False. In finding analytic solutions of forced differential equations, the initial conditions should be considered along with the homogeneous solution and the particular solution.
The initial conditions provide specific values for the unknown coefficients in the general solution, which is a combination of the homogeneous and particular solutions. The process of finding the general solution involves evaluating both the transient and steady state solutions and then combining them, taking into account the initial conditions. A solution to a mathematical problem or a differential equation is an answer that satisfies the given conditions and rules. It can be an algebraic expression, numerical value, or a graph. Analytic solutions use mathematical techniques to find exact solutions, while numerical solutions approximate solutions using methods such as finite differences or integration. Both types of solutions are used to understand and make predictions about physical or real-world phenomena.
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two protons are separated by certain distance and each experience a repulsive force according to coulomb's law. if the two protons are replaced with two electrons, the force between the electrons is as compared to the force that existed between the two protons.
According to Coulomb's law, The force between two electrons will be the same as the force between two protons if they are separated by the same distance.
According to Coulomb's law the force between two charged particles is proportional to the magnitude of their charges and inversely proportional to the square of the distance between them. If electrons and protons both have a charge whose magnitude is same but has opposite sign, then the force between two electrons will be the same in magnitude but opposite in direction as the force between two protons.
Coulomb's law is referred as a fundamental principle in electrostatics which describes the interaction between electrically charged particles. Coulomb's law can mathematically be expressed as:
F = k * (q1 * q2) / r^2
where F is the force between the charges, k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
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(a) In unit-vector notation, what is the sum of a = (4.3 m )î + (3.4 m ) ĵ and b = ( − 13.0 m )î + (7.6 m )ĵ. What are (b) the magnitude and (c) the direction of a + b (relative to î)?
Answer: Hope this helps:
(a) The sum of two vectors a and b in unit-vector notation can be calculated using vector addition:
a + b = (4.3 m)î + (3.4 m)ĵ + (-13.0 m)î + (7.6 m)ĵ
= (4.3 m - 13.0 m)î + (3.4 m + 7.6 m)ĵ
= (-8.7 m)î + (11.0 m)ĵ
(b) The magnitude of a vector can be calculated using the Pythagorean theorem:
|a + b| = √((-8.7 m)² + (11.0 m)²) = 12.8 m
(c) The direction of a vector relative to î can be calculated using the tangent of the angle between the vector and the x-axis (î):
tan(θ) = |(11.0 m) / (-8.7 m)| = 1.26
θ = arctan(1.26) = 57.3°
So, the direction of the vector a + b is 57.3° relative to the x-axis (î).
. The classic Millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. In it, oil drops were suspended against the gravitational force by a vertical electric field. Given the oil drop to be 1.00um in radius and have a density of 920 kg/m: c. Find the weight of the drop in Newtons (N) (Hint 1: You can use the density and radius to find the mass. You may need to look up the formula for the volume of a sphere. Hint 2: Recall from PHYS 121/111, that mass is not the same as the weight) If the drop has a single excess electron, find the electric field strength needed to balance its weight d. microscope The Millikan oil drop experiment was originally used to determine the electron charge by measuring the electric field and mass of the drop.
The weight of the drop 4.19 × 10⁻¹⁸ and the electric field strength needed to balance its weight is 2.36 × 10⁵N/C.
What is the formula for the electric field?
Test = k | Q | r 2 when E = F q. The size of the electric field produced by a point charge Q is determined by this equation. The distance r in the denominator is the separation between the point of interest and the point charge, Q, or the center of a spherical charge.
a) The weight is just the mass of the drop times the acceleration of gravity.
W = mg
Or in terms of density.
W = рVg
We can calculate the volume (R=1 m = 0.000001 m) if we assume that a drop's volume is spherical.
