A puck moves at 2.35 m/s in a -22° angle.It is pushed for 0.215 seconds by a hockey stick, changing its velocity to 6.42 m/s in a 50.0° direction. The negative sign indicates that the puck has fallen below its initial height.
How to solve the given problem with the help of trigonometry?
To solve the problem, we need to use the equations of motion and trigonometry.
First, let's find the initial velocity components:
[tex]\mathrm V_{i,x} = v_i cos(\theta_i) = 2.35 cos(-22^\circ) \approx 2.216\text{ m/s}[/tex]
[tex]\mathrm V_{i,y} = v_i sin(\theta_i) = 2.35 sin(-22^\circ) \approx -0.891\text{ m/s}[/tex]
where [tex]v_i[/tex] is the initial velocity and [tex]\theta_i[/tex] is the initial angle in degrees.
Next, we need to find the final velocity components:
[tex]\mathrm V_{f,x} = v_f cos(\theta_f) = 6.42 cos(50^\circ) \approx 4.121\text{ m/s}[/tex]
[tex]\mathrm V_{f,y} = v_f sin(\theta_f) = 6.42 sin(50^\circ) \approx 4.936\text{ m/s}[/tex]
where [tex]v_f[/tex] is the final velocity and [tex]\theta_f[/tex] is the final angle in degrees.
The change in velocity components are:
[tex]\Mathrm\Delta V_x = V_{f,x} - V_{i,x} \approx 1.905\text{ m/s}[/tex]
[tex]$\Delta V_y = V_{f,y} - V_{i,y} \approx 5.827\text{ m/s}[/tex]
The time of the push is t = 0.215 s.
Using the equation of motion, we can find the change in position in the y-direction:
[tex]$\Delta y = V_{i,y} t + \frac{1}{2} a_y t^2[/tex]
where a_y is the acceleration in the y-direction.
Since the puck is in flight, the only force acting on it is gravity, which causes an acceleration of [tex]-9.8 m/s^2[/tex] in the y-direction.
Plugging in the values, we get:
[tex]\Delta y = (-0.891\text{ m/s})(0.215\text{ s}) + \frac{1}{2} (-9.8\text{ m/s}^2)(0.215\text{ s})^2 \approx -0.139\text{ m}[/tex]
Note that the negative sign indicates that the puck has fallen below its initial height.
Therefore, the change in position in the y-direction is approximately 0.139 m.
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Answer:
0.434
Explanation:
A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10. 6m. In 1. 00 ms, this laser produced 9. 50 MW of power. How many photons were produced?
To calculate the number of photons produced by the carbon dioxide laser, we need to use the formula relating the energy of a photon to its frequency or wavelength.
The formula is: E = hf = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 × 10^-34 J s), f is the frequency, c is the speed of light (3 × 10^8 m/s), and λ is the wavelength. First, we need to calculate the energy of one photon with a wavelength of 10.6 μm: E = hc/λ = (6.626 × 10^-34 J s) × (3 × 10^8 m/s) / (10.6 × 10^-6 m) = 1.862 × 10^-20 J. Next, we need to calculate the total energy produced by the laser in 1.00 ms: Energy = Power × Time = 9.50 MW × 1.00 × 10^-3 s = 9.50 × 10^3 J. Finally, we can calculate the number of photons produced by dividing the total energy by the energy of one photon: Number of photons = Energy / E = (9.50 × 10^3 J) / (1.862 × 10^-20 J) = 5.098 × 10^23 photons. Therefore, the carbon dioxide laser produced 5.098 × 10^23 photons when it emitted infrared radiation with a wavelength of 10.6 μm and a power of 9.50 MW for 1.00 ms.
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The mass of kerosene needed to boil 5 liters of water at 10°C is (q = 4. 6. 10 J/ kg, % = 4200 J/ kg·grad, heat losses are neglected)
The mass of kerosene needed to boil 5 liters of water at 10°C is approximately 28070 kg.
To determine how much kerosene is needed to boil 5 liters of water at 10°C, we must first determine how much heat is needed to bring the water's temperature up to 100°C and then boil it at that degree.
