30 POINTS - the cone moves with simple harmonic motion and it emits

Answer: We first calculate the acceleration on the ball using:

2as = v² - u²; u = 0 because ball is initially at rest

a = (36)²/(2 x  0.35)

a = 1850 m/s²

F = ma

F = 0.058 x 1850

= 107.3 Newtons

Explanation:

Answer:

The speed of wave is 3m/s

Answer:

The maximum possible number of components a vector can have is infinite

Explanation:

In mathematics, a vector is a mathematical object that has both magnitude and direction, and it can have any number of components, as long as it makes mathematical sense.

For example, a vector in two-dimensional space has two components (x and y), while a vector in three-dimensional space has three components (x, y, and z). However, vectors can also exist in higher-dimensional spaces, such as four-dimensional space or n-dimensional space, and in those cases, they can have more components.

It is worth noting that in practice, vectors with an extremely large number of components may not be useful or computationally feasible to work with. However, from a theoretical standpoint, vectors can have as many components as needed to describe a given situation.

Answer: The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased

Answer:

Explanation :

We have ,

According to Newton's second law of motion,

where F is force, m is mass and a is acceleration.

On putting the values in above formula we will get :

=> 48 = 12 × a

=> a = 48/12

Therefore,

Explanation:

(a) The graph of Force vs. Stretch for the given spring can be represented by a straight line passing through the origin with a slope equal to the spring constant. The equation of the line is:

Force = Spring constant × Stretch

F = kx

where k = 200 N/m and x is the stretch of the spring in meters. The graph is shown below:

Force vs. Stretch graph for a spring with k = 200 N/m

(b) When a mass of 0.8 kg hangs from the spring, it experiences a force due to gravity equal to:

F = m × g = 0.8 kg × 10 m/s² = 8 N

Since the spring is in equilibrium, the force exerted by the spring must be equal and opposite to the force due to gravity. Therefore, the stretch of the spring is given by:

F = kx

x = F/k = 8 N / 200 N/m = 0.04 m

The point corresponding to this stretch is marked on the graph as shown below:

Force vs. Stretch graph with a point for a hanging mass of 0.8 kg

(c) The potential energy stored in the spring when it is stretched from zero to 0.06 meters can be calculated using the formula:

U = (1/2) k x²

U = (1/2) × 200 N/m × (0.06 m)² = 0.36 J

(d) The work done to stretch the spring from 0.1 meters to 0.16 meters can be calculated by finding the area under the Force vs. Stretch graph between these two stretches. This represents the change in potential energy of the spring due to the stretching. The work done is given by:

W = ΔU = U₂ - U₁

where U₁ and U₂ are the potential energies of the spring at stretches of 0.1 m and 0.16 m, respectively.

Using the formula for potential energy, we have:

U₁ = (1/2) k x₁² = (1/2) × 200 N/m × (0.1 m)² = 1 J

U₂ = (1/2) k x₂² = (1/2) × 200 N/m × (0.16 m)² = 2.56 J

Therefore, the work done is:

W = ΔU = U₂ - U₁ = 2.56 J - 1 J = 1.56 J

The area under the graph representing this work is shown below:

Force vs. Stretch graph with shaded area representing work done

Answer:

We can use Hooke's Law to find the spring constant k:

F = kx

where F is the force applied to the spring, x is the displacement of the spring from its equilibrium length, and k is the spring constant.

We can find the force applied to the spring by using the weight of the 4.0 kg fish:

F = mg = (4.0 kg)(9.81 m/s^2) = 39.24 N

The displacement of the spring is the difference between its length with the fish and its equilibrium length:

x = 12.0 cm - 10.0 cm = 2.0 cm = 0.02 m

Now we can solve for k:

k = F/x = 39.24 N / 0.02 m = 1962 N/m

To find the length of the spring with an 8.0 kg fish suspended from it, we can use the same formula with the new weight:

F = mg = (8.0 kg)(9.81 m/s^2) = 78.48 N

We can solve for x, which is the new displacement of the spring:

x = F/k = 78.48 N / 1962 N/m = 0.04 m

Therefore, the length of the spring will be:

10.0 cm + 4.0 cm = 14.0 cm

Explanation:

0.002355 N-m torque must the motor deliver if the turntable is to reach its angular speed in 2.20 revolutions starting from rest

Torque is a measure of the twisting force that causes rotational motion. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation at which the force is applied.