V = 4/3πR³
V = 4/3π(10⁻⁶)³
V = 4.19 × 10⁻¹⁸
Then, using equation (1), the weight will be:
W = 920 × 4.19 × 10⁻¹⁸×9.81
W = 3.78 × 10⁻¹⁴
b) To balance the weight, the electric field times the charge must be the same value in the opposite direction, which means:
W - qE = 0
E = W/q electron
E = 3.78 × 10⁻¹⁴/1.60 × 10⁻¹⁹
E = 2.36 × 10⁵N/C.
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classify each change of state (melting, freezing, vapor- ization, condensation, and sublimation) as endothermic or exothermic.
The change of state such as melting, condensation and freezing are exothermic reaction, whereas vaporization and sublimation are considered as endothermic reaction.
What characterizes endothermic from exothermic phase changes?Heat is absorbed throughout endothermic reactions, and a positive enthalpy change results. Heat is released during exothermic reactions, and a negative enthalpy change arises.
What causes endothermic melting?Since liquid water can rotate and vibrate but solid ice could only vibrate, water has a higher energy state than ice. This implies that in order for ice to change into a state with higher energy (water), it must absorb energy; as a result, the process is endothermic with reference to the system (surrounding temperature decreases).
What causes endothermic sublimation?Heat absorption causes to sublimation since this gives some molecules the energy they need to overcome the forces that draw them to one another and escape into the vapour phase. This process is an endothermic transformation since it uses more energy.
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fill in the blank. your ability to perceive the color of a vibrant blue sky or a red rose depends on the responses of the in your retina, and your ability to find your way to the bathroom in the dark depends upon the___in your retina.
Your ability to perceive the color of a vibrant blue sky or a red rose depends on the responses of the in your retina, and your ability to find your way to the bathroom in the dark depends upon the rods in your retina.
Retinal rods are in charge of seeing in low or obscured light. They aid in peripheral (side) vision and are found on the retina's outer margins. Night vision is only visible in black and white since rods lack color vision. 500 to 1,000 times more sensitive to light than cones, rods are.
The rods utilise rhodopsin as their photopigment. For night vision, it is essential. The pigments in these materials break down in intense light, making them less sensitive to low light. The process of "dark adaption" in which darkness causes the molecules to rebuild. In light of this, the eye adapts to see in low light.
Rhodopsin regenerates after being exposed to darkness. As a result, over time, the retina's sensitivity rises (this can take approximately one hour). Reflexive changes in pupil size take place throughout this adaptation phase.
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here is an `x` by `x 1` rectangle and a `1` by `x` rectangle. the rectangles are similar. determine the value of `x` to show the possible dimensions for these rectangles.
Here is an `x` by `x 1` rectangle and a `1` by `x` rectangle. the rectangles are similar. The value of `x` to show the possible dimensions for these rectangles is x = (-1 + √5) / 2 or x = (-1 - √5) / 2
The similar rectangles have proportional sides. Given that one rectangle is x by x + 1 and the other is 1 by x, the ratio of their sides must be equal, so:
x / (x + 1) = 1 / x
Solving for x:
x^2 + x - 1 = 0
Use the quadratic formula to find the solutions:
x = (-1 ± √(1^2 - 4 * 1 * -1)) / (2 * 1)
x = (-1 ± √(1 + 4)) / 2
x = (-1 ± √5) / 2
Thus, the possible values of x are:
x = (-1 + √5) / 2 or x = (-1 - √5) / 2
Note that these are the Golden Ratio and its inverse, respectively
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the shape of the term structure include which of the following? multiple select question. stock price to earnings ratios risk expected inflation expectations of future interest rate changes
The link between short-term and long-term interest rates is referred to as the structure.
The term structure of interest rates reflects the market players' expectations for future changes in interest rates as well as their evaluation of the monetary system. Future cash flows' present values and timing are affected by changes in interest rates. The underlying value of a bank's assets and liabilities is subsequently altered. Real rate of interest, inflation premium, and interest rate risk premium are the three key factors that affect how term structures are shaped. Pure time value of money determines the real rate of interest. The necessity for compensating for anticipated future inflation gives rise to the inflation premium.