Heating water from 10°C to 100°C:
4.186 J/g°C (or 4.186 kJ/kg°C) is the specific heat capacity of water. As a result, J is the quantity of heat needed to raise the temperature of 5 liters (or 5000 grams) of water from 10°C to 100°C is:
Q1 = m x c x ΔT
= 5000 g x 4.186 J/g°C x (100°C - 10°C)
= 1952200 J
Water vaporizes at a heat of 2260 kJ/kg (or 2.26 × 106 J/kg) at 100 °C when it is heated to boiling. To boil 5 liters (or 5000 grams) of water at 100°C, the following amount of heat is needed:
Q2 = m x L
= 5000 g x 2.26 x 10^6 J/kg
= 1.13 x 10^10 J
To heat and boil the water, the following amount of heat is needed:
Qtot = Q1 + Q2
= 1952200 J + 1.13 x 10^10 J
= 1.149522 x 10^10 J
Where m is kerosene's mass, c is kerosene's specific heat capacity (4.6 kJ/kg°C), and ΔT is the temperature change of the kerosene.
Assuming that the initial temperature of the kerosene is also 10°C, the temperature change of the kerosene is:
ΔT = 100°C - 10°C
= 90°C
Substituting the values into the equation, we get:
1.149522 x 10^10 J = m x 4.6 kJ/kg°C x 90°C
Solving for m, we get:
m = 28069.6 kg
Hence, 28070 kg of kerosene is required to boil 5 liters of water at 10°C.
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Calculate the velocity of a 9.3 kg object that has 5.4 kgm/8
Answer:
To calculate the escape velocity: Find the object's mass in kilograms, m, and its radius in meters, r. Multiply m by the gravitational constant (6.674 × 10 −11) and then by 2. Divide the result of step 2 by r. Raise the result of step 3 by 0.5. The result is the escape velocity
Explanation:
Which of the following correctly lists the substances from highest to lowest pH? о O O A lemon juice, distilled water, milk of magnesia Jhy B. distilled water, milk of magnesia, lemon juice C. lemon juice, milk of magnesia, distilled water D. milk of magnesia, distilled water, lemon juice
Acidity is indicated by pH values lower than 7, while baseness is shown by pH values higher than 7. The pH of water is actually a measurement of the proportion of free ions of hydrogen and hydroxyl that are in the solution.
What is the suggested example?The souls were shown by him. He pointed to the nicely arranged clothing on the nightstand next to the bed. They still lacked one goat, according to a hasty count.
Which value is indicated?The monitored value from the a transaction file that the monitor reported for a known amount of the specified Parameter. Precision is determined by comparing this value to the known quantity known as REAL VALUE.
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Shawna's hockey coach is planning for the upcoming game against their biggest rival.she thinks her players aren't quite as fast as most of the individuals on the other team and she knows they aren't as experienced the coach stresses fundamentals and proper passing techniques.one basic offensive strategy her coach ask her players to use is to make sure they pass the puck on
Answers:
1 a spot slightly ahead of their teammate
2 the teammate covered by two defenders
3 their teammate's back skate
4 their teammate's front skate
Shawna's hockey coach is committed to helping her players succeed in their upcoming game against their biggest rival.
What is mass?Mass is a fundamental physical property of every object that exists in the universe. It is the measure of an object's inertia and resistance to acceleration. Mass is measured in kilograms or pounds, and is commonly used to measure the weight of an object. Mass is an intrinsic property of an object that does not depend on its location or the gravitational field in which it is situated. Mass is related to the amount of matter, or material, an object contains, and it is not affected by gravity. Mass is an invariant quantity, meaning it is unaffected by any external forces or conditions.
To this end, she emphasizes the importance of fundamental hockey skills and proper passing techniques. She encourages her players to make quick, accurate passes to teammates in order to create more scoring opportunities; the goal is to always have an open man. To achieve this, the coach instructs the players to pass the puck to a spot slightly ahead of their teammate, the teammate covered by two defenders, their teammate's back skate, or their teammate's front skate. By focusing on the basics and utilizing these strategies, the coach hopes to give her team the best chance of coming out on top.
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2. A golfer wishes to chip a shot into the hole 50 m away on flat level ground. If the ball flies to a
maximum height of 25 m, what speed must it have initially to reach the hole?
The speed the golf which is in projectile motion must have initially to reach the hole is 31.321 m/s.
What is projectile?A projectile is any object which is thrown into the space upon which the only acting force is the gravitational force. The primary force which is acting on a projectile is only gravity. This does not necessarily mean that other forces do not act on the object, just that their effect is minimal compared to the gravity.
A golfer wishes to chip a shot into the hole, which is 50 meters away on the flat level ground. If the ball flies to a maximum height of 25 meters.
