what happens to a muscle when you exercise it?

The new period of the object's motion will increase by a factor of √2 of the initial period.

Centripetal acceleration, is the acceleration of a body traversing a circular path.

Mathematically, it is given as

a = v²/r

ar = v²

where;

v = 2πr/T

Substitute the value of v into the above equation;

ar = (2πr/T)²

ar = 4π²r²/T²

a =  4π²r/T²

from the equation above;

a₁T₁² = a₂T₂²

when the acceleration is reduced by half;

a₁T₁² = (0.5a₁)T₂²

T₁² = (0.5)T₂²

2T₁² = T₂²

T₂ = T₁√2

Thus, the new period of the object's motion will increase by a factor of √2 of the initial period.

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Final answer:

To halve the object's acceleration in uniform circular motion without changing the radius, the period must be multiplied by the square root of two. The closest option from the provided choices that would reduce the acceleration is doubling the period, which is option (2) 2T.

Explanation:

The acceleration a of an object in uniform circular motion can be calculated using the formula a = | v |²/r, where v is the velocity of the object and r is the radius of the circle. Alternatively, it can be calculated as a = 4π²r/T², with T being the period of the motion. In order to cut the acceleration in half, either the velocity needs to change or the period has to change since the radius R remains the same.

Given that only the period T can be altered, and based on the second formula for acceleration where the period is squared, if we want to cut the acceleration in half we need to increase the period by a factor that, when squared, equals two.

The square root of two is approximately equal to 1.414, so we need the new period to be T' = T × √2. Since none of the options directly match this value, we can't select an exact answer from the given choices (1) t/2, (2) 2t, (3) t/4, (4) 4t. However, the closest answer that would reduce the acceleration is doubling the period, which is option (2) 2T.

The right answer is 20 miles per hour East

Answer: A) 20 miles per hour East

Explanation:

We know that the distance is 10 miles (to the east)

and the time is 30 minutes, knowing that an hour has 60 minutes, we can write this as:

30 minutes = ((30 min)/(60 min) )* 1h = 1/2 hours = 0.5 hours.

Now, the velocity is defined as the distance traveled divided by the time needed to travel that distance (and remember that velocity is a vector, so this must have a direction, in this case, the direction is east)

v = distance/time = 10miles/0.5 hours = 20 mi/h

the velocity is 20 miles per hour to the east.

The correct option is A

Answer:

Option (d) is correct.

Explanation:

Speed is defined as the ratio of distance traveled to the time taken.

As distance is scalar quantity, time is also scalar, so the speed is a scalar quantity.

Velocity is defined as the ratio of change in displacement to the time take.

Here displacement is a vector quantity, so velocity is a vector quantity.

So, velocity includes the rate of change of displacement and the direction.

Answer:

For the answer to the question on how heat is being transferred to Megan, the heat of the fire is warming her skin by making the air hot while drinking the hot chocolate warms her from inside of her.

Suppose you have a container filled with iron and sand. You can separate the iron from the sand if you use a magnet so this is a mixture. Thus, the correct option is A.

A mixture is a compound which is made up of two or more chemical components in a mixture that are not chemically linked. A mixture is a physical blend of two or more different substances that preserve their identities and are blended in the form of solutions, suspensions, or colloids.

For example, water and salt particles are separate substances which, once mixed, create a mixture called seawater. Mixtures are the product of a combination of compounds and elements without the chemical change.

Therefore, the correct option is A.

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Answer:  Light travels at different speeds in different medium because of the varying densities.

Explanation: The reason for the straw to break at the water's surface is because of the process of refraction. Light travels at different speeds in different medium because of the varying densities.

The light travels from air to water and thus the difference in speed results in an apparent shift of the position of part of straw under water and thus the part appears broken. This phenomenon is called as refraction.

Answer:

1. A - mass number

2. B - 146

3. B - 20

Answer: B.

refraction

Explanation: ed mentum or plato

The 20 or so minerals that predominantly compose Earth's crust are called rock-forming minerals, including silicates like quartz and feldspar, which account for over 90% of the crust.

The approximately 20 or so minerals that make up the bulk of Earth's crust are commonly referred to as rock-forming minerals. Most rocks are composed of these common minerals, and they include silicates such as quartz, feldspar, mica, amphibole, pyroxene, olivine, and various clay minerals. Silicates form over 90 percent of the Earth's crust because the building block of these minerals, the silica tetrahedron, combines one silicon atom with four oxygen atoms.

These rock-forming minerals are significant due to the high abundance of a few key elements in the crust, including oxygen and silicon, which make up about 75% of the Earth's crust by weight. The importance of managing these mineral resources sustainably is also highlighted, as they serve as essential resources for both plant growth and industrial applications.