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Convert 25 meters per second (m/s) to feet per second (ft/s)
Answer: 82.021 Feet per second
Explanation:
Answer:
82.021 Feet per second
Explanation:
Light takes about 8.3 minutes to travel from the Sun to Earth. When it is closest, Neptune is 30.0 times farther from Earth than the Sun is. How long does it take for light from the Sun to reach Neptune, measured in minutes?
Answer:
it takes light approximately 0.25 minutes to travel from the Sun to Neptune.
Explanation:
The distance from Neptune to the Sun is 30.0 times farther than from the Earth to the Sun, so it's 30.0 * 93 million miles = 2,790 million miles.
The speed of light is approximately 186,282 miles per second, so it takes light approximately 2,790 million miles / 186,282 miles/second = 14.97 seconds to travel from the Sun to Neptune.
Since there are 60 seconds in a minute, this is equivalent to 14.97 seconds / 60 seconds/minute = 0.25 minutes.
So, The distance from Neptune to the Sun is 30.0 times farther than from the Earth to the Sun, so it's 30.0 * 93 million miles = 2,790 million miles.
The speed of light is approximately 186,282 miles per second, so it takes light approximately 2,790 million miles / 186,282 miles/second = 14.97 seconds to travel from the Sun to Neptune.
Since there are 60 seconds in a minute, this is equivalent to 14.97 seconds / 60 seconds/minute = 0.25 minutes.
so it takes light approximately 0.25 minutes to travel from the Sun to Neptune.
NEC sections 422.30 through 422.35 allow which of the following disconnecting means for fixed appliances not over 300 VA or 1/8 horsepower?
I. branch circuit breaker
II. attachment plug cap
III. separate disconnect switch
III separate disconnect switch allows disconnecting means for fixed appliances through NEC sections.
What does the disconnecting means NEC code mean?Unless the location and configuration make the function obvious, each disconnecting device should be legibly labeled to show what it is intended to do. The marking must indicate the circuit source that supplies the disconnecting mechanism in all constructions other than one- or two-family homes.
What does the National Electric Code's Article 422.30 mean?Each appliance must be concurrently unplugged from all ungrounded conductors in line with Part III of Article 422 per Section 422.30.
What is the highest voltage drop that the NEC permits?In accordance with the NEC, the maximum voltage drop for either the feeder or branch circuit shouldn't exceed than 3% and the combined maximum shouldn't be more than 5%.
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a wire with mass 0.397 g is stretched between two points 88 cm apart. if the tension of the string is 110 n, the frequency of the second harmonic is hz. (give answer to the nearest ones place.)
When a wire with a mass of 0.397 g is stretched between two places 88 cm apart, the frequency of the second harmonic is 143 Hz.
What is frequency?The frequency of a repeated event is the number of occurrences per unit of time. It is separate from angular frequency and is sometimes referred to as temporal frequency. The unit of frequency is hertz, which equals one occurrence every second.
Here,
To calculate the frequency of the second harmonic, we need to know the tension and the linear mass density of the wire. The linear mass density can be calculated as:
mass/length = 0.397 g / 88 cm = 0.0045 g/cm
We can then use the formula for the frequency of a string under tension:
f = (1 / 2L) * (T / μ)^0.5
where f is the frequency, L is the length of the string, T is the tension, and μ is the linear mass density.
Substituting the values from the problem, we get:
f = (1 / 2 * 88 cm) * (110 N / 0.0045 g/cm)^0.5 = (1 / 176 cm) * (24444 N/g)^0.5
f = (24444 N/g)^0.5 / 176 cm
f = 143 Hz
So, the frequency of the second harmonic is 143 Hz when a wire with mass 0.397 g is stretched between two points 88 cm apart.
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the video states that the planetary orbits are shown to scale. which statement correctly describes the way the planet sizes are shown compared to their orbits?
In relation to their orbits, all of the planets are substantially too big. According to Kepler's first law, the Sun is at one focus of each planet's elliptical orbit.
