When the spring is replaced with a spring with double of initial spring constant k2 = 2k₁, the new period, T2, is \(\sqrt{\frac{1}{2} } \ T_1\).
Period of the mass oscillation
The period of the oscillation of the mass or cart on the spring is given by the following formula;
\(T = 2\pi \sqrt{\frac{m}{k} } \\\\\)
at a costant mass;
\(T_1\sqrt{k_1} = T_2\sqrt{k_2} \\\\T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{k_2} }\)
when spring constant is doubled, k2 = 2k1. the new period, T2 is determined as follows;
\(T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{2k_1} } \\\\T_2 = \frac{T_1\sqrt{k_1} }{\sqrt{2} \times \sqrt{k_1} } \\\\T_2 = \frac{T_1}{\sqrt{2} }\\\\T_2 = \sqrt{\frac{1}{2} } \ T_1\)
Thus, when the spring is replaced with a spring with double of initial spring constant k2 = 2k₁, the new period, T2, is \(\sqrt{\frac{1}{2} } \ T_1\).
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Which law of thermodynamics does each of the following scenarios violate (if any)?
A machine that can turn 1000J of heat directly into 1000J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
Answer: The scenario violates the second law of thermodynamics.
Explanation: The second law states that heat cannot be converted into work without some loss of usable energy, and that the amount of usable energy in a closed system will always decrease over time. Therefore, the machine described in the scenario cannot exist because it would violate the second law by converting all of the heat into electricity without any loss of usable energy.
What is an easy way to encourage students to stay hydrated?
Let them know hydration improves performance.
Encourage them to drink water between each class.
Tell them to drink 8 glasses of water per day.
Have them track their hydration with a "water diary."
An easy way to encourage students to stay hydrated is to let them know hydration improves performance.
Drinking water is essential for our body system to function well. It helps in the regulation of the body temperature, the prevention of infections, as well as the delivery of nutrients to different parts of the body.
Staying hydrated is also vital in getting enough sleep and keeps the body in shape.
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Which is NOT a function of the skeletal system?
Answer:produces red and white blood cells
Explanation: the bone marrow helps with the blood but cannot produce red and white blood cells
Answer:
"prevents movement of limbs and digits" is NOT a function of the skeletal system.
PLEASE HELP I NEED THE CORRECT ANSWER TODAY
Answer:
The most common oxidation numbers for a given element
g Light that is incident upon the eye is refracted several times before it reaches the retina. As light passes through the eye, at which boundary does most of the overall refraction occur?
Answer
Explanation
:giác mạc
1. A Ograph A Ograph B Ograph c Which graph represents what happens to the pressure in a tire as air is added to the tire, assuming the temperature is constant?
Answer:
Explanation:
It's graph A because the pressure in the tire is increasing as the amount of air going into it increases. B says the pressure drops exponentially as air goes in, and C says that the pressure stays the same as air goes in. Pressure in a tire increases proportionally to the amount of air in it.
A right triangle has side lengths of 4 centimeters and 5 centimeters. What is the length of the hypotenuse?
O A. 3 cm
B. 4 cm
C. 5 cm
D. 41 cm
A 250 N to the east and a 30 N force to the west act on an object. What is the net force on the object? (Remember ΣF also equals the sum of all forces)
Answer:
280N
Explanation:
As the statement put in parenthesis state-You need to add up all the forces acting on the object to find the net force, so over here-
250+30=280N
What are the magnitude and the direction of the electric field that will allow an electron to fall with an acceleration of 4.3 m/s2?
Answer:
Explanation:
The acceleration of an electron in an electric field is given by the equation:
a = qE/m
where a is the acceleration, q is the charge of the electron, E is the electric field, and m is the mass of the electron.
Given that the acceleration of the electron is 4.3 m/s^2, and the mass of the electron is 9.11 × 10^-31 kg, and the charge of the electron is -1.6 × 10^-19 C, we can solve for the electric field E:
E = ma/q
E = (4.3 m/s^2) × (9.11 × 10^-31 kg) / (-1.6 × 10^-19 C)
E = -2.44 × 10^4 N/C
The negative sign indicates that the direction of the electric field is opposite to the direction of the electron's motion. Therefore, the magnitude of the electric field required to accelerate an electron with an acceleration of 4.3 m/s^2 is 2.44 × 10^4 N/C and the direction is opposite to the direction of motion of the electron.