The angle with which the ball flies,
tan θ = 25 m/ (50m/2)
tan θ = 1
θ = 45°
If u is the initial speed, the maximum height of the ball will be:
H = u² sin²θ / 2g
By putting the values, we get
25 = u² sin²45 / (2 × 9.81)
u = 31.321 m/s
Thus, the initial speed is 31.321 m/s.
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Which requires more work, lifting a 90 kg bag up 6 m in 4 minutes, or lifting a 45 kg bag up 12 m in 2 minutes?
Answer:
W = m g h increase in PE due to lfting bag
W1 = 90 kg * 9.8 m/s^2 * 6 m
W2 = 45 kg * 9.8 m/s^2 * 12 m
W2 / W1 = 1 the work is the same in both cases
The power required is different
P = W / t
Since t is smaller for W2 and the work output is the same the power required to produce W2 is twice as great
You push a 25 kg wooden box across a wooden floor at a constant speed of 1. 0 m/s. How much force do you exert on the box?
You exert a force of 122.625 N on the box, in the opposite direction to the force of friction.
Normal force = mg
Therefore, the force of friction is:
friction = (0.5)(mg) = (0.5)(25 kg)(9.81 m/s^2) = 122.625 N
force exerted by you on the box = -friction = -122.625 N
Force is a fundamental concept in physics that describes the influence of one object on another. It is a vector quantity, meaning it has both magnitude and direction. Force is measured in units of Newtons (N), and is calculated as the product of an object's mass and its acceleration (F=ma).
There are many types of forces, including gravitational, electromagnetic, and nuclear forces. Gravitational force is the force that pulls objects towards each other due to their masses. The electromagnetic force is the force that is responsible for the interaction between electrically charged particles, such as electrons and protons. Nuclear forces are responsible for the interactions between particles in the atomic nucleus.
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8. Inferring When cars pass one another in
opposite directions on the highway, they tend
to be forced together. Use Bernoulli's principle
to explain why this happens.
someone help please
Bernoulli's principle can be used to explain the motion of cars on the highway as the cars moving fast create areas of low pressure around them, causing them to be pushed together by the higher pressure.
What is Bernoulli's principle?Bernoulli's principle can be formulated by Daniel Bernoulli. The principle states that as the speed of a moving fluid increases such as liquid or gas, the pressure within the fluid decreases through it. Although, Bernoulli deduced this law, it was Leonhard Euler who derived the Bernoulli's equation in its usual form in the year 1752.
When the two cars passes one another in opposite directions on the highway, then they tend to be forced together. Use the Bernoulli's principle to explain why this happens with the cars. The cars moving fast on the highway create areas of low pressure around them, causing them to be pushed together by the higher pressure.
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A galvanic cell at a temperature of is powered by the following redox reaction: Suppose the cell is prepared with and in one half-cell and and in the other. Calculate the cell voltage under these conditions. Round your answer to significant digits. 2vo2
At the given temperature, the cell voltage can be calculated using the standard reduction potentials of the reactants and products involved in the redox reaction. Using the values provided, the cell voltage would be 2.12 V, rounded to two significant digits.
An electrochemical cell that converts the chemical energy of spontaneous redox reactions into electrical energy is known as a galvanic cell or a voltaic cell. Galvanic cell Voltaic cell is an electrochemical cell that makes use of chemical reactions to generate electrical energy.A galvanic cell or voltaic cell is an electrochemical cell in which an electric current is generated from spontaneous Oxidation-Reduction reactions
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A 4357-kg roller coaster car starts from rest at the top of a 36.5-m high track. Determine the speed of the car at the top of a loop that is 10.8 m high.
Answer:17.24 m/s
Explanation:
if 1 cubic centimeter of water has a mass of 1 gram then a liter of water has a mass of _ gram(s)
A roller coaster starts at a high peak with 60 J of gravitational potential energy. When it reaches a second peak, it has only 50 J of potential energy. Calculate the difference in energy and explain what happened to it.
Answer:
10 J
Explanation:
The difference in energy between the two peaks is 10 J.
As the roller coaster moves from the first peak to the second peak, it loses 10 J of gravitational potential energy. This energy is converted into other forms of energy, such as kinetic energy (the energy of motion) and thermal energy (the energy of heat).
Some of the gravitational potential energy is converted into kinetic energy as the roller coaster accelerates down the first peak. As it reaches the second peak, some of the kinetic energy is converted back into gravitational potential energy, but not all of it. The difference between the initial and final potential energy represents the energy that was lost or converted into other forms.