What one of the following traits does each planet inside the solar system share?It specifies three requirements for a planet: It must revolve around the Sun, a planet in our solar system. It must be large enough for gravity to pull it in a spherical direction. It must have been large enough that any nearby objects of a similarly sized were removed by its gravitational pull.
Which of following traits applies to all four inner solar system planets?The interior planets are all solid rocky, dense planets The moons of the inner planets are either absent or limited to one Earth or three Mars. The inner planets don't have any rings. The planets orbits have smaller orbits all around Sun than the outer planets, but they all rotate more slowly.
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a rubber ball moving with an initial mom p collides with a vertical wall. which of the following is the correct direction of changeable momentum vector than the ball experience during the collision
Arrοw to the right, is correct about the vector of impulse that the call experiences during the cοllision.
Thus οption 2 is correct
What is the mοmentum vector's direction?
The ball's velοcity and the momentum vector have the same general directiοn.
It was stated befοre that an object moves in the same general direction as the velοcity vector.
Mοmentum will remain constant regardless of the impact type.
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Cοmplete question:
A rubber ball mοving with an initial momentum p1 collides elastically with a vertical wall. Which of the fοllowing is correct about the vector of impulse that the call experiences during the cοllision?
MomentumArrow to the rightMomentum of the system is conservedVector UpA small car of mass 500 kg is pushing a large truck of mass 980 kg due east on a level road. The car exerts a horizontal force of 1500 N on the truck. What is the magnitude of the force that the truck exerts on the car
Answer:
Below
Explanation:
Equal and opposite 1500 N
in order to determine the size of the heating element of a new oven, we wish to determine the rate of heat loss through the walls, door, and the top and bottom sections of the oven. in your analysis, would you consider this to be a steady or
Since the thermal conditions in the kitchen and the oven, in general, fluctuate over time, heat transfer through the walls, door, and top and bottom sections of an oven is temporary in nature.
However, under the worst predicted conditions, such as the oven's highest temperature setting and the kitchen's projected lowest temperature (the so-called "design" conditions), we would examine this issue as a steady heat transmission problem. If the oven's heating element is big enough to maintain the intended temperature setting under the worst case scenario, it is also big enough to do so by cycling on and off under all circumstances.
Since heat will be entering the oven through each of its six sides, heat transfer from the oven will be three-dimensional in nature. Though it can be considered as being one-dimensional, heat transfer through any wall or floor occurs in the direction normal to the surface. Therefore, by assuming that the heat transfer is one-dimensional at each of the four sides as well as the top and bottom portions, as well as by summing the computed values of heat transfers at each surface, this problem can be substantially simplified.
The question is incomplete, it should be:
In order to determine the size of the heating element of a new oven, it is desired to determine the rate of heat transfer through the walls, door, and the top and bottom section of the oven. In your analysis, would you consider this to be a steady or transient heat transfer problem? Also, would you consider the heat transfer to be one-dimensional or multidimensional?
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Identify which of the following you would expect to be characteristic of a solid with the formula P4. Drag the appropriate items to their respective bins: poor thermal conductivity, very hard, low melting point, high electrical conductivity
Characteristic
Not characteristic
Thermal conductors are substances that are efficient thermal energy conductors. Metals are excellent conductors of heat. Heat insulators are substances that have a low thermal conductivity. Materials like plastic and wood are heat insulators, as are gases like air.
How do electrical conductivity and melting point relate to one another?The electrical conductivity changes with temperature as a new property, declines after the melting point is reached, and ultimately totally disappears. Many experimental tests, including the phase change of metals utilising electrical wire bursts, have seen this disappareance.
High thermal conductivity materials will transmit heat quickly, either by absorbing heat from another material that is hotter than them or by transferring heat to another material that is cooler.
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an electric field of magnitude 3.54 kn/c is applied along the x axis. calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if the following conditions are true
Complete question: Conditions are:
(A) The plane and the yz plane are parallel. You could be presuming that the electric field and rectangular plane are not in the same relative direction.
