A coil spring stretches by 2.50 cm when a mass of 750 g is suspended from it. (a) Find the force constant of the spring. (b) How much will the spring stretch if 800 g is suspended from it

Answer:

1.74 x 10^6

Explanation:

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The approximate radius of the Moon is \(1.736 * 10^7\) meters, or 17,360 kilometers.

To find the radius of the Moon, we can use Newton's law of universal gravitation, which relates the acceleration due to gravity (g) to the mass of the celestial body (M) and the distance (radius, r) between the center of the body and the object experiencing the gravitational force.

The formula for the acceleration due to gravity on the surface of a celestial body is:

\(g = G * (M / r^2),\)

where:

g = acceleration due to gravity on the Moon's surface (\(1.62 m/s^2\)),

G = universal gravitational constant (approximately\(6.67430 * 10^{-11\) m^3/kg/s^2),

M = mass of the Moon (\(7.35 * 10^{22\) kg), and

r = radius of the Moon (what we want to find).

Let's rearrange the formula to solve for the radius (r):

\(r^2\) = G * (M / g).

Now, we can plug in the known values:

\(r^2 = (6.67430 * 10^{-11} m^3/kg/s^2) * (7.35 * 10^{22} kg / 1.62 m/s^2)\).

Calculate the value of \(r^2\):

\(r^2\) ≈ \(3.018 * 10^{14} m^2.\)

Finally, take the square root of both sides to find the radius (r):

r ≈ \(\sqrt{(3.018 * 10^{14} m^2)\)≈ \(1.736 * 10^7\) meters.

So, the approximate radius of the Moon is\(1.736 * 10^7\) meters, or 17,360 kilometers.

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Answer:

75 cm/second.

Explanation:

Formula:

Walking speed = stride length / time per step

Walking speed = 90cm/time per step

                         = 90cm/1.2 seconds (a common estimate time per step)

                         = 75cm/second.

No, the gradient of the potential is the field. Therefore, in any area where the potential is constant, the electric field is zero. Constant does not always equate to zero.

The force per unit charge that an infinitesimally small positive test charge would experience if held fixed at a given point in space is the concept of the electric field at that location.

According to Gauss's law, the divergence of the electric field and the enclosed surface integral of the electric field are both zero in a vacuum, which is the absence of electric charges. Electric potential and electric field are both 0 at infinity if only a single point is taken into consideration.

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The velocity of this automobile as a function of time. At t = 5 seconds, the automobile is 90 meters from its initial position.

To determine the distance traveled by the automobile from its t = 0 initial position, we need to calculate the area under the velocity-time graph up to t = 5 seconds.

The graph shows the velocity of the automobile as a function of time. Let's assume that positive velocity represents forward motion, and negative velocity represents backward motion.

Since velocity represents the rate of change of displacement, the area under the velocity-time graph represents the displacement or distance traveled. In this case, the area will consist of two parts: the area above the x-axis (forward motion) and the area below the x-axis (backward motion).

To calculate the area, we can break it down into two separate integrals:

1. The area above the x-axis (forward motion):

Since the velocity is constant at 20 m/s for the first 4 seconds, the area is a rectangle:

Area1 = velocity * time = 20 m/s * 4 s = 80 m

2. The area below the x-axis (backward motion):

The velocity changes to -10 m/s at t = 4 seconds. From t = 4 seconds to t = 5 seconds, the velocity is -10 m/s. The area is a rectangle:

Area2 = velocity * time = -10 m/s * 1 s = -10 m

To find the total distance traveled, we add the absolute values of the areas:

Total distance = |Area1| + |Area2| = |80 m| + |-10 m| = 80 m + 10 m = 90 m

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Answer:

(a) To solve for the initial speed of the rock at launch, we can use the kinematic equation:

v = v0 + at

Where:

v = final velocity (15m/s)

v0 = initial velocity (what we're solving for)

a = acceleration due to gravity (-9.8m/s^2)

t = time (2.0s)

Plugging in the values, we get:

15m/s = v0 - 9.8m/s^2 (2.0s)

v0 = 34.6m/s

Therefore, the initial speed of the rock at launch was approximately 34.6m/s.

(b) To solve for the speed of the rock 5.0s after launch, we can use the same kinematic equation:

v = v0 + at

But this time, we need to add the additional time and distance that the rock traveled after the initial 2.0s. To do this, we'll use the equation:

d = v0t + 1/2at^2

Where:

d = distance traveled

v0 = initial velocity (34.6m/s)

a = acceleration due to gravity (-9.8m/s^2)

t = time (5.0s - 2.0s = 3.0s)

Plugging in the values, we get:

d = (34.6m/s)(3.0s) + 1/2(-9.8m/s^2)(3.0s)^2

d = 103.8m - 44.1m

d = 59.7m

So, the rock traveled 59.7m in the additional 3.0s after the initial 2.0s. Now we can find its speed using the kinematic equation:

v = v0 + at

Where:

v0 = final velocity from before (15m/s)

a = acceleration due to gravity (-9.8m/s^2)

t = time (3.0s)

Plugging in the values, we get:

v = 15m/s - 9.8m/s^2 (3.0s)

v = -12.6m/s

Note that the velocity is negative because the rock is now moving downward. Therefore, the speed of the rock 5.0s after launch is approximately 12.6m/s.

a student rises their 15 kg back pack from the floor at a constant velocity of 5.0 m/s then they apply of 37.5 N of force.