If the speed of an object is 20m/s for 4 minutes, what can be inferred about the motion of the object?A. AcceleratingB. Constant motionC. DeceleratingD. Insufficient Data
Answer:
B. Constant motion
Explanation:
There is acceleration or deceleration when the speed changes in an interval of time. In this case, the speed of the object is 20 m/s in the 4 minutes, so we can say that the speed was constant and then it is a constant motion.
Then, the answer is
B. Constant motion
1.How are elements arranged on the periodic table in terms of valence electrons?
2. Show some evidence using data tables
3. Explain how the evidence supports your claim. Explain how the evidence from your data table shows the trends for valence electrons for both groups and periods on the periodic table.
Elements are arranged on the periodic table in terms of valence electrons based on their atomic number and electron configuration.
1. Elements are arranged on the periodic table in terms of valence electrons based on their atomic number and electron configuration. The valence electrons are the outermost electrons in an atom's electron shell, and they are crucial in determining the chemical properties and reactivity of elements.
2. Evidence from data tables can be shown by examining the electron configuration and the group and period numbers of various elements on the periodic table. Here is a simplified example:
Element | Electron Configuration | Group | Period |
--------------------------------------------
Hydrogen | 1s^1 | 1 | 1 |
Lithium | [He] 2s^1 | 1 | 2 |
Carbon | [He] 2s^2 2p^2 | 14 | 2 |
Oxygen | [He] 2s^2 2p^4 | 16 | 2 |
Neon | [He] 2s^2 2p^6 | 18 | 2 |
--------------------------------------------
3. The evidence from the data table supports the claim that the arrangement of elements on the periodic table is based on valence electrons.
- Group Trend: Elements within the same group (vertical columns) share the same number of valence electrons. In the example table, Hydrogen, Lithium, and Neon are all in Group 1, indicating they have 1 valence electron.
- Period Trend: Elements within the same period (horizontal rows) have the same number of electron shells. In the example table, Hydrogen and Lithium are in Period 1, indicating they have their valence electron in the first energy level. Carbon, Oxygen, and Neon are in Period 2, indicating they have their valence electrons in the second energy level.
By examining the electron configurations, group numbers, and period numbers, we can clearly see the trends and patterns in the number of valence electrons for both groups and periods on the periodic table. This evidence supports the claim that the arrangement of elements on the periodic table is based on their valence electrons, which play a crucial role in determining their chemical behavior and properties.
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The person kicks the ball in the image below 20 meters. Suppose the soccer ball in the image is replaced by one that is twice the mass of a regular soccer ball. How could the person kick the ball the same distance as the first soccer ball?
( will give brainliest if you help! )
( no trolling or I’ll report you)
Answer:
D
Explanation:
I NEED HELP THIS QUESTION IS SO HARDDD!!
Answer:
c
Explanation:
search it up
Answer:
Option A.
Explanation:
Because this is a lunar eclipse it normally happens 2 times a year. This is a decently rare phenomenon due to the positions they have to be in to make a lunar eclipse. Therefore, it is option A.
A train moves from rest to a speed of 25 m/s in 30.0 seconds. What is its
acceleration? (Answer in number only and round to 2 places after the
decimal.) *
Your answer
Answer:
0.83 m/s
Explanation:
25-0÷30=0.83 m/s
in a typical cop movie we see the hero pulling a gun firing that gun straight up into the air and shouting
It is not recommended to fire a gun straight up into the air.
When a bullet is fired into the air, it will eventually come down and can pose a danger to people and property below. The bullet can still be lethal when it reaches the ground, especially if it lands on a hard surface or hits someone directly.
Additionally, firing a gun in a residential area can be illegal and can result in legal consequences. In general, guns should only be fired in designated shooting ranges or in self-defense situations where there is an immediate threat to life. It is important to handle firearms responsibly and follow all safety guidelines to prevent accidents and injuries.