Given:

Angular speed, ω = 3.49 rad/s

Number of revolutions, N = 2.20 rev

Diameter of disk, D = 30.5 cm = 0.305 m

Mass of disk, m = 0.240 kg

The moment of inertia of a uniform disk about its center is (1/2) * m * r^2, where r is the radius of the disk. Here, r = D/2 = 0.1525 m.

Moment of inertia, I = (1/2) * m * r^2 = (1/2) * 0.240 kg * (0.1525 m)^2 = 0.002198 J-s^2/rad

The torque required to bring the disk to its angular speed can be found using the formula:

τ = I * α

where α is the angular acceleration of the disk. Since the disk starts from rest, we have:

α = ω^2 / (2 * π * N)

where π is the constant pi. Substituting the given values, we get:

α = (3.49 rad/s)^2 / (2 * π * 2.20 rev) = 1.071 rad/s^2

Therefore, the torque required is:

τ = I * α = 0.002198 J-s^2/rad * 1.071 rad/s^2 = 0.002355 N-m

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The stars are not fixed but they are just constantly moving. We see them in the same position every night because they seem to be very small to us and also due to the earth's revolution.

If you factor out the daily motion of the stars across the sky due to the earth's rotation, you end up with a pattern of stars that seems to never change. The stars seem so fixed that ancient sky-gazers mentally connected the stars into figures called constellations that we can still make out today. But in reality, the stars are constantly moving every time. They are just so far away that the eye without any instrument cannot see their movement. But sensitive instruments can detect their movement.

Answer:

Let's start by calculating how much of a head start Car A has in distance before Car B starts.

In 3 minutes, Car A will have travelled:

d = r * t = (60 km/h) * (3/60) h = 3 km

So when Car B starts, Car A is 3 km ahead.

Now let's consider the time it takes for both cars to meet. Let's call the time it takes for both cars to meet t.

During that time, Car A will travel at a speed of 60 km/h, and Car B will travel at a speed of 70 km/h.

The distance that Car A will travel during that time is:

dA = 60 km/h * t

The distance that Car B will travel during that time is:

dB = 70 km/h * t

The total distance between the two cars when they meet is:

d = dA + dB

We want to find the value of t that makes dA + dB = 3 km (the distance that Car A is ahead of Car B when Car B starts).

Substituting the expressions for dA and dB, we get:

60 km/h * t + 70 km/h * t = 3 km

Simplifying, we get:

130 km/h * t = 3 km

t = 3 km / 130 km/h

t = 0.0231 h

Now we can calculate the distance that both cars will have travelled when they meet:

dA = 60 km/h * 0.0231 h = 1.38 km

dB = 70 km/h * 0.0231 h = 1.61 km

d = dA + dB = 1.38 km + 1.61 km = 2.99 km

Therefore, the two cars will draw level after travelling approximately 2.99 km from the starting point.

Answer:

Explanation:

a) To find a z value such that the probability of obtaining a larger z value is 0.05, we need to find the z value such that the area to the right of it is 0.05. Using a standard normal distribution table or calculator, we find that z = 1.645.

b) To find a z value such that the probability of obtaining a larger z value is 0.025, we need to find the z value such that the area to the right of it is 0.025. Using a standard normal distribution table or calculator, we find that z = 1.96.

c) To find a z value such that the probability of obtaining a larger z value is 0.20, we need to find the z value such that the area to the right of it is 0.20. This is equivalent to finding the z value such that the area to the left of it is 0.80. Using a standard normal distribution table or calculator, we find that z = 0.84 (rounded to two decimal places).

Answer:

Explanation:

To verify the hypothesis that the Earth has a liquid outer core and a solid inner core, we can use seismographs to study seismic waves that pass through the Earth's interior. The experiment can be set up as follows:

1. Select multiple seismograph stations around the globe to record seismic waves.

2. Choose a location for an earthquake to occur. The earthquake should be large enough to generate seismic waves that travel through the Earth's interior and be located far away from the selected seismograph stations.

3. Record the seismic waves generated by the earthquake at the various seismograph stations.

4. Analyze the seismic waves to determine how they interact with the Earth's interior. Specifically, we will study how the seismic waves pass through the Earth's outer and inner core.

5. Repeat the experiment using earthquakes of different magnitudes and at different locations, and record the resulting seismic waves.

Equipment needed for the experiment include seismographs, computers for data analysis, and earthquake monitoring systems. Seismographs can be installed in various locations around the globe to record the seismic waves generated by the earthquake. Data from these seismographs can be collected and analyzed using computer software to determine how the seismic waves interact with the Earth's interior.