The particles that would be attracted to each other are electrons and protons. The reason for this is because protons contain a positive charge, and electrons contain a negative charge. According to Coulomb's law, particles with opposite charges attract each other.

In the context of particle physics, the particles that would be attracted to each other are option B - electrons and protons. Protons contain a positive charge, and electrons have a negative charge. According to Coulomb's law, particles with opposite charges attract each other. Therefore, an electron (negative charge) and a proton (positive charge) would attract each other. In contrast, electrons and neutrons would not, as neutrons are neutrally charged and do not interact with charged particles in terms of electromagnetic force.

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Wagon A will have a higher acceleration compared to Wagon B is correct when two wagons are pulled with equal force. Wagon A is empty.

Wagon B is carrying enough bricks to double the mass of the wagon. To understand how their accelerations compare, we can use Newton's Second Law, which states that F = ma, where F is the force applied, m is the mass, and a is the acceleration.

Wagon A is empty, so it has a certain mass m. Let's denote its acceleration as a. Using F = ma for Wagon A gives:

F = m * a

Wagon B has double the mass of Wagon A, so its mass is 2m. Using the same applied force F and applying F = ma for Wagon B gives:

F = 2m * a'

Since the forces are equal, we can set the equations equal to each other:

m * a = 2m * a'

Solving for a' (the acceleration of Wagon B):

a' = a / 2

Answer:

D) The force multiplied by the time the objects are in contact

Explanation:

The impulse is defined as the change in momentum of an object:

[tex]I=\Delta p[/tex]

We know that momentum is the product between mas (m) and velocity (v), so assuming the mass of the ball to be constant, its change in momentum will be the product between the mass and the change in velocity:

[tex]I=\Delta p=m\Delta v[/tex]

Now we can multiple and divide by [tex]\Delta t[/tex], the time of collision:

[tex]I=m\Delta v \frac{\Delta t}{\Delta t}=m \frac{\Delta v}{\Delta t}\Delta t[/tex]

But [tex]\frac{\Delta v}{\Delta t}[/tex] is the acceleration, so:

[tex]I=m a \Delta t[/tex]

And (ma) is the force, so we have

[tex]I=(ma)\Delta t=F\Delta t[/tex]

Answer:

B. Decrease

Explanation: When an spacecraft is flying away from the moon, the moons gravitational pull on the spacecraft will decrease because gravitational force is directly proportional to the mass of the moon and mass of the spacecraft while inversely proportional to the square of the distance between them. So as the spacecraft moves away from the moon, gravitational pull will decrease.

The yellow arrows in this illustration represent movement of earth’s tectonic plates.

A tectonic plate (also called lithospheric plate) is a massive, irregularly shaped slab of solid rock, generally composed of both continental and oceanic lithosphere.

Plate size can vary greatly, from a few hundred to thousands of kilometers across; the Pacific and Antarctic Plates are among the largest. Plate thickness also varies greatly,

ranging from less than 15 km for young oceanic lithosphere to about 200 km or more for ancient continental lithosphere (for example, the interior parts of North and South America).

How do these massive slabs of solid rock float despite their tremendous weight? The answer lies in the composition of the rocks.

Continental crust is composed of granitic rocks which are made up of relatively lightweight minerals such as quartz and feldspar. By contrast, oceanic crust is composed of basaltic rocks,

which are much denser and heavier. The variations in plate thickness are nature's way of partly compensating for the imbalance in the weight and density of the two types of crust.

Because continental rocks are much lighter, the crust under the continents is much thicker (as much as 100 km) whereas the crust under the oceans is generally only about 5 km thick.

Like icebergs, only the tips of which are visible above water, continents have deep "roots" to support their elevations.

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The basis for dividing the atmosphere into layers is temperature changes with altitude. The correct option is a.

The primary reason for layering the atmosphere is the variation in temperature with height.

Temperature changes occur when we ascend through the atmosphere as a result of a variety of causes, including the absorption of solar radiation, the presence of ozone, and the drop in air pressure.

Within the atmosphere, these temperature variations produce separate areas or layers. The troposphere, stratosphere, mesosphere, thermosphere, and exosphere are among the layers.

The occurrence of particular atmospheric phenomena, temperature profiles, and weather patterns are only a few of the distinctive qualities that each layer has.

As a result, the basic framework for classifying the atmosphere into strata is provided by temperature variations with altitude.

Thus, the correct option is a.