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NEED HELP ON QUESTION ASAP! !
If answer is correct I'll rate you five stars a thanks and maybe even brainliest!
Please can you explain what this paragraph is trying to say. Also what does it mean in the sentence 'the difference in charge across the battery provides push for current' and what is the difference in charge.
Here's paragraph I need to have a simple definition of:
A high waterfall is also like a large voltage. It will transfer a lot of energy to the water (charge), making the river flow very fast (a large current) the difference in height makes the river flow. In a circuit , the difference in charge across battery provides push for the current.
A man whose mass is 69 kg and a woman whose mass is 52 kg sit at opposite ends of a canoe 5 m long, whose mass is 20 kg. Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water
Answer:
the canoe moved 1.2234 m in the water
Explanation:
Given that;
A man whose mass = 69 kg
A woman whose mass = 52 kg
at opposite ends of a canoe 5 m long, whose mass is 20 kg
now let;
x1 = position of the man
x2 = position of canoe
x3 = position of the woman
Now,
Centre of mass = [m1x1 + m2x2 + m3x3] / m1 + m2 + m3
= ( 69×0 ) + ( 52×5) + ( 20× 5/2) / 69 + 52 + 20
= (0 + 260 + 50 ) / ( 141 )
= 310 / 141
= 2.19858 m
Centre of mass is 2.19858 m
Now, New center of mass will be;
52 × 2.5 / ( 69 + 52 + 20 )
= 130 / 141
= 0.9219858 m { away from the man }
To get how far, the canoe moved;
⇒ 2.5 + 0.9219858 - 2.19858
= 1.2234 m
Therefore, the canoe moved 1.2234 m in the water
The canoe move in the water will be 1.2234 m. The canoe move depending on the center of mass of the bodies.
What is the center of mass?The center of mass of an item or set of objects is a place specified relative to it. It's the average location of all the system's components, weighted by their mass.
The centroid is the location of the center of mass for simple rigid objects with homogeneous density. The center of mass of a uniform disc shape, for example, would be at its center.
The given data in the problem is;
m₁ is the mass of man = 69 kg
m₂ is the mass of woman whose= 52 kg
m₃ is the mass of canoe = 20 kg
L is the length of canoe = 5 m
x₁ is the position of the man
x₂ is the position of the canoe
x₃ is the position of the woman
The center of mass will be;
\(\rm COM= \frac{[m_1x_1 + m_2x_2 + m_3x_3]}{ m1 + m2 + m3} \\\\ \rm COM= \frac{[69 \times 0 +52 \times 5 + 20 \times 2.5]}{ 69+ 52 + 20} \\\\ \rm COM= (0 + 260 + 50 ) / ( 141 )\\\\ \rm COM = 310 / 141 \\\\ \rm COM = 2.19858 m\)
The new center of mass is;
\(\rm COM= \frac{52 \times 2.5 }{69+52+20} \\\\ \rm COM=\frac{130}{141} \\\\ \rm COM= 0.9219 m\)
The distance to find how the canoe moved will be found by;
\(\rm x= 2.5+0.9219-2.1985 = 1.2234\)
Hence the canoe move in the water will be 1.2234 m.
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two wharves A and B are directly opposite each other on a 40m wide river which flows in the direction shown. a boat leaves A and heads at constant speed at right angles to the flow of the river. it lands at point C, with the trip taking 20 seconds.
find;
a) the displacement from C to A
b) the speed of the boat as seen by people standing at A.
c) the speed of the water in the river
d) the speed of the boat as seen by a fish drifting with the river.
e) Draw a vector diagram and u
se it to find the direction the boat should head ( at the same constant speed as before) if it is to travel directly from A to B.
Answer:
a)40 meters
b)2 m/s
c)2 m/s
d)0 m/s
e)45 degrees northeast
Explanation:
a) The displacement from C to A is the distance directly across the river, which is 40 meters.
b) The speed of the boat as seen by people standing at A is the magnitude of the boat's velocity vector, which is equal to the displacement divided by the time taken:
Speed = displacement / time = 40 m / 20 s = 2 m/s.
c) Let v be the speed of the water in the river. The boat is moving at right angles to the flow of the river, so the water exerts a perpendicular force on the boat. The time taken for the boat to travel from A to C is 20 seconds, during which time the boat will have been carried downstream by the river by a distance equal to v times the time taken.