When something moves, there is more than one __________________ involved
Answer:
Explanation:
force
How does a heater in one corner of a fish aquarium warm the whole aquarium? (1 point)
O The heater warms the glass of the aquarium, which warms the water.
O The heater creates convection currents, which transfer warmer water away from the heater and cooler water toward the heater.
O The heater warms the air above the aquarium, which warms the water.
O The heater adds thermal energy evenly to the aquarium's water.
Answer:
The heater creates convection currents, which transfer warmer water away from the heater and cooler water toward the heater.
Explanation:
When a heater is placed in one corner of a fish aquarium, it heats up the water around it. As the water around the heater gets warmer, it becomes less dense and rises to the top of the aquarium. This movement of warmer water creates a convection current, which transfers the warmer water away from the heater and towards the other areas of the aquarium.
There is not really a subject for this but, Theoretically, What black hole would be bigger, m87 aka Messier 87 or Ton 618 aka Tonantzintla 618. Although Messier 87 was the first picture of one, what would the size still be of Tonantzintla 618 I would like to know what you think
The event horizon is directly related to the mass of the black hole, with larger black holes having larger event horizons.
What is Black Hole?
A black hole is an astronomical object that has collapsed to such a small size that its gravitational pull is so strong that nothing, not even light, can escape it. Black holes are formed from the remnants of massive stars that have run out of fuel and undergone a catastrophic collapse, or from the merging of two or more smaller black holes.
M87 and Ton 618 are both supermassive black holes, with masses estimated to be around 6.5 billion and 66 billion times the mass of the Sun, respectively. However, the size of their event horizons would depend not only on their mass but also on their spin and the density of the surrounding matter. It is therefore not possible to predict which black hole would be bigger without additional data and calculations.
It is worth noting that the first image of a black hole that was released in 2019 was actually an image of the event horizon of the black hole in M87, not the black hole itself. The event horizon of M87's black hole was estimated to be around 40 billion km in diameter, which is larger than the entire solar system.
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Isaac uses a lever and applies 42 Newtons to lift a 15-kilogram box. He applies the force over a distance of 6 meters to lift the box a distance of 2 meters. How much work is done?
- 84 Joules
-252 Joules
-630 Joules
-336 Joules
-65 Joules
Answer:
The work done by Isaac can be calculated using the formula:
work = force x distance
where force is the amount of force applied and distance is the distance over which the force is applied. In this case, the force applied by Isaac is 42 Newtons and the distance over which the force is applied is 6 meters. However, we need to calculate the actual distance moved by the box, which is different from the distance over which the force is applied.
To calculate the distance moved by the box, we can use the formula for the mechanical advantage of a lever:
mechanical advantage = distance moved by effort / distance moved by load
In this case, the effort is the force applied by Isaac, the load is the weight of the box (15 kg), and the mechanical advantage is the ratio of the distances moved. We can rearrange this formula to solve for the distance moved by the load:
distance moved by load = distance moved by effort / mechanical advantage
In this case, the distance moved by effort is 2 meters (the height the box is lifted), and the mechanical advantage can be calculated using the ratio of the lengths of the lever arms (assuming the lever is a simple machine). Let's say the lever has two arms, one on each side of the pivot point, with lengths of L1 and L2. The mechanical advantage of the lever is:
mechanical advantage = L2 / L1
Assuming Isaac applied the force at the end of one arm, and lifted the load at the end of the other arm, we can say that the ratio of the lengths of the arms is:
L2 / L1 = 2 / 6
Simplifying, we get:
L2 = L1 / 3
This means that the load is lifted a distance of 2/3 meters (or 0.67 meters), which is the distance moved by the load. Now we can calculate the work done by Isaac:
work = force x distance
= 42 N x 6 m
= 252 J
Therefore, the amount of work done by Isaac to lift the 15-kilogram box is 252 Joules. The correct answer is (B) 252 Joules.
A bottle has a mass of 10.00g when is empty and 84.70g when is filled with water. When is filled with another fluid, the mass is70.00g. What is the specific gravity of the fluid?
Answer:
To find the specific gravity of the fluid, we need to compare its density to that of water.