Force is responsible for the motion of an object. it produces acceleration in the body. According to newton's second law force is mass times acceleration i.e. F =ma. Its SI unit is N which is equivalent to kg.m/s². There are two types of forces, balanced force and unbalanced force.

In this problem student rises 15 kg of backpack at constant velocity and it happens in 2s, so consider time t = 2s.

Force is change in velocity with respect to time multiplied by mass.

F = m dv/dt

F = 15 kg × 5.0 m/s/2s

F = 37.5 N

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Answer:

False

Explanation:

A land breeze is when air flows from land to water. The question above is describing a sea breeze, which is when cool ocean air blows toward land.

The  equation describes the sum of the vectors plotted below is: \(\vec{r} = 4 \vec{x}+2 \vec{y}\)

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

According to the final position of the vector as shown in the figure, The final x co-ordinate is 4 and  the final y co-ordinate is 2.

the  equation describes the sum of the vectors plotted below is: \(\vec{r} = 4 \vec{x}+2 \vec{y}\)

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Answer:

25 miles per hour

Explanation:

It was 20 miles per hour the next day.  We don't have enough information to calculate the average speed for the whole trip.

The property that is oscillating would be the electric and magnetic fields.

For light, the property that is oscillating or vibrating at a particular frequency is the electric and magnetic fields.

Light is an electromagnetic wave, which means that it consists of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation.

The frequency of the wave corresponds to the number of complete oscillations of the electric and magnetic fields that occur per second, and is measured in hertz (Hz).

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Answer:

 θ = 32.4º

Explanation:

For this exercise let's use Malus's law

         I = Io cos² θ

in this case it indicates that the incident intensity is 370 W/m², when the first polarization passes, only the radiation with the same polarization of the polarizer emerges, that is, vertical

         I₀ = 370/2 = 185 W / m²

this is the radiation that affects the second polarizer, let's apply the expression of Maluz

         θ = cos⁻¹ (\(\sqrt{\frac{I}{I_o} }\))

         θ = cos⁻¹ (\(\sqrt{132/185}\))

         θ = cos⁻¹ (0.844697)

         θ = 32.4º

Answer:

Having the inside dimensions (ID) and the outside dimensions (OD) will allow you to figure out the wall thickness on tubing. You would need to subtract the ID from the OD and then divide by two. This number is the wall thickness.

Explanation:

Answer:

Impulse of force = 300Ns

Explanation:

Given the following data;

Mass = 25kg

Change in velocity = 12m/s

To find the impulse;

Impulse is given by the formula;

\( Impulse \; of \; force = mass * change \; in \; velocity \)

Substituting into the equation, we have;

\( Impulse \; of \; force = 25 * 12 \)

Impulse of force = 300Ns

Knowing the exits are exactly 7 km apart, the cars pass each other at 9:29 and 15 seconds a.m.

The relative velocity of the cars is 30 m/s - 26 m/s = 4 m/s.

The distance between the cars is 7 km = 7000 m.

The time it takes for the cars to pass each other is 7000 m / 4 m/s = 1750 seconds.

1750 seconds is 29 minutes and 15 seconds.

To calculate the time in minutes;

Let:

v_p = the speed of car P (m/s)

v_q = the speed of car Q (m/s)

d = the distance between the cars (m)

t = the time it takes for the cars to pass each other (s)

Given that:

v_p = 30 m/s

v_q = 26 m/s

d = 7000 m

Use the equation for relative velocity to find the velocity of the cars relative to each other:

v_r = v_p - v_q

v_r = 30 m/s - 26 m/s = 4 m/s

Use the equation for distance to find the time it takes for the cars to pass each other:

d = v_r × t

7000 m = 4 m/s × t

t = 7000 m / 4 m/s = 1750 s

Convert 1750 seconds to minutes and seconds:

1750 s = 29 minutes and 15 seconds

Therefore, the cars pass each other at 9:29 and 15 seconds a.m.

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Answer:

EXAMPLE: If the California interstate went all the way to Jupiter and you could drive there going 65 mph, it would take you almost 850 years.

This question involves the concepts of the equations of motion, kinetic energy, and potential energy.

a. The kinetic energy of the rocket at launch is "3.6 J".

b. maximum gravitational potential energy of the rocket is "3.6 J".

The kinetic energy of the rocket at launch is given by the following formula:

\(K.E=\frac{1}{2} m v_i^2\)

where,

Therefore,

\(K.E=\frac{1}{2}(0.05\ kg)(12\ m/s)^2\)

K.E = 3.6 J

First, we will use the third equation of motion to find the maximum height reached by rocket:

\(2gh=v_f^2-v_i^2\)

where,

Therefore,

2(-9.81 m/s²)h = (0 m/s)² - (12 m/s)²

h = 7.34 m

Hence, the maximum gravitational potential energy will be:

P.E = mgh

P.E = (0.05 kg)(9.81 m/s²)(7.34 m)

P.E = 3.6 J

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Answer:

false

Explanation:

The electrical force is much weaker than the force of gravity. False. Thomas Edison argued that our electrical system should use direct current because he felt that alternating current was dangerous.