Distance carried downstream = v × time = v × 20 m.
Since the boat landed at C, which is directly across the river from A, the distance it traveled horizontally is 40 meters. Therefore:
40 m = (boat speed) × (time taken) = (boat speed) × 20 s.
Hence, the speed of the boat is:
Boat speed = 40 m / 20 s = 2 m/s.
So, we have two equations:
Distance carried downstream = v × 20 m
Boat speed = 2 m/s
From the first equation, we get:
v × 20 m = 40 m
Therefore, the speed of the water in the river is:
v = 40 m / 20 m = 2 m/s.
d) The speed of the boat as seen by a fish drifting with the river is the difference between the speed of the boat and the speed of the water in the river:
Boat speed - Water speed = 2 m/s - 2 m/s = 0 m/s.
So, the speed of the boat as seen by a fish drifting with the river is zero.
e) The boat should head in a direction that makes its velocity vector point directly from A to B. Since A and B are directly opposite each other, this means the velocity vector should be perpendicular to the line connecting A and B.
We know the boat's velocity vector has a magnitude of 2 m/s and is at right angles to the velocity vector of the water in the river, which has a magnitude of 2 m/s. So, we can draw a vector diagram with the velocity vector of the boat pointing straight up and the velocity vector of the water pointing straight to the right. The vector connecting the tail of the water velocity vector to the head of the boat velocity vector will then point directly from A to B.
The angle between the boat's velocity vector and the line connecting A and B can be found using trigonometry. Let θ be this angle. Then:
tan(θ) = (boat speed) / (water speed) = 2 m/s / 2 m/s = 1.
Taking the inverse tangent of both sides gives:
θ = tan^(-1)(1) = 45°.
So, the boat should head in a direction 45 degrees to the right of straight up, or northeast.
Here is Mr. Legare, skateboarding, again ...
He’s riding his skateboard down a ramp. Assume that his acceleration is 1.0 m/s2 how much force does it take for him to accelerate at this rate? He has a mass of 85 kg.
A. 0.011 N
B. 85 N
C. 7225 N
D. 85 kg
Answer:
B. 85 N
Explanation:
Newton's second law:
F = ma
F = (85 kg) (1.0 m/s²)
F = 85 N
34. [8 Marks] A spring is compressed with a 5.0 kg mass by 20.0 cm from its equilibrium position. When the spring is released, the 5.0 kg mass travels along a smooth horizontal surface and then up a frictionless plane at 30° to the horizontal. Calculate the distance it would travel up the inclined plane before coming back down again.
Answer and Explaination:
To solve this problem, we can analyze the forces acting on the mass as it travels up the inclined plane. We'll consider the gravitational force and the force exerted by the spring.
1. Gravitational force:
The force due to gravity can be broken down into two components: one perpendicular to the inclined plane (mg * cosθ) and one parallel to the inclined plane (mg * sinθ), where m is the mass and θ is the angle of the inclined plane.
2. Force exerted by the spring:
The force exerted by the spring can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The force can be written as F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
Given:
Mass (m) = 5.0 kg
Compression of the spring (x) = 20.0 cm = 0.20 m
Angle of the inclined plane (θ) = 30°
First, let's find the force exerted by the spring (F_spring):
F_spring = -kx
To find k, we need the spring constant. Let's assume that the spring is ideal and obeys Hooke's Law linearly.
Next, let's calculate the gravitational force components:
Gravitational force parallel to the inclined plane (F_parallel) = mg * sinθ
Gravitational force perpendicular to the inclined plane (F_perpendicular) = mg * cosθ
Since the inclined plane is frictionless, the force parallel to the inclined plane (F_parallel) will be canceled out by the force exerted by the spring (F_spring) when the mass reaches its highest point.
At the highest point, the gravitational force perpendicular to the inclined plane (F_perpendicular) will be equal to the force exerted by the spring (F_spring).
