4 kg steel ball is attached to a vertical spring. It starts a simple harmonic oscillation between a high point A and a low point B that are 20cm apart, with a period of t seconds. a) What is the amplitude of the oscillation? b) Spring constant of the spring? c) Maximum speed? d) Where is the location of the ball when it has the maximum kinetic energy (use A or B as reference points)?

Given,

We need to find,

Using Newton's first law of motion .

➵ 25.1 = Mass × 3.4

➵ 25.1 ÷ 3.4 = Mass

➵ Mass = 7.38 kg

Answer:

Explanation: Mary has 20 joules of Kinetic energy

2. Yes his kinetic energy be twice as much

3. If Roberto runs twice as fast, his Kinetic energy will be 4 times as much

4. 16875 Joules

5. 5.77 m/s

6. 8 kg

7. 345600 J

Answer:

In simple terms, fats are animal fats whereas oils are vegetable oils. The other difference is fats tend to be solids at room temperature; on the other hand, oils tend to be liquid at room temperature.

Explanation:

Answer:

k = 10000

Explanation:

F = k(x)

Where k is the spring constant.

F = 1500N

x = 0.15m

=> 1500 = k (0.15)

=> k (0.15) = 1500

=> k = 1500/0.15

=> k = 150000/15

=> k = 10000

The dot product is 25, the angle is \(\theta = cos^{-1} \frac{25}{\sqrt{35} \times \sqrt{21}}\), the cross product is 1i + (-6)j + (-7)k, and the area of the parallelogram spanned by vectors A and B is \(\sqrt{86}\).

Given,

A = 5i + 3j + k

B = 4i + j + 2k

i. Dot Product (A · B):

The dot product of two vectors A and B is given by the sum of the products of their corresponding components.

\(A.B = (A_x \times B_x) + (A_y \times B_y) + (A_z \times B_z)\\A.B = (5 \times 4) + (3 \times 1) + (1 \times 2) \\= 20 + 3 + 2 \\= 25\)

ii. Angle between vectors A and B:

The angle between two vectors A and B can be calculated using the dot product and the magnitudes of the vectors.

\(cos\theta = (A.B) / (|A| \times |B|)\\\theta = \frac{1}{cos} ((A.B) / (|A| \times |B|))\\A = \sqrt{(5^2 + 3^2 + 1^2)} =\\ \sqrt{35}\\B = \sqrt{(4^2 + 1^2 + 2^2)} \\= \sqrt{21}cos\theta = \frac{(A.B) / (|A| \times |B|)\\\theta = \frac{1}{cos} \frac{25}{\sqrt{35} \times \sqrt{21}}}\)

iv. Cross Product (A × B):

The cross product of two vectors A and B is a vector that is perpendicular to both A and B and its magnitude is equal to the area of the parallelogram spanned by A and B.

\(A\times B = (A_y \timesB_z - A_z \timesB_y)i + (A_z \timesB_x - A_x \timesB_z)j + (A_x \times B_y - A_y \times B_x)k\\A\times B = ((3 \times 2) - (1 \times 1))i + ((1 \times 4) - (5 \times 2))j + ((5 \times 1) - (3 \times 4))k\\= 1i + (-6)j + (-7)k\)

Area of the parallelogram spanned by vectors A and B:

The magnitude of the cross product A × B gives us the area of the parallelogram spanned by A and B.

Area = |A × B|

Area of the parallelogram spanned by vectors A and B:

Area = |A × B| =

\(\sqrt{(1^2 + (-6)^2 + (-7)^2}\\\sqrt{1+36+49\\\\\sqrt{86}\)

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Answer:

The answer to this question would be 3.6 m/s

Explanation:

Plants, as a autotrophs have chlorophyll to capture light energy from sun to make starch and sugar. Then, consumers eat plants, and the sugar is transferred to higher trophic level in a form of organic food. Nevertheless, energy is lost by uneaten food, indigestible food, unabsorbed food, excretory waste (eg co2) and heat loss by respiration.

Answer:

The Food Chain

Explanation:

The food chain is conducted of a web connected to three classifications. Each transfering energy to one a other when nutrients and living matter is passed from producers (one class) to consumers (another class), and is broken down by the decomposers (third class) lastly.