First, we need to find the mass of the water in the bottle:
Mass of water = Mass of filled bottle - Mass of empty bottle
Mass of water = 84.70 g - 10.00 g
Mass of water = 74.70 g
Next, we can calculate the volume of water in the bottle using the density of water, which is 1 g/mL:
Volume of water = Mass of water / Density of water
Volume of water = 74.70 g / 1 g/mL
Volume of water = 74.70 mL
Now we can use the mass of the bottle when it is filled with the other fluid to find the mass of the fluid:
Mass of fluid = Mass of filled bottle - Mass of water - Mass of empty bottle
Mass of fluid = 70.00 g - 74.70 g - 10.00 g
Mass of fluid = -14.70 g
This result is negative, which means that the mass of the fluid is less than the mass of the water. This could be due to a variety of factors, such as air bubbles trapped in the fluid or an error in the measurements.
Assuming that the mass of the fluid should have been greater than the mass of the water, we can still calculate the specific gravity using the volume of water we calculated earlier:
Density of fluid = Mass of fluid / Volume of water
Density of fluid = (70.00 g - 10.00 g - 74.70 g) / 74.70 mL
Density of fluid = -14.70 g / 74.70 mL
Density of fluid = -0.196 g/mL
Again, this result is negative and therefore not physically meaningful. It is possible that there was an error in the measurements or that the assumption about the mass of the fluid being greater than the mass of the water was incorrect. Without additional information, we cannot calculate the specific gravity of the fluid.
Explanation:
Why do some people deny climate change, despite overwhelming evidence to the contrary?
Most typically, a person who denies the effects of climate change makes decisions based on their emotions, especially those they have toward the things they fear.
Why do some people choose to disregard climate change?The psychological distance is the first. Many people don't consider the possibility of climate change to be serious enough. Its impacts might not be immediately apparent unless you wake up to find your kitchen under water.
Why do people disregard concerns about sustainability?Depression may result from feeling constantly threatened, or it may result from our defensive system activating, forcing us to overlook the issue in order to deal. Dissonance, denial, and identification are three further difficulties cited by Stoknes.
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En un momento dado , la nadadora de una prueba de natación de 100 m espalda está debajo de la cuerda falsa de salida. Indica a) El camino recorrido si acaba de salir b) El camino recorrido si ya ha tocado el final de la piscina c) El desplazamiento de la nadadora en los casos a y b ¿Coincide en algún caso con el camino recorrido?
If at a given moment, the swimmer in a 100m backstroke swimming race then,
a) The distance traveled if she has just started is 0 meter.
b) The distance traveled if she has just started is 100 meters.
c) The displacement is 0 m in case a and 100 m is case b. No they do not coincide.
Since the swimmer has just started, therefore she has not traveled any distance yet.
As it is mentioned that the swimmer has already touched the end of the pool, she has traveled a distance of 100 meters.
The displacement of the swimmer in cases a and b is zero because displacement is the distance between the starting point and the ending point, regardless of the path taken. In case a, the swimmer has not moved from the starting point yet, so the displacement is zero. In case b, the swimmer has returned to the starting point, so the displacement is also zero.
No, the displacement does not coincide with the distance traveled in either case because the swimmer's path is not necessarily a straight line from the starting point to the ending point. The displacement only considers the initial and final positions of the swimmer, while the distance traveled takes into account the length of the path taken by the swimmer.
Therefore, it could be concluded that at the start diatance is 0m and at the end it is 100m and the displacement at starting is 0m and at the end it is 100m. These do not coincide with each other.
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The question is :
At a given moment, the swimmer in a 100m backstroke swimming race is below the false start rope. State :
a) The distance traveled if she has just started
b) The distance traveled if she has already touched the end of the pool
c) The displacement of the swimmer in cases a and b. Does it coincide with the distance traveled in any case?
. Predicting Water is nearly incompressible.
Air is easily compressed. Predict what will
happen when an air-filled balloon is pulled to
the bottom of a swimming pool.
someone help
Plesde
What light phenomena can be explained using the particle-bullet model of light? check all that apply. What light phenomena can be explained using the particle-bullet model of light?check all that apply. Why shadows and semi-shadows form. Why different media bend light differently. Why the angles of incidence and reflection are the same. Why light travels in a straight line
Answer:
The particle-bullet model of light can explain why shadows and semi-shadows form and why light travels in a straight line. It cannot explain why different media bend light differently or why the angles of incidence and reflection are the same.
Help quick.
Two objects, m1 and m2, have an elastic collision. The initial velocity of m1 is +6.0 m/s and of m2 is +4.0
m/s. After the collision, the velocity of m1 is +5.0m/s. What is the velocity of m2?
Answer:
u
1
=
6.0
m
/
s
u
2
=
4.0
m
/
s
v
1
=
5.0
m
/
s
Explanation:
help pls Cuban tree frogs are skilled jumpers. They can launch themselves at 4.5 meters per second at an angle of 26 above horizontal. Assuming the frog is jumping on level ground, what is the frog’s hang time in the air during a single jump?
a.0.92 s
b.1.2 s
c.0.77 s
d.0.40 s
To solve this problem, we need to use the kinematic equations of motion to determine the hang time of the Cuban tree frog during a single jump.
What is Velocity?
It is defined as the displacement of an object per unit time in a particular direction.
In other words, velocity is the speed of an object in a given direction. It is a vector quantity because it has both magnitude (the speed) and direction.
First, we need to find the vertical component of the initial velocity vector (v0) using the sine function:
sin(26°) = vy / 4.5 m/s
vy = 4.5 m/s sin(26°) = 1.98 m/s
The vertical component of the velocity vector determines how high the frog will jump.
Next, we can use the following kinematic equation to solve for the hang time (t) of the frog:
Δy = v0yt - 1/2 gt^2
where Δy is the vertical displacement (i.e., how high the frog jumps), v0y is the vertical component of the initial velocity vector, g is the acceleration due to gravity (9.8 m/s^2), and t is the hang time.
Since the frog jumps on level ground, its vertical displacement is zero (i.e., it returns to its original height). Therefore, we can simplify the equation as follows:
0 = v0yt - 1/2 gt^2
t(1/2 g t - v0y) = 0
t = 0 or t = 2v0y / g
We can discard the solution t = 0 because it is not physically meaningful. Therefore, the hang time of the Cuban tree frog during a single jump is:
t = 2v0y / g = 2(1.98 m/s) / 9.8 m/s^2 = 0.40 s
Therefore, the answer is (d) 0.40 s.
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A Copper rod whese lenght at 30°C is 10cm is heated find its new length. Take linear expansivity of copper as 0000017k
If a copper rod whose coefficient of linear expansion is 0.000017 is heated at 30⁰C and its length is 10cm, Then the new length of the copper rod is 10.0051cm.
What is linear expansion?If a body is subjected to expansion by virtue of temperature then its length gets increased by some extent that new length is given by,
Ln=L₀(1+[tex]\alpha[/tex]Δt)
where Ln = New length after expansion.
L₀= Original length of the body.
[tex]\alpha[/tex]= Coefficient of linear expansion.
Δt= Change in temperature.
Here in the question, given
L₀=10cm
t= 30°C
[tex]\alpha[/tex]= 0.000017
new length
Ln= 10(1+0.000017×30)
Ln=10.0051cm
Hence the new length of the copper rod after the expansion is 10.0051cm.
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23. Describe the objects or materials that
vibrated to produce three of the sounds
10 you've heard today
Answer: 1. flushing the toilet,
2. oil popping in a pan,
3. the clicking of a mouse on a computer,
Explanation: Lu-.v u
If an object with a charge of 0.08 C experiences an electric force of 5.0 what is the electric field strength ?
Please show you work.
The electric field strength is 62.5 N/C.
What is electric field strength ?Electric field strength (E) is a physical quantity that describes the intensity of the electric field at a particular point in space.
The electric field strength (E) can be calculated using the formula:
E = F/q
Where
F is the electric force and q is the charge.Substituting the given values, we get:
E = 5.0 N/0.08 C
E = 62.5 N/C
Therefore, the electric field strength is 62.5 N/C.
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A 10 kg block that is attached to a 5 kg block by a light inextensible string of negligible mass is pulled with a force of 50N at an angle of 30 degrees along with the horizontal. The 10 kg block experiences a kinetic frictional force of 20N. The coefficient of kinetic friction between the surface and the 5kg block is 0.2
The two blocks have an acceleration of 4.12 m/s^2.
String calculationsTo solve this problem, we need to draw a free-body diagram of both blocks and apply the laws of motion.
Let's assume that the positive x-direction is to the right, and the positive y-direction is upwards.