Therefore, we have:
F_perpendicular = F_spring
mg * cosθ = -kx
Now, let's substitute the known values and solve for k:
(5.0 kg * 9.8 m/s^2) * cos(30°) = -k * 0.20 m
49.0 N * 0.866 = -k * 0.20 m
42.426 N = -0.20 k
k = -42.426 N / (-0.20 m)
k = 212.13 N/m
Now that we know the spring constant, we can calculate the maximum potential energy stored in the spring (PE_spring) when the mass reaches its highest point:
PE_spring = (1/2) * k * x^2
PE_spring = (1/2) * 212.13 N/m * (0.20 m)^2
PE_spring = 4.243 J
The maximum potential energy (PE_spring) is equal to the maximum kinetic energy (KE_max) at the highest point, which is also the energy the mass has gained from the spring.
KE_max = PE_spring = 4.243 J
Next, we can calculate the height (h) the mass reaches on the inclined plane:
KE_max = m * g * h
4.243 J = 5.0 kg * 9.8 m/s^2 * h
h = 4.243 J / (5.0 kg * 9.8 m/s^2)
h = 0.086 m
The height the mass reaches on the inclined plane is 0.086 m.
Now, we can calculate the distance traveled.
A 5.0 kg object compresses a spring by 0.20 m with a spring constant of 25 N/m. It climbs an incline, reaching a maximum height of 0.0102 m before coming back down, traveling a total distance of 0.0428 m.
Given data: Mass of the object, m = 5.0 kg, Displacement of the spring, x = 20.0 cm = 0.20 mAngle of the inclined plane, θ = 30°Calculating the spring constant, k. Using Hooke’s Law; F = -kx Where F is the restoring force required to bring the spring back to its equilibrium position.From the equation, F = ma For the object attached to the spring,m * a = -kx. On integrating,∫ma dt = -∫kx dt .On integrating the left side with limits from 0 to t and right side with limits from 0 to x, where the limits on the left are for acceleration and the right are for the displacement of the spring; mv - mu = -½ kx²At maximum compression, the velocity of the mass is zero, i.e., v = 0 and the initial velocity is also zero. Therefore, mv - mu = -½ kx²0 - 0 = -½ k (0.20)²∴ k = 25 N/mWork done on the spring in compressing it, W = ½ kx² = 0.5 * 25 * (0.20)² = 0.5 JSince the inclined plane is frictionless, the only force acting on the object will be the component of its weight acting along the plane. Hence, it will move up the incline with an acceleration of, a = g sin θ = 9.8 * sin 30° = 4.9 m/s²When the object has reached its maximum height, its velocity will be zero. Using the equation of motion; v² - u² = 2as0 - u² = 2as∴ s = u² / 2a. Now, the initial velocity of the object up the incline is,u = √(2gH)Where H is the height to which it climbs, and is given by, H = W / m g Where W is the work done on the object in lifting it to height H, and m is the mass of the object. W = 0.5 J, m = 5 kg. So, H = 0.5 / (5 * 9.8) = 0.0102 m∴ u = √(2gH) = √(2 * 9.8 * 0.0102) = 0.4525 m/sNow, the distance traveled by the object up the incline is,s = u² / 2a = (0.4525)² / (2 * 4.9) = 0.0214 m. When the object comes back down, it will travel the same distance down the incline, before coming to rest. Therefore, the total distance travelled up and down the incline is,2s = 2 * 0.0214 = 0.0428 m.For more questions on the spring constant
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A projectile is launched at an angle of 30° above the horizontal with an initial velocity (vo) of 42.2 m/s. After some time passes, the projectile reaches the peak of its trajectory.Its horizontal velocity (vx) at the peak of its trajectory is ____ m/s.
First, for us to start, let us draw the problem:
When we analyse this problem, we can see that the only velocity that changes overtime is the vertical velocity (due to gravity), so the horizontal speed is the same throughout the whole movement. This gives us the following:
\(v_x=42.2*cos(30°)=36.546\frac{m}{s}\)Then, the horizontal speed at the peak of the trajectory (and also during the whole movement) is v=36.546m/s
find the rms speed of a sample of oxygen at 30° C and having a molar mass of 16 g/mol.