(b) The plane is perpendicular to the x-y plane. [tex]N·m^2/C \s[/tex]
(C) The y-axis is contained within the plane, and its normal intersects the x-axis at a 39.0° angle. [tex]Nm2/C[/tex]
Values of electric flux for different conditions in electric field are (a) 0.861 [tex]Nm^2/C[/tex], (b) no electric flux and (c) 0.697 [tex]Nm^2/C[/tex]
The electric flux is the flow of electric field through a surface and is calculated by multiplying the surface area with the component of the electric field that is perpendicular to the surface.
In electric flux of electric field:
(a) If the rectangular plane is parallel to the yz plane, the electric field is perpendicular to the plane and the electric flux will be equal to the surface area multiplied by the electric field. The surface area of the plane is 0.350 m * 0.700 m = 0.245 [tex]m^2[/tex]. Thus, the electric flux = 0.245 [tex]m^2[/tex]* 3.54 kN/C = 0.861 [tex]Nm^2/C.[/tex]
(b) If the plane is parallel to the xy plane, the electric field will be parallel to the plane and there will be no electric flux through the plane.
(c) If the plane contains the y axis and its normal makes an angle of 39.0° with the x axis, the component of the electric field perpendicular to the plane will be 3.54 kN/C * cos(39.0°). The electric flux = 0.245 [tex]m^2[/tex] * 3.54 kN/C * cos(39.0°) = 0.697 [tex]Nm^2/C[/tex].
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imagine dropping a rubber ball to the floor describe what happens to the ball after you release it what kind of sights and/or sounds occur when the rubber ball reaches the floor
The ball's gravitational potential energy is converted into kinetic energy as it falls toward the ground. The ball's kinetic energy will keep rising as it picks up speed until it eventually slams into something.
When a rubber ball is dropped and hits the ground, what force causes it to bounce?Gravity draws a ball toward the floor when you drop it. The ball gains kinetic energy, the energy of motion. That energy must go somewhere when the ball stops rolling and reaches the ground. The ball is bent from its original round shape to a squashed shape by the energy.
What occurs when a ball is dropped?Gravity drags the ball down and increases its speed as you drop it. At the instant of impact, it squashes when it meets the ground. The floor presses against the squished ball as it returns to its former shape, and the floor pushes back in response.
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When a rubber ball is dropped to the floor, the ball's elasticity causes it to bounce upon impact.
What is rubber ball?
Rubber ball is a soft, bouncy ball made of rubber. It is generally used as a toy, but can also be used in sports and games. Rubber balls are available in a variety of sizes, shapes, and colors. They are usually made from natural latex rubber, but some are made from synthetic materials like polymers and silicone. Rubber balls are lightweight, durable, and can bounce off a variety of surfaces. Because of their bounciness and softness, rubber balls are great for bouncing, throwing, catching, and playing games. They are also great for kids because they are safe and easy to handle. Rubber balls can be used in games like catch, dodgeball, and even for juggling. They can also be used for bouncing off walls and obstacles. Rubber balls are a great way to have fun, get exercise, and develop coordination skills.
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A blue ball is thrown upward with an initial speed of 22.8 m/s, from a height of 0.7 meters above the ground. 2.8 seconds after the blue ball is thrown, a red ball is thrown down with an initial speed of 9.9 m/s from a height of 29.5 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s2.
1) What is the speed of the blue ball when it reaches its maximum height?
0
m/s
2) How long does it take the blue ball to reach its maximum height?
2.35
s
3) What is the maximum height the blue ball reaches?
27.22242
m
4) What is the height of the red ball 3.64 seconds after the blue ball is thrown?
17.7290323
m
5) How long after the blue ball is thrown are the two balls in the air at the same height?
4
s
[Delayed Feedback]
6) Which plot correctly shows the velocity of the two balls as a function of time?Three plots of velocity vs time for the red and blue balls
A
B
C
[Delayed Feedback]
7) Which statement is true about the blue ball after it has reached its maximum height and is falling back down?