Evidence that proves the outer core is liquid includes the observation of seismic waves that cannot travel through the liquid outer core, resulting in a shadow zone on the opposite side of the Earth from the earthquake. This shadow zone indicates that the seismic waves are refracted or absorbed by the liquid outer core. In contrast, evidence that proves the inner core is not liquid includes the observation of seismic waves that are reflected and refracted by the inner core boundary. This is due to the fact that the inner core is solid and has a different density and composition than the outer core.

To use repeatability to show whether the hypothesis is valid or not, we can repeat the experiment using earthquakes of different magnitudes and at different locations, and record the resulting seismic waves. If the results from multiple experiments are consistent with the hypothesis, then we can have greater confidence that the hypothesis is valid. If the results from multiple experiments are inconsistent, then we would need to investigate further to determine the cause of the inconsistency and revise the hypothesis accordingly.

Answer: 6.7 CENTIMETERS

Explanation: 15 EAST AND 8.3 WAST

NET DISPLACEMENT 15-8.3= 6.7

The trajectory of the shuttlecock before it was smashed by the player and right after it went down on the other side of the net is shown in the attachment.

The trajectory of a projectile is the path that an object takes through the air when it is thrown, and launched into the air.

The trajectory of a projectile is affected by several factors including the initial velocity of the object, the angle at which it was launched, the air resistance, and the gravitational pull of the earth.

In the absence of air resistance, the trajectory of a projectile would follow a parabolic path. However, in the presence of air resistance, the trajectory of the projectile will be affected by the forces of air resistance, and the path will deviate from a perfect parabolic shape.

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Answer:30m/s square

Explanation: V-VO =  V

                        T          T

\overline{a} = average acceleration

v = final velocity

v_0 = starting velocity

t = elapsed time

=90-0 =30m/s square

   3

The torque 0,1 acting on the meter stick due to 1 is 3.92Nm.

The torque 0,2 acting on the meter stick due to 1 is 20.94Nm.

The torque 0,stick due to weight of meter stick is 2.45Nm.

The torque 0,pivot acting due to pivot is 0.

The rotating equivalent of force is torque. The moment of force is another name for it (also abbreviated to moment). It illustrates how a force can cause a change in the body's rotational motion.

The definition of torque is the product of the force's perpendicular component's magnitude and the force's line of action's separation from the point being measured. Torque can also be understood in terms of the law of conservation of energy.

Using the formula:

τ= r × F

where,

τ is the torque,

F is the force and,

r is the distance of the line of action of a force from the point around which torque is being determined.

Substituting the values and solving for torque:

The torque 0,1 acting on the meter stick due to 1 is 3.92Nm.

The torque 0,2 acting on the meter stick due to 1 is 20.94Nm.

The torque 0,stick due to weight of meter stick is 2.45Nm.

The torque 0,pivot acting due to pivot is 0.

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The magnitude of the car's centripetal acceleration will be equal to the magnitude of its tangential acceleration 12.5 seconds after starting.

The centripetal acceleration, ac, of an object moving in a circular path of radius r and tangential speed v is given by:

ac = v^2/r

The tangential acceleration, at, is given by:

at = a

where a is the constant tangential acceleration.

Let's assume that the car starts at rest at the edge of the track, so its initial tangential speed, v0, is zero. Then the tangential speed of the car at time t is:

v = v0 + at = at

The time t when the magnitudes of ac and at are equal can be found by setting ac = at and solving for t:

ac = at

v^2/r = a

(at)^2/r = a

t = sqrt(ar/at)

Substituting r = 125 m and a = 1.5 m/s^2:

t = sqrt((1.5 m/s^2)(125 m)/(1.5 m/s^2)) = 12.5 s

Therefore, the magnitude of the car's centripetal acceleration will be equal to the magnitude of its tangential acceleration 12.5 seconds after starting.

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Answer: Both objects have small masses, and are close together.

Explanation:

Answer for A) momentum = 10 N/s B) momentum = 400 N/s C) momentum = 4000 N/s D) momentum = 0 N/s. Hence, the option C has the most momentum.

To determine which of the given options has the most momentum, we need to calculate the momentum of each object using the formula:

momentum = mass x velocity

A) 50 g bullet moving at 200 m/s:

mass = 50 g = 0.05 kg

velocity = 200 m/s

momentum = 0.05 kg x 200 m/s = 10 N/s

B) 50 kg boy running at 8 m/s:

mass = 50 kg

velocity = 8 m/s

momentum = 50 kg x 8 m/s = 400 N/s

C) 1000 kg automobile moving at 4 m/s:

mass = 1000 kg

velocity = 4 m/s

momentum = 1000 kg x 4 m/s = 4000 N/s

D) 1,000,000 kg Cruise ship docked in a harbor:

mass = 1,000,000 kg

velocity = 0 m/s (since the ship is docked)

momentum = 1,000,000 kg x 0 m/s = 0 N/s

Therefore, option C, the 1000 kg automobile moving at 4 m/s, has the most momentum with a value of 4000 N s. This is because momentum is directly proportional to both mass and velocity. The greater the mass and velocity of an object, the greater its momentum will be.