At the lowest point of her swing, she can withstand a maximum speed of 10.78 m/s.

Given that,

Mass of the carpenter = 61.7 kg

Length of the rope = 11.5 m

Capable force = 1229 N

Centripetal force acting on the body,

F = mv²/r = (61.7× v²)/11.5 = 5.37 v²

Gravitational force acting on her is

F = m × g = 61.7 × 9.81 = 605.28 N

By summing up gravitational and centripetal forces to get the total available force,

5.37 v² + 605.28 = 1229

5.37 v² = 623.72

v² = 116.15

v = 10.78 m/s

Hence, the maximum speed at the low point of her swing is 10.78 m/s.

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Answer:

They would all most likely have the same weight

Explanation:

Think about it the smaller the person or object the smaller the weight. But theyre all the same height now. And its not like you don't have any weight in the moon. So in conclusion they would all be the same weight

The % error in the computing of the resistivity of wire of resistance 1.04 Ω estimated error 0.01, length = 53.4 cm estimated error 0.1 cm, diameter = 0.57 mm estimated error 0.01 mm is 4.7 %

ρ = π d² R / 4 l

ρ = Resistivity

R = Resistance

d = Diameter

l = Length

R = 1.04 Ω

ΔR = 0.01 Ω

l = 53.4 cm

Δl = 0.1 cm

d = 0.57 mm

Δd = 0.01 mm

Δρ / ρ = 2 Δd / d + ΔR / R + Δl / l

Δρ / ρ = 2 ( 0.01 / 0.57 ) + ( 0.01 / 1.04 ) + ( 0.1 / 53.4 )

Δρ / ρ = 0.035 + 0.01 + 0.002

Δρ / ρ = 0.047

Δρ / ρ = 4.7 %

Therefore, the % error in the computing of the resistivity is 4.7%

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Answer:

b: density decreases

e: volume increases

Explanation:

When the water changes to ice, there won't be a loss of water, so the mass will be the same. However the ice will occupy more space, so the volume will increase. Then, since density is the mass divided by the volume, if the volume increase and the mass stays the same, the density decreases.

So, the answers are:

b: density decreases

e: volume increases

There are properties can be used to differentiate between oxygen and helium, based on the information in the chart.

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Given data

*The given mass of the car is m = 1610 kg

*The given effective force constant is k = 5.75 × 10^4 N/m

(a)

The formula for the period of oscillation of a 1610 kg car is given as

Substitute the known values in the above expression as

Hence, the time period of oscillation of a 1610 kg car is T = 1.05 s

(b)

As from the given data, the amplitude of the oscillation of the car decreases by a factor of 5.00. Then, the expression for the amplitude of the oscillation, and the damping constant (b) is calculated as

Substitute the known values in the above expression as

Hence, the damping constant is b = 9871.2 kg/s

Answer:

A lightning conductor is made up of a sharp pointed metal (usually copper metal, as it is a very good conductor) connected directly to the ground. ... The lightning conductor is placed higher than the roof so that if lightning strikes, it strikes the conductor before it can reach the house.

Explanation:

A lightning conductor is made up of a sharp pointed metal (usually copper metal, as it is a very good conductor) connected directly to the ground. ... The lightning conductor is placed higher than the roof so that if lightning strikes, it strikes the conductor before it can reach the house.

The main answer to the question is (a) true.  Capacitance is the capacity of a dielectric to hold or store an electric charge.

Capacitance is a measure of an object's capacity to store an electric charge.

Capacitance is determined by the characteristics of the object's dielectric, which is an insulating material that exists between two electrical conductors in the presence of an electrical field. The capacity of a dielectric to hold or store an electric charge is referred to as its capacitance.

A capacitor is a component that is used to store electrical energy. Capacitors store energy in an electrical field, and the amount of energy that they can store is determined by their capacitance.

A capacitor consists of two conducting plates separated by a dielectric material. When a voltage is applied across the plates, a charge builds up on them, and an electrical field is created between the plates.

The capacitance of a capacitor is determined by a number of factors, including the size of the plates, the distance between them, and the type of dielectric material that is used. The capacitance of a capacitor is measured in farads (F), which is the unit of capacitance. The higher the capacitance of a capacitor, the more electrical energy it can store.

