If the velocity of a moving object decreases from 60 m/s to 30 m/s, what happens to its momentum? It is reduced by half It stays the same It doubles It quadruples

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The maximum speed with which this car can round a second unbanked curve is 40 m/s

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Centripetal Acceleration can be formulated as follows:

[tex]\large {\boxed {a = \frac{ v^2 } { R } }[/tex]

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

[tex]\texttt{ }[/tex]

Centripetal Force can be formulated as follows:

[tex]\large {\boxed {F = m \frac{ v^2 } { R } }[/tex]

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

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Given:

initial speed of the car = v₁ = 20 m/s

radius of first curve = R₁ = 80 m

radius of second curve = R₂ = 320 m

Asked:

final speed of the car = v₂ = ?

Solution:

Firstly , we will derive the formula to calculate the maximum speed of the car:

[tex]\Sigma F = ma[/tex]

[tex]f = m \frac{v^2}{R}[/tex]

[tex]\mu N = m \frac{v^2}{R}[/tex]

[tex]\mu m g = m \frac{v^2}{R}[/tex]

[tex]\mu g = \frac{v^2}{R}[/tex]

[tex]v^2 = \mu g R[/tex]

[tex]\boxed {v = \sqrt { \mu g R } }[/tex]

[tex]\texttt{ }[/tex]

Next , we will compare the maximum speed of the car on the first curve and on the second curve:

[tex]v_1 : v_2 = \sqrt { \mu g R_1 } : \sqrt { \mu g R_2 }[/tex]

[tex]v_1 : v_2 = \sqrt { R_1 } : \sqrt { R_2 }[/tex]

[tex]20 : v_2 = \sqrt { 80 } : \sqrt { 320 }[/tex]

[tex]20 : v_2 = 1 : 2[/tex]

[tex]v_2 = 2(20)[/tex]

[tex]\boxed {v_2 = 40 \texttt{ m/s}}[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Circular Motion

The component of the gravitational force parallel to the hill is mg⋅sin(65°). The acceleration of the rollercoaster down the hill is (mg⋅sin(65°))/m.

To determine the value of the component of the gravitational force parallel to the hill, we can use trigonometry. The component of the weight parallel to the hill is given by the equation mg⋅sinθ. In this case, θ is 65 degrees. So the value of the component of the gravitational force parallel to the hill is mg⋅sin(65°).

To find the acceleration of the rollercoaster down the hill, we can use Newton's second law, which states that force equals mass times acceleration. In this case, the force is the component of the gravitational force parallel to the hill, and the mass is given as 300 kg with passengers. So the acceleration is a = F/m = (mg⋅sin(65°))/m.

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Answer:

Should be same

Explanation:

An experiment is conducted to test a theory. It is expected that the result of the experiment would match with the theoretical result. Also, if the experiment is repeated by the same or another person, it should give the same result. If not, then either there is error in conduction of experiment or in the theory.

You are facing North. Turn 90 degrees left. W.

Turn 180 degrees right. E.

Reverse direction. W.

Turn 45 degrees left. S.W.

Reverse direction. N.E.

In which direction are you now facing? North East

In physics, some data points may need to be ignored just before and after a collision. This is done to remove errors and focus on the specific moment of collision.

In physics, it may be necessary to ignore some of the data points just before and just after a collision for various reasons. One reason is to remove outliers or errors in the measurements that could skew the results. For example, if there is a sudden spike or dip in the data due to a measurement error, it would be necessary to exclude those points to ensure accurate analysis.

Another reason is to focus on the specific moment of collision. By excluding the data points surrounding the collision, it allows for a clearer observation and analysis of the collision itself. This is important for understanding the dynamics and effects of the collision.

Therefore, it is not necessary to ignore both sets of data equally, but rather selectively remove data points that may introduce errors or hinder the analysis of the collision.

Final answer:

To find the cat's speed at the top of the incline, we use the Work-Energy Theorem. The work done moving the cat up the ramp increases her kinetic energy, resulting in a final speed of 5.1 m/s.

Explanation:

To determine the speed of the cat at the top of the incline, we can apply the Work-Energy Theorem. The theorem states that the work done on an object is equal to the change in its kinetic energy. In mathematical terms, Work = ΔKE = KEfinal - KEinitial, where KE is kinetic energy given by ½mv2. The work done on the cat by pushing her up the ramp can be calculated as the force applied (parallel to the ramp) times the distance moved along the ramp, which is Work = Force × Distance = 41.0 N × 2.00 m = 82.0 J.

The initial kinetic energy of the cat can be calculated using her initial speed at the bottom of the ramp, KEinitial = ½ × 8.50 kg × (1.90 m/s)2. Plugging in the values, we get KEinitial = 15.33 J. The final kinetic energy at the top of the incline can be found by adding the work done to the initial kinetic energy: KEfinal = KEinitial + Work = 15.33 J + 82.0 J = 97.33 J. Solving for the final speed, we set KEfinal = ½ × 8.50 kg × v2 equal to 97.33 J and solve for v, finding that the cat's speed at the top of the ramp is 5.1 m/s.