The acceleration is positive and it is speeding up
The acceleration is negative and it is speeding up
The acceleration is positive and it is slowing down
The acceleration is negative and it is slowing down
A blue ball is thrown upward at an initial speed of 30.6 meters per second from a height of 0.7 meters above the ground. The blue ball is tossed, and with 2.8 seconds left, a red ball is released.
What is the unit of measurement for speed?
An Sunt unit, kilometers an hour (symbol km/h), metres per second (icon mi/h or mph), naval km/h (symbol kn or km), foot each minute (symbol dps or feet high), feet per minute (symbol m s 1 and m/s), and Mach are all metric units of speed.
What elements make up speed?
Time split by distance are the speed-related metrics. The measurement unit of speed is the meter per second.
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which of the following units would need to be converted before being used for a caculation
Answer:
it depends what are the units
Explanation:
Answer:
What and where are the units that you are talking about in your question that you are asking about.
Explanation:
A bicycle has wheels of radius 0.330 m. Each wheel has a rotational inertia of 0.0800 kg⋅m2 about its axle. The total mass of the bicycle including the wheels and the rider is 72.0 kg. When coasting at constant speed, what fraction of the total kinetic energy of the bicycle (including rider) is the rotational kinetic energy of the wheels?
The ratio of the rotational kinetic energy of the rider and the bicycle is 0.0205.
What is Rotational kinetic energy?
Rotational energy or the angular kinetic energy is the kinetic energy which is due to the rotation of an object and is also a part of the total kinetic energy.
We know that Rotational Kinetic Energy is given by,
KE(rid) = 1/2 Iω²
KE(rid) = 1/2 I (v/r)²
KE(rid) = 1/2 I (v²/r²)
where, I is the inertia and ω is the angular velocity.
That equation are perfect for the 4 wheel, however we need a similar expression for the cycle
KE (bicycle) = 1/2 mv²
The total energy can be expressed as follow,
Kt = K(rid) + K(bicycle)
Kt = 1/2 I (v²/r²) + 1/2 mv²
K(rid)/ K(bicycle) = 2I/ (2I + mr²)
(You only need to put the previous values and simplify)
Substituting , I = 0.0800, m = 72kg, and r = 0.330 m
We have,
K(rid)/ K(cycle) = 2I/ (2I + mr²)
K(rid)/ K(cycle) = 2 × 0.080/ (2 × 0.080 + 72×(0.330)²)
K(rid)/ K(cycle) = 0.16/ (0.16 + 72 × 0.108)
K(rid)/ K(cycle) = 0.16/ (0.16 + 7.776)
K(rid)/ K(cycle) = 0.16/ 7.936
K(rid)/ K(cycle) = 0.0205
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|| A 180 g air-track glider is attached to a spring. The glider is pushed 10.2 cm against the spring, then released. A student with a stopwatch finds that 14 oscillations take 10.5 s. What is the spring constant?
The spring constant of the spring is 4.013 N/m
The formula for calculating the period of oscillation is as follows:
T = 2π √(m / k)
m = the spring's massk = the spring constantTo find the spring constant, we can retrofit the formula as follow:
k = 4π² (m / T²)
From the question, we are told that the student finds that 14 oscillations take 10.5 s, meaning the number of oscillations in one second is 0.75 (f = 0.75).
Period (T) = 1/0.75 - 1.33 sec
Apply that number to the formula above:
k = 4π² (m / T²)
k = 4 * 3.14² (0.18 / 1.33²)
k = 4.013 N/m
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a 0.010 kg bullet is fired into a stationary block of wood of mass 5.0 kg suspended from a string. the bullet imbeds in the block, and the block/bullet swing to an elevation 0.10 m above where they started.
The initial momentum of the bullet is 0.01 kg m/s. After it embeds in the wooden block, the momentum of the block and bullet together is 0.01 kg m/s.
The conservation of momentum states that momentum is conserved, so the total momentum of the block and bullet must remain the same. This means the final velocity of the block and bullet is 0.01 kg m/s.
To find the maximum height that the block and bullet will reach, you can use the equation for the kinetic energy of an object: [tex]KE =\frac{1}{2} mv^{2}[/tex]. The kinetic energy of the block and bullet is equal to the potential energy they gain when they reach a height of 0.10 m. So, the equation would look like this:
[tex]KE =\frac{1}{2} mv^{2} = mgh[/tex]
Where m is the mass of the block and bullet, v is the velocity (0.01 m/s), and h is the height (0.10 m). Solving for h, we get h = [tex](\frac{1}{2} )(\frac{v^{2} }{g} )[/tex]= 0.25 m.
So, the maximum height that the block and bullet will reach is 0.25 m.
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two rods, one made of brass and the other made of copper, are joined end to end. the length of the brass section is 0.200 m and the length of the copper section is 0.800 m . each segment has cross-sectional area 0.00700 m2 . the free end of the brass segment is in boiling water and the free end of the copper segment is in an ice-water mixture, in both cases under normal atmospheric pressure. the sides of the rods are insulated so there is no heat loss to the surroundings. part a what is the temperature of the point where the brass and copper segments are joined? express your answer in degrees. activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type t
The temperature of the point where the brass and copper segments are joined will be less than 100°C because k1 < k2
How to calculate?The rate of heat flow from the boiling water to the junction is given by:
q1 = k1 * A * (T1 - Tj) / L1
The rate of heat flow from the ice-water mixture to the junction is given as :
q2 = k2 * A * (Tj - T2) / L2
Because heat is conserved, q1 = q2, so we have:
k1 * A * (T1 - Tj) / L1 = k2 * A * (Tj - T2) / L2
Finding for Tj, we have :
Tj = (k1 * T1 * L1 + k2 * T2 * L2) / (k1 * L1 + k2 * L2)
Substituting the given values, we have:
Tj = (k1 * 100 * 0.200 + k2 * 0 * 0.800) / (k1 * 0.200 + k2 * 0.800) = 100 * 0.200 / (0.200 + 0.800 * k1/k2)
In conclusion, Tj will be less than 100°C
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a 60 g tennis ball with an initial speed of 35 m/s hits a wall and rebounds with the same speed. (figure 1) shows the force of the wall on the ball during the collision.
The value of Fmax, the maximum value of the contact force during the collision is 1050N
Given the mass of tennis ball (m) = 60g
The speed of ball (v) = 35m/s
We know that when the ball hits the wall and rebound momentum acts on it such that momentum before and after collision should be same.
Momentum before hitting the wall is (p1) = mv = [tex]60 x 10^-3 x 35[/tex] = 2.1
Momentum after rebound is (p2) = -mv = -2.1
The change in momentum is calculated as: Δp = p1- p2
Then, Δp = 2.1 - (-2.1) = 4.2
We know that change in momentum is also called impulse such that:
Δp = F(t)dt
We need to evaluate area under curve which is trapezium =
[tex]6 +2/2 x 10^-3 x Fmax[/tex] = [tex]4 x 10^-3xFmax[/tex]
Fmax = 1050N
Hence the maximum force of collision is 1050N
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complete question: a 60 g tennis ball with an initial speed of 35 m/s hits a wall and rebounds with the same speed. (figure 1) shows the force of the wall on the ball during the collision. What is the value of Fmax, the maximum value of the contact force during the collision?
A car of 1000kg moves at a constant speed of 20m/s along a horizontal road. If the frictional force is 200N, calculate the power developed by the engine
The power developed by the engine is 4 kilowatts.
What is Frictional force?Friction force can be defined as the force resisting the relative motion of solid surfaces, fluid layers and material elements sliding against each other.
To calculate the power developed by the engine, we need to find the net force acting on the car and multiply it by its velocity.
Since the car is moving at a constant speed, the net force acting on it is equal to the frictional force:
Net force = Frictional force = 200 N
Power = Force x Velocity = 200 N x 20 m/s = 4000 Watts = 4 kilowatts.