Answer:

False

Explanation:

electrical force is billions and trillions and trillions times stronger than gravity. Gravity is a weak force compared to electrical force.

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Answer:

90J

Explanation:

The only time work is being done is when he lifts the box off the ground. Therefore, using the work formula, 2 x 45, you get 90J. Hope this helps someone.

Answer:

It is 2 seconds.

The period of a wave will bed 2 second. Frequency is the inverse of the time period;Option A is correct.

Frequency is defined as the number of repetitions of a wave occurring waves in 1 second.

Frequency is given by the formula as,

\(\rm f = \frac{1}{t} \\\\ t= \frac{1}{f} \\\\ t= \frac{1}{0.5} \\\\ t= 2\ second\)

The period of a wave will be 2 second.

Hence, option A is correct.

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Answer:

A

Explanation:

The sun is an emits energy in the form of light and heat.

The planets absorb this energy which helps keep them in motion. The closer they are to the sun, the more energy, the more speed and less the time it takes a planet to orbit the sun.

The gravitational pull of the Sun contributes motion of the planets because here the gravitational pull of the sun is balanced by the centrifugal force produced by the revolution of planets. The correct option Is A.

Centrifugal force is the pseudo-force that occurs only in the rotating frame of reference (non-inertial frame). it is directed away from the center. Its magnitude is,

F=\(\frac{mv^{2} }{r}\)

where m= mass of the body in kg.

v= velocity f the body in m/s.

r = radius in m.

The star sun has a  gravitational pull that is about 274 m/s²  which is greater than the other planets. Due to this pull the planets tend to pull toward the sun but it does not happen because the pull force is balanced by the centrifugal force that is produced by the revolution of the planets around the sun.

Hence The Sun's gravitational pull contributes to the motion of the planets.

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Answer:

Mirage is a phenomenon which can be seen when the surface air gets heated up and it becomes lighter. Lighter air moves up in the atmoshphere.

Explanation:

When the lighter air from cooler areas to warmer areas are refracted and they bent upwards.and it dispers

,

Answer:

This is because the X chromosome is large and contains many more genes than the smaller Y chromosome. In a sex-linked disease, it is usually males who are affected because they have a single copy of X chromosome that carries the mutation.

Explanation:

The speed of player B before they collide is 2.75 m/s

Momentum is defined as the product of mass and velocity. It is expressed as

Momentum = mass × velocity

This is defined as the change in momentum of an object.

Impulse = change in momentum

Impulse = final moment – Initial momentum

Since net momentum after the collision is 0 Ns, it means that:

Momentum of A = Momentum of B

With the above, idea, we can obtain the speed of player B as illustrated below:

Momentum of A = Momentum of B

105 × 3.3 = 126 × speed of B

346.5 = 126 × speed of B

Divide both sides by 126

Speed of B = 346.5 / 126

Speed of B = 2.75 m/s

Thus, the speed of player B before the collision is 2.75 m/s

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Answer:

Explanation:

4. Convergent boundary- when two plates move closer together.

5. Divergent boundary- when two plates move apart

6. Transform boundary- when two plates move past each other

The airplane will strike the ground at a horizontal distance of 490 meters.

To determine how far the airplane will strike on the ground, we need to consider the horizontal distance traveled by the airplane during its flight.

The horizontal distance traveled by an object can be calculated using the formula:

Distance = Speed × Time

In this case, the speed of the airplane is given as 100 meters per second and the time it takes to cover the distance of 490 meters is unknown. Let's denote the time as t.

Distance = 100 m/s × t

Now, to find the value of time, we can rearrange the equation as follows:

t = Distance / Speed

t = 490 m / 100 m/s

t = 4.9 seconds

Therefore, it takes the airplane 4.9 seconds to cover a horizontal distance of 490 meters.

Now, to calculate the distance on the ground where the airplane will strike, we can use the formula:

Distance = Speed × Time

Distance = 100 m/s × 4.9 s

Distance = 490 meters

It's important to note that this calculation assumes a constant speed and a straight flight path. In reality, various factors such as wind conditions, changes in speed, and maneuvering can affect the actual distance traveled by the airplane.

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(A) When an air particle bombards a smoke particles, the smoke particle moves to the same direction as the air particle that hit it. When another air particle hits the smoke particle, it changes its direction to that of the second air particle, and so on. This is called Brownian motion.

(B) If the temperature of the surroundings is increased the air particles would gain kinetic energy resulting in more frequent collisions with the smoke particles. Therefore, the smoke particles would be seen moving haphazardly.

(C) The microscope helps magnify the smoke particles for a much more better observation. The lens help in focusing. As the air particles are really small and cannot be observed; therefore, smoke particles are used as they are easy to see and observe; thus, ensuring a better experiment.