by experiments that are carried out to measure the consequences derived from it.
A model is viable if the assumptions that answer it are in accordance with the fundamental principles or laws of physics and if it gives conclusions that can be tested with experiments. Models that meet these conditions are said to be viable
A car must cover a distance of 300 km in 3 hours. However, for the first 2
hours it only travels 150 km. At what speed must it travel for the rest of the
distance in order to complete the journey on time?
Answer:
150 km/h
Explanation:
After the first two hours, you have traveled 150km (given) which means that you still have 300km - 150km = 150km left to travel. Since you have already traveled 2 hours, that means you must travel the remaining 150km in 3hours - 2hours = 1hour. Assuming the answer is in km/hour, you will need to travel at a speed of 150km/1h = 150km/h for the remaining of the distance.
Help pleaseeee need the answers ASAP
Answer:
- 670 kg.m/s
Explanation:
Newton's third law states that to every action, there is equal and opposite reaction force. Since the force will be same but different in direction and acted in the same time then the impulses ( force multiply by time) of the two car be same in magnitude but different in direction - 670 kg.m/s
A Motorcycle Jump. You are planning to make a jump with your motorcycle by driving over a ramp that will launch you at an angle of 30.0° with respect to the horizontal. The front edge of the ramp on which you are supposed to land, however, is 25.0 ft lower than the edge of the launch ramp (i.e., your launch height).
(a) Assuming a launch speed of 55.0 mph, at what horizontal distance from your launch point should the landing ramp be placed?
(b) In order to land smoothly, the angle of the landing ramp should match the direction of your velocity vector when you touch down. What should be the angle of the landing ramp?
a. the landing ramp should be placed at 276.298 ft horizontally from the launch point.
(b) the angle of the landing ramp is 30°.
How do we calculate?(a)
Launch speed = 55.0 mph * (1.467 ft/s)
= 80.685 ft/s
Horizontal distance = Launch speed * Time of flight
Vertical velocity = Launch speed * sin(30.0°)
Time to reach maximum height = Vertical velocity / g
Vertical distance = (1/2) *g * t²
and Time = √(2 * Vertical distance / g)
Total time of flight = 2 * Time to reach maximum height + Time for descent
Horizontal distance = Launch speed * Total time of flight
The Vertical velocity = 80.685 ft/s * sin(30.0°)
= 40.3425 ft/s
Time to reach maximum height = 40.3425 ft/s / 32.2 ft/s²
Time to reach maximum height = 1.253 s
Time of descent = √(2 * 25.0 ft / 32.2 ft/s²)
Time of descent = 0.913 s
Total time of flight = 2 * 1.253 s + 0.913 s
Total time of flight = 3.419 s
In conclusion, the horizontal distance = 80.685 ft/s * 3.419 s
horizontal distance = 276.298 ft
b.
the angle of the landing ramp is 30.0 be the same as the launch angle.
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please help !!!!! please note that two images are there................ i am urgently needs this question
Answer:
can you tell me about this property
How does simple machines make work easier?
The simple machines can help make work easier by working quicker than the people and making other peoples jobs easier.
Explanation:
I hope this helped.
The chains of a swing on a playground swing set are 4.0 m
long. What is the period of this swing?
Express your answer to two significant figures and include the appropriate units.
Answer:
2.54 seconds
Explanation:
The period of a swing on a playground swing set can be calculated using the formula:
T = 2π√(L/g)
where T is the period, L is the length of the swing's chain, and g is the acceleration due to gravity, which is approximately 9.81 m/s².
Substituting the given values, we get:
T = 2π√(4.0 m/9.81 m/s²)
T = 2π√0.407
T = 2.54 s (rounded to two significant figures)
Therefore, the period of the swing is 2.54 seconds.
Hope this helps!
Choose the answer choice that BEST completes the following sentence:
The
of the Sun is the interior or center part of this star.
O Radiative Zone
O Core
O Convective Zone
O Photosphere
The core of the Sun is the interior or center part of this star.
The features of the sunThe sun is one of the stars of the solar system that gives life to the planet earth. All the other planets revolves round it.
The features of the sun include the following:
sunspots, solar prominences, solar flares, and coronal mass ejections.The sun is also made up of several parts which include:
Hydrogen and helium.The core,The radiative zone,The convective zone, and The photosphere.The innermost or central part of the sun is the core that is made up of the highest amount of hydrogen atoms.