For the 10 kg block:
The weight force (W) acts downwards and has a magnitude of 10 x 9.8 = 98 N
The force of tension (T) acts upwards and is transmitted through the string from the 5 kg block
The frictional force (f) acts in the opposite direction to the motion and has a magnitude of 20 N
The force applied (F) acts at an angle of 30 degrees with the horizontal
We can resolve the applied force into its x- and y-components:
The x-component of the force (F cos 30) opposes the frictional force
The y-component of the force (F sin 30) opposes the weight force and is balanced by the tension force
Therefore, we can write the following equations of motion for the 10 kg block:
ΣFx = [tex]\sqrt{x}[/tex]T - F cos 30 - f = ma
ΣFy = T - W - F sin 30 = 0
For the 5 kg block:
The weight force (W) acts downwards and has a magnitude of 5 x 9.8 = 49 N
The force of tension (T) acts upwards and is transmitted through the string to the 10 kg block
The frictional force (f) acts in the opposite direction to the motion and has a magnitude of μkN, where μk is the coefficient of kinetic friction and N is the normal force
We can write the following equation of motion for the 5 kg block:
ΣFx =Δ f - T = ma
Now, we can solve for the unknowns.
From the equation ΣFy = T - W - F sin 30 = 0, we get:
T = W + F sin 30
T = 10 x 9.8 + 50 sin 30
T = 109.8 N
From the equation ΣFx = T - F cos 30 - f = ma, we get:
a = (T - F cos 30 - f) / m
a = (109.8 - 50 cos 30 - 20) / 10
a = 2.33 m/s^2
From the equation ΣFx = f - T = ma, we get:
a = √(f - T) / m
a = (0.2 x N - 109.8) / 5
a = -4.96 m/s^2
Since the acceleration of the two blocks is the same (due to the inextensible string), we can equate the two values of acceleration and solve for N:
2.33 = -4.96
N = 73.8 N
Now we can calculate the frictional force on the 5 kg block:
f = √μkN
f = 0.2 x 73.8
f = 14.76 N
Finally, we can use the equation ΣFx = T - F cos 30 - f = ma to find the acceleration:
a = (T - F cos 30 - f) / m
a = (109.8 - 50 cos 30 - 14.76) / 10
a = 4.12 m/s^2
Therefore, the two blocks accelerate to the right with an acceleration of 4.12 m/s^2.
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You have studied and researched different forms of renewable and nonrenewable resources. what recommendations would you make to the committee regarding the types of resources that could be used to generate electricity? This paragraph should be a persuasive writing piece as you consider all you have learned based upon evidence. (8 pts.)
Based on my research and analysis of different renewable and nonrenewable resources, I strongly recommend that the committee prioritize the use of renewable resources for electricity generation. Renewable resources such as solar, wind, hydro, and geothermal power have numerous advantages over nonrenewable resources such as coal, oil, and gas.
First and foremost, renewable resources are more sustainable and environmentally friendly than nonrenewable resources. They do not emit harmful pollutants, greenhouse gases, or other harmful substances that contribute to climate change and environmental degradation. In addition, renewable resources are abundant and can be harnessed from various sources, making them a more reliable and long-term solution for electricity generation.
Furthermore, renewable resources have become more affordable and cost-competitive with nonrenewable resources over time. The cost of solar and wind power has decreased significantly, making them more accessible to households, businesses, and industries. On the other hand, the price of nonrenewable resources is highly volatile and subject to global market fluctuations, making them a less stable and unpredictable source of electricity.
In conclusion, I strongly recommend that the committee prioritize the use of renewable resources such as solar, wind, hydro, and geothermal power for electricity generation. Not only are these resources more sustainable and environmentally friendly, but they are also becoming more affordable and accessible to the general population. By embracing renewable energy, we can create a cleaner, more sustainable, and more prosperous future for ourselves and future generation
25,000 newtons accelerating 10m/s2
The mass of the object is 2,500 kg according to Newton's second law of motion.
What is Newton's second law of motion?Newton's second law of motion states that the force acting on an object is equal to the product of its mass and acceleration. Mathematically, F = ma, where F is the force, m is the mass of the object, and a is its acceleration.
If a force of 25,000 N is applied to an object, and the object is accelerating at a rate of [tex]10 m/s^2,[/tex] then the mass of the object can be calculated using Newton's second law of motion:
F = ma
where F is the force, m is the mass of the object, and a is its acceleration.
Rearranging this equation, we get:
m = F/a
Plugging in the values given in the problem, we get:
[tex]m = 25,000 N / 10 m/s^2 = 2,500 kg[/tex]
Therefore, the mass of the object is 2,500 kg
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