In conclusion, capacitance is the capacity of a dielectric to hold or store an electric charge. This makes option (a) true.

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Answer:

3

Explanation:

Answer is what its supposed to be. lol.

Stick with it brother. You GOT THIS!!! 100%

b.

Answer:

B

Explanation:

All the other ones are opinions or opinion based

The question that how many hours a day dolphins sleep requires the collection of data to answer it. Hence, option B is correct.

Dolphins are small-toothed cetaceans that are distinguished by their always open, curving mouths. Every ocean contains one of the 36 dolphin species. The majority of dolphins are marine mammals that inhabit the sea or coastal environments with brackish water. However, there are a few species that live in freshwater streams and rivers, including the South Asian river dolphin and the Amazon River dolphin, or boto.

The orca, the biggest dolphin, can reach lengths of more than 30 feet. The Maui dolphin, which is the smallest, is only five feet long.

Dolphins mostly consume fish and squid, which they can locate via echolocation, an inbuilt sonar system that reflects sound waves off prey to disclose details about its location, size, and shape. Up to a thousand clicking sounds can be heard every second from an echo locating bottlenose dolphin.

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Answer:

The value of acceleration due to gravity is independent of mass of the body.

Explanation:

Let us consider the mass of the object as m and mass of earth as M

Therefore, force between the object and earth would be given by: F = GMm/d²

This force is equal to the weight of the object, i.e. mg

Thus;

mg = GMm/d²

g = GM/d²

Therefore, the value of acceleration due to gravity is independent of mass of the body.

Given:

Ray diagrams

To find:

A ray diagram showing the path of the reflected light ray.

Explanation:

According to the law of reflection, when a light ray falls on the surface and reflects back, the angle of incidence and angle of reflection that it makes with the surface is equal.

In the given diagrams, we see that the only option in which the angle of incidence is equal to the angle of reflection is option B. Whereas, in all other options, the angle of incidence is not equal to the angle of reflection.

Conclusion:

Thus the correct light path for a reflected light ray is shown in figure B. Thus the correct option is option b.

A fuel-filled rocket is at rest. It burns its fuel and expels hot gas. The gas has a momentum of 1,500 kg m/s backward. So, The momentum of the rocket is -1500 kg m/s.

According to the law of conservation of momentum, in a closed system, the total momentum before and after a process remains constant.

A fuel-filled rocket that is initially at rest expels hot gas as it burns its fuel. The gas has a momentum of 1500 kg m/s backward.

We are required to determine the momentum of the rocket.

Consider the fuel-filled rocket as a system.

We have: Momentum before the burn = 0 kg m/s (since the rocket was at rest initially)Momentum after the burn = momentum of the expelled gas

We can therefore say that the initial momentum of the system was zero (0), and after the burn, the total momentum of the system remains the same as the momentum of the expelled gas.

Therefore: Momentum of rocket = - momentum of expelled gas

The negative sign signifies that the rocket's momentum is in the opposite direction of the expelled gas.

Hence, the momentum of the rocket is -1500 kg m/s.

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Answer:

The final velocity of the car after the acceleration takes place is 13 m/s.

Explanation:

The final velocity can be calculated using the following equation:

\( V_{f} = V_{0} + at \)

Where:

\(V_{0}\): is the initial velocity = 0 (starts from rest)

a: is the acceleration = 2 m/s²

t: is the time = 6.5 s

Hence, the final velocity is:

\( V_{f} = V_{0} + at = 0 + 2 m/s^{2}*6.5 s = 13 m/s \)

Therefore, the final velocity of the car after the acceleration takes place is 13 m/s.

I hope it helps you!

Answer:

P = 113.4 N

Explanation:

We know that if it is on the Moon it has another gravity. Therefore, it is known through the International System that the gravity of the Moon is 1.62 m/s², so..

Data:

Use formula:

Replace and solve:

The man's weight is 113.4 Newtons.

Greetings.