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A system consists of two uncharged metal spheres, each suspended on an insulating string and connected to the other by a thin
conducting wire. A positively charged rod is brought near, but does not touch, the left sphere, and the sphere is attracted to the rod. Which
of the following is correct about the net charge on the right sphere as a result?
The right sphere will acquire an equal and opposite net positive charge to balance the negative charge on the left sphere.
Electrostatic attractionSince the left sphere is attracted to the positively charged rod, it means that the left sphere acquires a temporary negative charge due to induction.
The positive charge on the rod repels electrons in the left sphere, causing them to move away from the rod side and accumulate on the opposite side, resulting in a net negative charge on the left sphere.
According to the principle of charge conservation, the net charge on the system must remain zero. Therefore, the right sphere acquires an equal and opposite net positive charge to balance the negative charge on the left sphere.
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What is the acceleration of an object that takes 20 sec to change from a speed of 200 m/s to 300 m/s ?
Given:
initial velocity, u = 200 m/sFinal velocity, v = 300 m/s Time taken, t = 20 secTo be calculated:
Calculate the acceleration of given object ?
Formula used:
Acceleration = v - u / t
Solution:
We know that,
Acceleration = v - u / t
☆ Substituting the values in the above formula,we get
Acceleration ⇒ 300 - 200 / 20
⇒ 100/20
⇒ 5 m/s²
A. A ball is thrown directly up with an initial speed of 4.00 m/s at y = 0. What is the maximum height h that it achieves, and what time th did that take? Show the final formulas for the quantities, along with the numerical answers. At 30 fps how many frames would be recorded in a video of the throw? At 120 fps?
B. From the height h in slide 2 the ball then drops back to y = 0. Find the time t0 that takes, and the velocity there (magnitude and direction). Show the final formulas for the quantities, along with the numerical answers.
C. Find the two times the ball is at the height y = ½ h. Show the final formula and the numerical answers.
D. Roughly sketch on a piece of paper what you expect the plots of y versus t and vy versus t will look like, take a picture, and paste them here.
Answer:
A) t = 0.40816 s , y = 0.916 m
Explanation:
A) For this problem we use the kinematic relations
v = v₀ - g t
the highest point zero velocities (v = 0)
t = (v₀-v) / g
t = (4 - 0) / 9.8
t = 0.40816 s
to calculate the height let's use
v² = v₀² - 2 g y
y = vo2 / 2g
y = 4 2 / (2 9.8)
y = 0.916 m
To find the number of photos, we can use a direct proportions rule, if you take 30 photos in a second in 0.40816 s how many photos does it take
# _photos1 = 0.40916 (30/1)
# _photos1 = 12
yes i take 120 fps
#_fotod = 0.40916 (120/1)
#photos = 5.87 10³
B) The ball is released from a latura h how long it takes to reach the floor
v² = v₀² + 2 g y
where the initial velocity is zero and the velocity with which the expert leaves is equal to the velocity with which v = 4 m / s leaves
v² = 2gy
v = √ (2 9.8 0.916)
v = √ (2.1397 101)
v = 4.6257 m / s
c) we ask us for the time for latura
y = L / 2
y = 0.916 / 2
y = 0.458 m
now we can use the formula
y = v₀ t - ½ g t²
0.458 = 4.00 t - ½ 9.8 t²
4.9 t² - 4t + 0.458 = 0
t² -0.8163 t +0.09346 = 0
we solve second degree execution
t = [0.8163 ±√ (0.8163² - 4 0.09346)] / 2
t = [0.8163 ± 0.540] / 2
t₁ = 0.678 m
t₂ = 0.2763 m
the shortest time is for when the ball goes up and the longest when it goes down
D) the graph of vs Vs is expected to be a closed line
and the graph of position versus time a parabola
A bullet is shot straight up with an initial speed of 180 m/s. How long is the bullet in the air and how high does the bullet go? (neglect air resistance)
Answer:
Explanation:
Time of flight is the time taken by the bulet in air. Time of flight is expressed as T = Usinθ/g where;
U is the initial velocity = 180m/s
θ is the angle of launch = 90° (Since the bullet is shot upwards)
g is the acceleration due to gravity = 9.81m/s²
T = 180sin90/9.81
T = 180/9.81
T = 18.35s
Hence the bullet will spend 18.35s in air
The height covered by the bullet is the maximum height. Maximum height is expressed as;
H = u²sin²θ/2g
H = 180²sin²90/2(9.81)
H = 180/19.62
H = 9.17m
Hence the bullet will go 9.17m high
You hike two thirds of the way to the top of a hill at a speed
of 3.5 mi/h and run the final third at a speed of 6.5 mi/h.