So, the power developed by the engine is 4 kilowatts.
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Mark climbs up onto the roof of his house to hang a new flood light above the garage. Being afraid of heights, Mark carefully looks over the edge and ponders a possible fall to the ground below. The top of the roof is 5 meters above the ground below. If Mark has a mass of 65 kg, which of the following values Mark's gravitational potential energy?
A- 3188 J
B- 325 J
C- 49 J
D- 638 J
This potential energy is known as gravitational potential energy. It is the gravitational field's potential energy that is released when two objects fall in close proximity to one another.
The short answer to the question of potential energyThe term "potential energy" refers to the energy that is conserved or stored in a material or object. The location, configuration, or status of the substance or object determines the stored energy.
Which potential energy is an example?Energy that has been stored is called potential energy. A battery, a stretched spring, and lifting an object are some examples. There are two major categories of energy: potential and kinetic.
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find the speed v0 with which the quarterback must throw the ball. answer in terms of d , tc , vr , and g .
The required speed v₀ with which the quarterback must throw the ball is v₀ = √(vr^2 + 2gd) / cos(tc).
What is Speed?Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.
According to question:The speed v₀ with which the quarterback must throw the ball can be determined using the following formula:
v₀ = √(vr^2 + 2gd) / cos(tc)
where:
d is the distance from the quarterback to the receiver,
tc is the angle between the ground and the trajectory of the ball,
vr is the velocity of the receiver (assumed to be moving horizontally), and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Note that this formula assumes that the ball is thrown with a velocity that is equal to the initial velocity of the receiver. If the receiver is moving in a different direction, or with a different speed, the formula may need to be adjusted accordingly.
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a ball is dropped from the top of a building 96 ft. tall. the height after time (in seconds) is given by , where is the height of the ball when dropped.
That graph of your function is a parabola, which is the first thing to notice in this situation. For a parabola, the vertex at point y = ax2 + bx + c is the (h, k).
How do you find the height of where a ball was dropped?The height at which a ball was thrown can be determined in several ways.
In free fall, objects are known to follow the equation h=-4.9t2+c, where t is the time in seconds and c is the starting height. Timed by a student, the plunge occurred in 1.46 seconds. Use this to calculate the height, to at least two decimal places, where the ball was dropped.
Using this equation y = -16t2 + 96t + 3, we know that a = -16, b = 96, and c = 3 h = -b/2a h = -(96) / 2(-16) h = -96 / -32 h = 3 seconds.
This indicates that in three seconds, the ball will have reached its highest point. However, the question of what height that is poses a challenge. Let's thus add t=3 to our equation as a last step.
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A student puts a strong magnet on the outside of a copper pipe and notices the pipe is nonmagnetic. The student then drops the magnet through the pipe and the magnet immediately descends at a constant rate. Which of the following describes why the magnet moves as described?
The interaction with the copper pipe induces a current in the magnet.
The moving magnetic field induces a current in the copper pipe.
The downward motion of the magnet induces a magnetic field, which attracts the magnet to the copper.
The strong magnetic field causes air turbulence in the pipe.
The interior of the copper pipe is magnetic and attracts the magnet.
The flowing magnetic field creates a current in the copper pipe, which causes the magnet to move as specified.
What is magnetism?Magnetism is a physical quality mediated by a magnetic field that refers to the ability to create attracted and repulsive occurrences in other substances. Diamagnetic materials are those that magnetize freely when put in a magnetic field. However, the magnetization is oriented in the opposite direction as the magnetic field. These materials' magnetism is referred to as diamagnetism.
Here,
The flowing magnetic field creates a current in the copper pipe, which causes the magnet to move as specified. This is known as electromagnetic induction, and it occurs when a changing magnetic field generates an electric field, which induces a current in a conductive substance such as copper. The induced current generates its own magnetic field, which opposes the magnetic field of the magnet, slowing it down and forcing it to drop at a steady pace.
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