Option A, the 50 g bullet moving at 200 m/s, has a smaller momentum compared to the others due to its low mass despite having a high velocity.

Option B, the 50 kg boy running at 8 m/s, has a higher momentum than the bullet but lower than the automobile because of its higher mass but lower velocity.

Lastly, option D, the 1,000,000 kg Cruise ship docked in a harbor, has zero momentum since it is not moving (velocity is zero).

The momentum of an object is an important concept in physics that describes the quantity of motion possessed by it. It is determined by the product of mass and velocity, and the object with the highest mass and velocity has the greatest momentum.

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Answer:

Given:

Distance between the balloons (r) = 0.75 m

Charge on balloon 1 (q1) = 2.6 E−6 C

Charge on balloon 2 (q2) = 2.2 E−7 C

Electric constant (k) = 8.99 × 10^9 N·m^2/C^2

Unknown:

Electrical force (F) between the two balloons

The equation for the electrical force between two point charges is:

F = k * (q1*q2)/r^2

Substituting the given values, we get:

F = (8.99 × 10^9 N·m^2/C^2) * ((2.6 E−6 C) * (2.2 E−7 C))/(0.75 m)^2

F = 4.16 × 10^-6 N

Therefore, the electrical force between the two balloons is 4.16 × 10^-6 N.

Explanation:

Answer:

The electrical force between two balloons is 67.5N.

Explanation:

There are two charged balloons, let's say a and b.

The charge on the balloon a = C

The charge on the balloon b = C

Both balloons are 1 cm apart; it means that the distance r between the balloon a and the balloon b is 0.01 m (since 1 cm = 0.01 m).

We need to find the electrical force between them. By using the Coulomb's law, the magnitude of the electrical force between both the balloon is given as follows:
---------------
Hence, the electrical force between two balloons is 67.5N (three significant figures).

Answer:

a) the car lands in the ocean 85.1 meters away from the base of the cliff.

b) the length of time the car is in the air is 2.50 seconds.

Explanation:

Let's start with part (a) of the problem.

First, we need to find the car's velocity at the bottom of the incline using the kinematic equation:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity (which is 0 m/s), a is the acceleration (which is 3.67 m/s^2), and s is the distance traveled down the incline (which is 50.0 m).

Plugging in these values, we get:

v^2 = 0^2 + 2(3.67 m/s^2)(50.0 m)

v^2 = 367 m^2/s^2

v = 19.1 m/s (rounded to one decimal place)

Next, we can use the vertical motion equations to find the time it takes for the car to fall from the cliff to the ocean. We'll use the equation:

h = ut + (1/2)at^2

where h is the height of the cliff (35.0 m), u is the initial vertical velocity (which is 0 m/s), a is the acceleration due to gravity (-9.81 m/s^2), and we're solving for t.

Plugging in these values, we get:

35.0 m = 0 m/s * t + (1/2)(-9.81 m/s^2)t^2

19.9 = t^2

t = 4.46 s (rounded to two decimal places)

Therefore, the car is in the air for 4.46 seconds.

Finally, to find the car's position relative to the base of the cliff when it lands in the ocean, we can use the horizontal motion equation:

s = ut + (1/2)at^2

where s is the horizontal distance the car travels (which is what we're solving for), u is the horizontal velocity (which is the same as the velocity at the bottom of the incline, 19.1 m/s), a is the horizontal acceleration (which is 0 m/s^2), and t is the time the car is in the air (which is 4.46 s).

Plugging in these values, we get:

s = 19.1 m/s * 4.46 s + (1/2)(0 m/s^2)(4.46 s)^2

s = 85.1 m (rounded to one decimal place)

Therefore, the car lands in the ocean 85.1 meters away from the base of the cliff.

The image of the reflected sound wavefronts traveling through a liquid is found in the attachment.

Reflected sound wavefronts refer to the waves of sound that are bounced back or reflected off of a surface such as a wall, ceiling, or floor.

When a sound wave travels through the air and encounters a surface, some of the sound energy is absorbed by the surface, while some of it is reflected back into the air.