Using the law of conservation of momentum, which states that initial momentum equals final momentum in a closed system, the initial speed of the truck before it collided with the stationary car is calculated to have been 12 m/s.

This question pertains to the concept of momentum in physics. The law of conservation of momentum states that the total momentum of a system of objects is constant if no external forces are acting on it. In this case, the truck and the car form the system of objects.

The initial momentum of the system before the collision is given by the momentum of the truck, since the car is stationary. The final momentum after the collision is given by the combined mass of the truck and car, multiplied by their common speed.

So, if we denote the initial speed of the truck as V, we have: 3000kg * V (initial momentum of truck) = (3000kg + 1000kg) * 9m/s (final momentum of the system)

Solving for V, we find the initial speed of the truck to have been 12 m/s.

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Answer:

4560m=4.560km

Explanation:

Analysis conceptual

We know that:

1km=1000m

Then, the conversion factor from meters to kilometers is: 1km/1000m

Known data:

4560 m

problem development

We multiply the amount given in m by the conversion factor (1km/1000m ):

[tex]4560 m(\frac{1km}{1000m} )=4.560km[/tex]

4560m=4.560km

The position vector with magnitude [tex]10 \ m[/tex] points to the right and up. its x-component is  [tex]6.0\ m[/tex] and its y-component is  [tex]8\ m[/tex].

A vector is a physics term for a quantity with both magnitude (size) and direction. Physical quantities including each of these properties are represented by vectors, such as displacement, velocity, force, and acceleration.

The resultant vector is the vector that is created when two or more vectors are added together. It depicts the final result of mixing the various vectors. The vector addition of the various vectors yields the resultant vector.

Given:

Magnitude = [tex]10 \ m[/tex]

x- component = [tex]6\ m[/tex]

The resultant vector is given as:

[tex]r = sqrt(x^2+y^2)\\10 = sqrt(6^2+y^2)\\y^2 = 100-36\\y = 8\ m[/tex]

Hence, the position vector with magnitude  [tex]10 \ m[/tex] points to the right and up. its x-component is [tex]6.0\ m[/tex] and its y-component is [tex]8\ m[/tex].

To learn more about Vector quantity, here:

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The minimum speed the rock must have at the top of the circular path to always stay in contact with the bottom of the bucket is approximately 5.04 m/s, based on principles of circular motion and gravitational force.

This problem can be solved using the principles of circular motion and Newton's laws of motion. When the rock is at the top of the vertical circle, the minimum speed it should have is equal to the speed at the point where the gravitational force acting downwards equals the required centripetal force to maintain circular motion. To achieve this, you can use the formula v² = 2gy to find out the minimum velocity needed.

Given:
Mass of the rock (m) = 500g = 0.5kg
Gravitational acceleration (g) = 9.81m/s²
Radius of the circle (r), since diameter = 2.6m, r = d/2 = 1.3m

The minimum speed needed at the top of the circle, v, is found by rearranging the equation to v = √(2gr). Substituting the given values, we get: v = √(2*9.81m/s²*1.3m) = √(25.386) ≈ 5.04 m/s

So, the rock must have a minimum speed of 5.04 m/s at the top of its circular path to ensure it stays in the bucket.

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The scenario presented is a physics problem that involves the concepts of forces and circular motion. It necessitates determining the minimum velocity a rock must have when at the highest point of its circular path to maintain contact with the bucket. The calculated velocity required at the highest point of the trajectory, based on the provided diameter of the circle and the force of gravity, is approximately 3.5 m/s.

The scenario is a physics problem that deals with centripetal force and gravity. The minimum speed the rock needs to have at the top of the circle to stay in contact with the bucket can be calculated using the centripetal acceleration equation, ac = v²/r. Here, we know that the centripetal acceleration must be at least equal to gravity (9.8 m/s²) to maintain contact. We also know that the radius (r) of the circle is the diameter divided by two, which is 2.6m/2 = 1.3m. So, we can set up the equation 9.8m/s² = v²/1.3m, which when solved, gives us v = √(9.8m/s² * 1.3m) = √12.74 m²/s², resulting in v ≈ 3.5 m/s. So, the rock needs to travel at a speed of about 3.5 m/s at the top of the circle to stay in contact with the bucket.

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Answer: A, B, C, E

Explanation:

Plastics have a number of properties that make them useful solutions to many complex problems in the world, such as being chemically resistant, durable, non-reactive, and easy to manufacture, which are options A, B, C, and E.

Plastics have a number of properties that make them a popular choice in many industries, such as chemical resistance, which is one of the most important properties of plastics, as they can resist a wide range of chemicals, including acids, bases, and solvents, which makes them ideal for use in chemical processing, pharmaceuticals, and food packaging. Durability is another important property of plastics.

They are resistant to wear and tear, impact, and weathering, which makes them suitable for use in various applications, such as building materials, automotive parts, and toys. Plastics are also non-reactive, which means that they do not react with other materials.

Hence, the correct answers are chemically resistant, durable, non-reactive, and easy to manufacture, which are options A, B, C, and E.

Learn more about plastic here.