The correct answer is 4.14456 mi/hour.
The entire distance that an object travels in a given amount of time is the definition of average speed for that object. You can figure it out by dividing the overall distance traveled by the overall journey time.
When an object travels a distance at a variety of speeds, its average speed is the speed at which, if the object moves uniformly, it will travel the same distance in the same amount of time.
average speed= total distance / total time
total distance = 1 mile
The total time = 2 / ( 3 × 3.5 ) = 0.190 hour
time for coming = 1 / (3 × 6.5 ) = 0.05128 hour
Thus the average speed = 1 / ( 0.190 + 0.05128 ) = 1 / 0.24128 = 4.14456 mi/hour.
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Two cars approach each other from opposite directions each
with a velocity of 54 km/h. One of the cars emits a note of frequency 480 Hz. What will be the approximate frequency
heard in the other car before they cross each other?
Answer:524 Hz
Explanation:
Approximate frequency, heard in other car, when two car approaches each other, before they cross each other is 524 Hz.
What is frequency?Frequency of wave is the number of waves, which is passed thorough a particular point at a unit time.
For the two cars approaching each other the Doppler formula to find the frequency of second car is given as,
\(f_2=\dfrac{V_s+V_2}{V_s-V_1}f_1\)
Here, \(V_s\) is the speed of the sound.
Two cars approach each other from opposite directions.The velocity of car one is 54 km/h and the velocity of the car two is also 54 km/h.
Convert the unit of velocity of the car as,
\(\rm 54km/s=54\times\dfrac{5}{18}m/s\\\rm 54km/s=15m/s\)
As we know that the speed of the sound is 340 m/s and one of the cars emits a note of frequency 480 Hz.
Thus, putting the values in the above formula to find out the frequency heard in the other car before they cross each other as,
\(f_2=\dfrac{340+15}{340-15}480\\f_2=524.3\rm Hz\)
The approximate frequency heard in the other car before they cross each other is 524 Hz.
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A 575-g steel hammer, with a specific heat capacity of 460 J/kg°C hits a titanium block at 14 m/s. If all the kinetic energy of the hammer was converted into thermal energy of the hammer. What is the increase in temperature of the hammer?
0.21 °C
0.53 °C
1.2 °C
1.8
Find the x-coordinate and y-coordinates of the center of gravity (as a multiple of a)
ANSWER
• x = 0.944a
,• y = 1.333a
EXPLANATION
x- coordinate
The x-coordinate of each pair of piled blocks are:
• x₁ = x₂ = a/2
,• x₃ = x₄ = 3a/2
The weights of the blocks are:
• W₁ = 20N
,• W₂ = 80N
,• W₃ = 70N
,• W₄ = 10N
The total weight is the sum of the individual weights,
\(W=W_1+W_2+W_3+W_4=20N+80N+70N+10N=180N_{}\)By the definition of center of gravity, the x-coordinate is,
\(x_{cg}=\frac{\sum ^{}_iW_ix_i}{W}=\frac{(W_1+W_2)x_1+(W_3+W_4)x_3}{W}\)Replace with the values and solve,
\(x_{cg}=\frac{(20N+80N)\cdot\frac{a}{2}+(70N+10N)\frac{3a}{2}}{180N}=\frac{50a+120a}{180a}=\frac{170}{180}a=0.944a\)y- coordinate
The same equations apply to the y-coordinate. The y-coordinates of each weight are:
• y₁ = y₄ = a/2
,• y₂ = y₃ = 3a/2
The y-coordinate of the center of gravity is,
\(y_{cg}=\frac{\sum ^{}_iW_iy_i}{W}=\frac{(W_1+W_4)y1_{}+(W_2+W_3)y_2}{W}\)Replace with the values and solve,
\(y_{cg}=\frac{(20N+10N)\frac{a}{2}_{}+(80N+70N)\frac{3a}{2}}{180N}=\frac{15a+225a}{180}=\frac{240a}{180}=1.333a\)Hence, the coordinates of the center of gravity are (0.944a, 1.333a).