1. With N = Newtons, m = meters, we have

\(F = -kx \iff \mathrm N = -k (\mathrm m) \implies k = \dfrac{\rm N}{\rm m}\)

N itself can be broken down according to Newton's second law,

\(F=ma \iff \mathrm N = \mathrm{kg} \, \dfrac{\rm m}{\rm s^2}\)

so the dimension of the force \(F\) is

\([F] = [M\cdot L\cdot T^{-2}]\)

(where M = mass, L = length, T = time) and hence the dimension of \(k\) is

\([k] = \left[\dfrac{M\cdot L\cdot T^{-2}}{L}\right] = \boxed{[M\cdot T^{-2}]}\)

2.

a. With N = Newtons, A = amperes, and m = meters,

\(F = \dfrac{k I_1 I_2}d \iff \mathrm N = \dfrac{k \,\mathrm A\,\mathrm A}{\rm m} \implies k = \boxed{\dfrac{\rm Nm}{\rm A^2}}\)

b. The dimension of \(k\) is

\([k] = \left[\dfrac{(M\cdot L\cdot T^{-2})\cdot L}{I^2}\right] = \boxed{[M\cdotL^2\cdot T^{-2}\cdot I^{-2}]}\)

(where I = current, with "I" as in capital i)

Answer:

An upwardly moving ball which is slowing down is said to be undergoing a downward acceleration. As the ball falls, it also undergoes a downward acceleration. A downwardly moving ball which is gaining speed is said to have a downward acceleration. This downward acceleration is attributed to the downward force of gravity which acts upon the ball. If the ball's motion can be approximated as projectile motion (that is, if the influence of air resistance can be assumed negligible), then there will be no horizontal acceleration. In the absence of horizontal forces, there would be a constant velocity in the horizontal direction. This explains why the ball would be located directly above the launcher from which it is projected.

Many would insist that there is a horizontal force acting upon the ball since it has a horizontal motion. This is simply not the case. The horizontal motion of the ball is the result of its own inertia. When projected from the truck, the ball already possessed a horizontal motion, and thus will maintain this state of horizontal motion unless acted upon by a horizontal force. An object in motion will continue in motion with the same speed and in the same direction ...

The observed distance of the moving ball is less when the observer is on the truck because the ball and truck are moving in the same direction.

The speed of an object, also referred to us v in kinematics, is a scalar quantity that refers to the size of the change in that object's motion over time or even the size of the change in that object's position per unit of time. The initial speed is the upper limit of the average pace as the length of the interval of time gets closer to zero. The average speed of such an object over a period of time is calculated by dividing the distance covered by the interval's duration. Velocity and speed are different concepts.

There is a common belief that because the ball is moving horizontally, there is a horizontal force acting onto it. That's just not true, at all. As a result of its inherent inertia, the ball is moving horizontally. The ball was already moving horizontally when it was launched from the truck, and it will continue to do so unless acted upon by a force that is also moving horizontally. The speed and direction of an object in motion will remain constant.

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Answer:

The walker travelled 3.6 miles.

Explanation:

d = vt

(v is velocity or speed and t is time, and d is distance.)

d=(3.0 mph)(1.2)

Leave the time in hours, since the unit for the speed is miles per hour.

d=3.6 miles

The distance will the walker travel if he walks at 3.0 miles per hour for 1 hour and 20 minutes is 3.6 km.

Distance is defined as the entire path traveled by an object in motion, regardless of path direction. The distance is symmetric, which means that for any two points P1 and P2, the distance between them is equal to the distance between them, or d(P1, P2) = d(P2, P1). 3. The triangle inequality is a less visible feature of the distance function. P1 for any point. The quantity of meters in a vector unit is the distance factor.

Distance = velocity x time

Given velocity = 3.0 miles per hour

Time = 1.2 hour

Distance = 3.0 x 1.2

Distance = 3.6 km/hour.

Thus, the distance will the walker travel if he walks at 3.0 miles per hour for 1 hour and 20 minutes is 3.6 km.

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Answer:

magnitude and a direction

Explanation:

The change in the momentum of an object caused by exerting a force on it for a period of time t is called impulse.

The momentum of a body is the product of the mass of the body and its velocity.

Momentum of a body ca change when an external force is applied over a period of time.

The change in the momentum of an object caused by exerting a force on it for a period of time t is called impulse.

In conclusion, the momentum of a body is the product of its mass and velocity.

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