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Sample Response: If the height of the cylinder increases, the temperature of the water increases, because a greater height means the cylinder has more potential energy that can be converted to thermal energy, increasing the temperature of the water.

r1 = 5*10^10 m , r2 = 6*10^12 m

v1 = 9*10^4 m/s

From conservation of energy

K1 +U1 = K2 +U2

0.5mv1^2 - GMm/r1 = 0.5mv2^2 - GMm/r2

0.5v1^2 - GM/r1 = 0.5v2^2 - GM/r2

M is mass of sun = 1.98*10^30 kg

G = 6.67*10^-11 N.m^2/kg^2

0.5*(9*10^4)^2 - (6.67*10^-11*1.98*10^30/(5*10^10)) = 0.5v2^2 - (6.67*10^-11*1.98*10^30/(6*10^12))

v2 = 5.35*10^4 m/s

The speed of a comet in an elliptical orbit around the sun can be calculated using Kepler's second law, which states that a planet sweeps out equal areas in equal amounts of time. This means that when a comet is closer to the sun, it moves faster, and when it is farther away, it moves slower.

The speed of a comet in an elliptical orbit around the sun can be calculated using Kepler's second law, which states that a planet sweeps out equal areas in equal amounts of time. This means that when a comet is closer to the sun, it moves faster, and when it is farther away, it moves slower. To find the speed of the comet when it is 6 x 10^12 m from the sun, we can use the fact that the area swept out by the comet is the same at both points. Using the distances given, we can calculate the speed of the comet when it is 6 x 10^12 m from the sun.

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In the 1960s, the West Coast saw the rise of Surf Rock, a dance style associated with the beach culture and the Black Arts Movement which promoted a blend of traditional and contemporary African American dance styles.

In the 1960s, on the West Coast, particularly in California, a new dance style known as Surf Rock emerged. This musical and dance movement was a product of the beach culture prevalent there. Bands like the Kingsmen and the Ventures popularized this genre, and the music often emphasized guitar riffs and had less focus on the lyrics, a shift influenced by the noisy dance halls where the bands performed. The dance associated with Surf Rock was an energetic response to the instrumental tunes and was part of the broader youth culture's expression at the time.

While Surf Rock mainly dominated, there were also important contributions to dance from African American communities. The Black Arts Movement arose during the 1960s and celebrated "Black Dance," which was a blend of different dance styles that included historical and traditional elements of African heritage. This movement was part of a broader spectrum of cultural expression during the decade which sought to empower and reconnect with African American roots.

Final answer:

During the 1960s, the West Coast saw the rise of Surf Rock, a dance genre closely connected to the laid-back, free-spirited surfing lifestyle and characterized by instrumental rock music.

Explanation:

In the 1960s, on the West Coast, particularly in California, a dance movement that emerged was Surf Rock. This genre of music created a unique dance vibe and culture, mostly due to its instrumental focus and connection with the surf scene. Surf Rock music was linked to a style of guitar-led rock music that often had a strong association with the surfing culture and lifestyle associated with Southern California. It helped define a youthful, beach-oriented counterculture that was free-spirited and often synonymous with the freedom and allure of the West Coast. Bands like the Kingsmen, famous for 'Louie Louie', and the Ventures with 'Walk Don't Run', became the soundscape of this era, influencing the dances that accompanied their music.

Final answer:

The magnitude of the acceleration of the larger block across the table is 2.45 m/s², calculated using the gravitational force acting on the hanging mass and applying Newton's second law to the system of both blocks.

Explanation:

To calculate the magnitude of the acceleration of the larger block across the table, we need to apply Newton's second law of motion which states that the force equals the mass times the acceleration (F = ma). In this scenario, only the gravitational force acting on the 10 kg hanging mass needs to be considered for the system of both blocks, as the table is frictionless and there are no other external forces acting on the horizontal block.
We calculate the gravitational force acting on the 10 kg block, which is the weight of the block (W = mg), where m is the mass and g is the gravitational acceleration (approximately 9.8 m/s2). For the 10 kg block, W = 10 kg × 9.8 m/s2 = 98 N. This force is the net force causing both blocks to accelerate, and because the rope is massless and the pulley is frictionless, the tension in the rope is uniform throughout.
The total mass of the system is 30 kg + 10 kg = 40 kg. Using the equation F = ma, rearrange to find acceleration (a = F/m). So the acceleration of the system is a = 98 N / 40 kg = 2.45 m/s2. Therefore, the magnitude of the acceleration of the larger block across the table is 2.45 m/s2.

Answer:

The horizontal and vertical velocity of the skier are both 29.4 m/s.

Explanation:

If no forces are acting in the horizontal direction, then the horizontal component of the velocity remains constant in time:

Vx = 29.4 m/s

For the vertical component the gravity acceleration must be considered, and the vertical velocity can be written as:

Vy = g*t

Here the value for g is 9,8 m/s2. Note that the initial vertical velocity is zero.  

Evaluating in the velocity’s expressions for a time of 3 seconds we obtain:

Vx = 29.4 m/s

Vy = 9.8 m/s2 * 3 s = 29.4 m/s