These reflected sound waves can interfere with the original sound waves, leading to complex patterns of sound intensity and phase.

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To increase the efficiency of the engine by 10%, the temperature of the cold sink needs to be lowered by 0.25 times the difference between the hot source and cold sink temperatures.

The efficiency of a Carnot engine is given by:

efficiency = (T_source - T_sink) / T_source

where;

If the efficiency of the engine increases by 10%, we can write:

new efficiency = 1.1 x old efficiency

Substituting the expression for efficiency of a Carnot engine, we get:

(T_source - new T_sink) / T_source = 1.1 x (T_source - T_sink) / T_source

Simplifying this equation, we get:

new T_sink = T_sink - 0.1 x (T_source - T_sink) / 0.4

new T_sink = T_sink - 0.25 x (T_source - T_sink)

new T_sink = 0.75 x T_sink + 0.25 x T_source

Therefore, the new temperature of the cold sink is given by 0.75 times the original temperature of the cold sink plus 0.25 times the temperature of the hot source.

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A force known as centripetal force causes centripetal acceleration.

An object must experience a force directed towards the centre of the circle in order to travel evenly in a circle, because all things moving in uniform circular motion accelerate towards the centre. Its motion is caused by centripetal force. Gravity creates centripetal force in the event of orbiting satellites such as the moon orbiting the earth or the earth orbiting the sun. As athletes spin a huge ball on a chain, such as in the Olympic hammer throw, they generate centripetal force, which is then transmitted through the chain.

Newton's second law states that force and acceleration are connected by the formula F=ma. We already have formulas that express the centripetal acceleration relationships, so we can easily tweak them to demonstrate the relationships.

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Answer:  lava is basically what is outside of the earth's surface. And magma is what's inside the earth's surface.

Explanation:

Scientists use the term magma for molten rock that is underground and lava for molten rock that breaks through the Earth's surface.

The speed of the bullet after it passed through the block is 198.138 m/s. We can make use of the conservation of momentum principle, which asserts that if no outside forces are acting on a system, its overall momentum will remain constant.

Mass in motion is quantified by momentum, which is the measure of how much mass is moving. It typically has the sign p.

Before the collision, the bullet has a momentum given by:

p1 = mv1

where m = mass of the bullet and v1 = velocity.

After the collision, the bullet and the wooden block move together with a common velocity v2. The momentum of the combined system is,

p2 = (m + M) v2

where M = mass of the wooden block.

Since there are no external forces acting on the system, we can equate the initial and final momenta:

p1 = p2

mv1 = (m + M) v2

Solving for v2:

v2 = (mv1) / (m + M)

Substituting the given values:

m = 7.00 g = 0.00700 kg

v1 = 200 m/s

M = 150 g = 0.150 kg

v2 = (0.00700 kg x 200 m/s) / (0.00700 kg + 0.150 kg)

v2 = 1.862 m/s

Since the wooden block gained a velocity of 180 cm/s (1.8 m/s) after the impact, the velocity of the bullet after passing through the block is:

v3 = v1 - v2

v3 = 200 m/s - 1.862 m/s

v3 = 198.138 m/s

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The left-right reversal of an object is called as : (a) lateral inversion

Apparent reversal of mirror image's left and right when it is compared with the object is called as lateral inversion. Lateral means sideways. In plane mirror, each point on image is as far behind the mirror plane as the corresponding point on object is in front.

The phenomenon where left appears as the right and vice versa in a mirror is known as lateral Inversion.

Lateral inversion is the side ways reversal of image's left and right when compared to that of the object and lateral inversion is observed in images formed by plane mirror.

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Warm, moist air rises because of the difference in densities between warm, moist air and cold air, which is essential for the formation of clouds.

The moisture in the air condenses into minute water droplets or ice crystals when warm, wet air rises and cools. Clouds are made up of these suspended ice crystals and water droplets.

By reflecting sunlight back into space and storing heat, clouds play a significant part in the Earth's climate system, influencing temperature and weather patterns.

Although lightning is frequently connected to clouds, moist air does not directly cause lightning to occur. Electric charge builds up in the atmosphere, typically during thunderstorms, which leads to lightning.

Snow is created by the freezing of water vapor in the atmosphere, just as stars are created by the gravitational collapse of gas and dust clouds in space.

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Answer:

Energy = Potential Energy + Kinetic Energy

E = M g h + 1/2 M v^2

On the way up h (height) is increasing and the velocity v is decreasing.

Between C and E the given conditions hold