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Your question seems incomplete, the probable complete question is:

what is the basis for dividing the atmosphere into layers

a) Temperature changes with altitude

b) Density changes with altitude

c) Humidity changes with altitude

d) Pressure changes with altitude

Answer:

The correct answer will be option-C.

Explanation:

The geocentric model is the model system which explained the planetary motion of the planets in the solar system.

The geocentric model was proposed by the Ptolemy which stated that earth is present at the center of the solar system and all the celestial bodies including planets and stars revolve around it.

This model system was disproved by Nicolas Copernicus which explained that Sun is present at the center of the solar system and all planets revolve around the sun,

Thus, Option-C is the correct answer.

The law of conservation of energy asserts that energy cannot be created or destroyed, only transformed. This principle applies to eating and exercising by showing that food energy is converted into physical activity and stored fat, highlighting the importance of balancing energy intake with expenditure to manage weight.

The law of conservation of energy states that energy can be neither created nor destroyed, only transferred or transformed from one form to another. In the context of eating and exercising, this principle indicates that the chemical energy from food is converted into various forms such as work (physical activity), thermal energy (heat), and chemical energy stored in body fat. Diets and exercise plans making extraordinary claims should be evaluated for their truthfulness based on this law. If a diet or exercise plan claims to 'destroy' energy or cause weight loss without considering energy intake and expenditure, it is likely not aligned with this fundamental law.

When discussing energy conservation, we can look at our own bodies as energy systems that convert the energy from food into necessary bodily functions and stored energy. If more energy is consumed than what is used for activity and maintaining body temperature, the excess energy is stored as fat. Conversely, if we consume less energy than we use, we tap into these fat reserves to maintain energy balance. Therefore, distinguishing between possible and impossible outcomes when considering exercise and dietary choices becomes clearer under the lens of energy conservation.

To perform a laboratory test of energy conservation, one might set up an experiment to measure the energy input and output in a system to confirm that, despite transformations, the total amount of available energy remains the same. This idea also broadly connects to understanding various forms of energy, such as calories in food, batteries, and heat, illustrating the interconnectedness of physical phenomena.

The correct answer of this question is : D) The initial momentum is 5 kg m/s, and the final momentum is 10 kg m/s

EXPLANATION :

Before going to answer this question, first we have to understand the momentum.

The momentum of a body is the amount of motion contained in a body. Quantitatively momentum is the product of mass with velocity.

Mathematically momentum p = mv.

Here, m is the mass of the body, and v is the velocity of the body.

As per the question, the mass of the ball m = 5 Kg.

The initial velocity of the ball u = 1 m/s.

Hence, initial momentum = m × u

                                          = 5 Kg × 1 m/s

                                          = 5 Kg.m/s

The final velocity of the ball v = 2 m/s

Hence, final momentum p = m × v

                                            = 5 Kg × 2 m/s

                                            = 10 Kg.m/s                        [ans]

To keep a sled accelerating downhill, the force of gravity must be greater than the frictional force.

When analyzing the motion of a sled sliding downhill, it's important to understand the forces acting on it and how they contribute to acceleration. Here’s a detailed explanation:

Forces Acting on the Sled

1. Force of Gravity:

  - Gravity: The force of gravity acts vertically downward with a magnitude of ( mg ), where ( m ) is the mass of the sled and ( g ) is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \))[/tex].

  - Component Parallel to the Slope: When the sled is on a slope, only a component of the gravitational force contributes to the sled's motion down the slope. This component is calculated as [tex]\( mg \sin(\theta) \), where \( \theta \)[/tex] is the angle of the slope. This component pulls the sled downhill.

2. Frictional Force:

  - Friction: Friction opposes the motion of the sled. On a slope, this force acts up the slope and is given by [tex]\( f_{\text{friction}} = \mu N \)[/tex], where ( mu ) is the coefficient of friction and ( N ) is the normal force.

  - Normal Force: The normal force is the component of the gravitational force perpendicular to the slope. It is given by [tex]\( N = mg \cos(\theta) \).[/tex]

Conditions for Acceleration

For the sled to accelerate downhill, the net force acting in the direction of the slope must be positive. This requires:

Where:

- [tex]\( F_{\text{gravity parallel}} = mg \sin(\theta) \)[/tex]

- [tex]\( F_{\text{friction}} = \mu mg \cos(\theta) \)[/tex]

Thus:

For the sled to accelerate downhill:

Simplifying this, we get:

In other words, the force of gravity acting parallel to the slope must be greater than the frictional force resisting the motion. If this condition is met, the sled will accelerate downhill. If not, the sled might move at a constant speed or even slide up the slope if the frictional force is greater than or equal to the component of gravity pulling it down.