At 30°C, the rms speed of a sample of oxygen with a molar mass of 16 g/mol is approximately 482.34 m/s.
The root mean square (rms) speed of a gas molecule is a measure of the average speed of the gas particles in a sample. It can be calculated using the formula:
vrms = √(3kT/m)
Where:
vrms is the rms speed
k is the Boltzmann constant (1.38 x 10^-23 J/K)
T is the temperature in Kelvin
m is the molar mass of the gas in kilograms
To calculate the rms speed of oxygen at 30°C (303 Kelvin) with a molar mass of 16 g/mol, we need to convert the molar mass to kilograms by dividing it by 1000:
m = 16 g/mol = 0.016 kg/mol
Substituting the values into the formula, we have:
vrms = √((3 * 1.38 x 10^-23 J/K * 303 K) / (0.016 kg/mol))
Calculating this expression yields the rms speed of the oxygen sample:
vrms ≈ 482.34 m/s
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difference between rest and motion
What kind of object are the light rays interacting with in the model below?
Convex mirror
Convex lens
Concave mirror
Concave lens
Answer:
Concave lens
.............
Predict the velocity vy when y=-3.5 meters. Use the average acceleration you calculated in Activity 1. Use the formula v = Vo2 + 2ay, where v = final velocity, Vo = initial velocity, a = average acceleration, and y = y displacement. (Note that v is the final velocity in the y direction: Vy.)
Answer:
8.1
Explanation:
Explosives are used to blow a rock apart. The explosion blows the rock into three fragments. Two fragments go off at a 102 degree angle to each other--a 5.8 kg piece at 28.9 m/s and a 4.9 kg piece at 30.4 m/s. Calculate the speed of the third piece, if it has a mass of 3.6 kg. 55.49 m/s
The speed of the third fragment is 68.4 m/s.
Resultant momentum of the two fragmentsThe resultant momentum of the two fragments at the given angle is calculated as follows;
\(P_3^2 = P_1^2 + P_2 - 2P_1P_2 cos(102)\\\\P_3^2 = (5.8 \times 28.9)^2 + (4.9 \times 30.4)^2 \ - \ 2(5.8\times 28.9)(4.9 \times 30.4)\times cos(102)\\\\P_3^2 = 50285.55 \ + \ 10382.55\\\\P_3^2 = 60668.1\\\\P_3 = \sqrt{60668.1} \\\\P_3 = 246.31 \ kgm/s\)
Speed of the third fragmentThe speed of the third fragment is calculated as follows;
P = mv
\(v = \frac{P}{m} \\\\v = \frac{246.31}{3.6} \\\\v = 68.4 \ m/s\)
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A smooth circular cylinder of radius 1.5m in a triangular grove, one side of which makes 15 °angle and the other 40° angle with the horizontal · Find the reaction. at the surface of contact, if there. is no fiction and the cylinder weigh 100N
Answer:
46.5 N
Explanation:
attached is explanation
Assume you are a trainer at a local gym. There is evidence that intense or exhaustive physical exercise can increase the production of free radicals. Antioxidants can be used to combat the damage caused by free radicals. One of your competitive athletes has heard bits and pieces of this information and asks you more about it. How would you counsel him?
Use language that the average person will understand, respond to this athlete and be sure to include the following information as a part of your response:
What is meant by oxidation and why can it be damaging to cells?What are free radicals?Why do we produce free radicals if they can damage my body?What are antioxidants? How do antioxidants combat free radicals?What foods are high in antioxidants?Should your friend buy an antioxidant supplement?
Which one of the following statements is not true.
A. Soil is the second layer of Earth's crust.
B. Metals can be extracted from minerals.
C. Oil is made from dead plants and animals.
D. Chemical weathering can break down rocks into fragments.
how cold does it have to be for a snowflake to form around a dust particle?
Answer:
32 degrees Fahrenheit
Snow forms when the atmospheric temperature is at or below freezing and there is a minimum amount of moisture in the air. If the ground temperature is at or below freezing, the snow will reach the ground.
Explanation: