Spaceship 1 and Spaceship 2 have equal masses of 200 kg. They collide.
Spaceship 1's final speed is 2 m/s, and Spaceship 2's final speed is 1 m/s in
the same direction. What is their combined momentum?
O
A. 200 kg-m/s
O
O
O
B. 400 kg-m/s
C. 800 kg-m/s
D. 600 kg-m/s

The volume of the gas does not change

Explanation:

To solve this problem, we can apply the ideal gas equation, which states that:

[tex]\frac{pV}{T}=const.[/tex]

where

p is the pressure of the gas

V is its volume

T is its absolute temperature

The equation can also be written as

[tex]\frac{p_1 V_1}{T_1}=\frac{p_2 V_2}{T_2}[/tex]

where in this problem we have:

[tex]p_1[/tex] is the initial pressure of the gas

[tex]V_1[/tex] is the initial volume

[tex]T_1[/tex] is the initial temperature

[tex]p_2 = 2 p_1[/tex] is the final pressure (twice the initial pressure)

[tex]V_2[/tex] is the final volume

[tex]T_2 = 2T_1[/tex] is the final temperature (twice the initial temperature)

Solving for V2, we find what happens to the volume of the gas:

[tex]V_2 = \frac{p_1 V_1 T_2}{p_2 T_1}=\frac{p_1 V_1 (2T_1)}{(2p_1) T_1}=V_1[/tex]

Therefore, the volume of the gas does not change.

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1) The horizontal range of the laptop is 75.0 m

2) The initial vertical component of the velocity is 14.7 m/s

Explanation:

1)

The motion of the laptopin this problem is a projectile motion, so it follows a parabolic path which consists of two independent motions:  

- A uniform motion (constant velocity) along the horizontal direction  

- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction  

To find the horizontal range of the laptop, we just need to analyze its horizontal motion.

We know that:

- The laptop moves horizontally with a constant velocity of [tex]v_x = 25 m/s[/tex]

- The time of flight of the laptop is [tex]t=3.00 s[/tex]

So, the horizontal range of the laptop is given by

[tex]d=v_x t = (25)(3.00)=75.0 m[/tex]

2)

The total time of flight of a projectile is given by

[tex]t=\frac{2u_y}{g}[/tex]

where

[tex]u_y[/tex] is the initial vertical component of hte velocity

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

Here we know that the time of flight is

[tex]t=3.00 s[/tex]

Therefore, we can solve the formula for [tex]u_y[/tex], to find the initial vertical velocity:

[tex]u_y = \frac{tg}{2}=\frac{(3.00)(9.8)}{2}=14.7 m/s[/tex]

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The heat transfer depends on the factors such as the amount of time of contact, the area of contact, and the specific heals of the substances.

The process of flow of energy from a body of higher temperature to a lower temperature is known as heat transfer.

The mathematical expressions governing the concept of heat transfer are given as follows-

Q = m × c × ΔT

here,

m is the mass of the body.

c is the specific heat.

ΔT is the change in temperature.

And,

Q = k × A×ΔT / L

here,

k is the thermal conductivity.

A is the area of contact and L is the length of the body.

So, clearly, heat transfer depends on the factors such as specific heat and the area of contact. Moreover, the time of contact is also a matter of discussion as the longer the contact time, the more amount of energy will get a transfer from one body to another.

Thus, we can conclude that the heat transfer depends on the factors such as the amount of time of contact, the area of contact, and the specific heals of the substances.

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1) His momentum before touching the ground is 442.5 kg m/s

2) The net force on the pole vaulter is 490 N

Explanation:

1)

The motion of the pole vaulter is a motion of free fall, so it is subjected only to the force of gravity. Therefore, he falls to the ground at constant acceleration ([tex]g=9.8 m/s^2[/tex], acceleration of gravity), so we can use the following suvat equation to find his final velocity:

[tex]v^2-u^2=2as[/tex]

where

v is the final velocity

u = 0 is the initial velocity

[tex]a=g[/tex] is the acceleration

s = 4 m is the distance covered during the fall

Solving for v,

[tex]v=\sqrt{u^2+2as}=\sqrt{0+2(9.8)(4)}=8.85 m/s[/tex]

And therefore, his final momentum before touching the ground is

[tex]p=mv[/tex]

where m = 50 kg is his mass. Substituting,

[tex]p=(50)(8.85)=442.5 kg m/s[/tex]

2)

As we said previously, the only force acting on the pole vaulter during his fall is the force of gravity, which is

[tex]F=mg[/tex]

where

m = 50 kg is the mass

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

Substituting, we find the force of gravity, and therefore the net force acting on the pole vaulter:

[tex]F=(50)(9.8)=490 N[/tex]

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Answer:

"Galloping Gertie" is an appropriate nickname for the bridge​ Tacoma Narrows.

Explanation:

The Tacoma Narrows Bridge is slender, elegent and graceful bridge is stretched like a steel ribbon across Puget Sound in 1940.

When Galloping Gertie splashed into Puget Sound, it created ripple effects across the nation and around the world. The event changed forever how engineers design suspension bridges.

Tacoma Narrows Bridge The original bridge received its nickname "Galloping Gertie" because of the vertical movement of the deck observed by construction workers during windy conditions.

Final answer:

The nickname 'Galloping Gertie' is appropriate for the bridge because it refers to the Tacoma Narrows Bridge, which famously collapsed due to strong winds.

Explanation:

The nickname 'Galloping Gertie' is appropriate for the bridge because it refers to the Tacoma Narrows Bridge, which famously collapsed due to strong winds. When the bridge experienced wind-induced vibrations, it appeared to be galloping like a horse, hence the nickname. The collapse of Galloping Gertie serves as an important lesson in engineering and the need for understanding the effects of forces on structures.

Answer:

26i-28j

Explanation:

Mathematically, rate of change of something with respect to another is obtained through the operation called differentiation. Integration is the reverse process of differentiation.

We know that force is the rate of change of momentum.

that is,

F=[tex]\frac{dP}{dt}[/tex]

where,

P=momentum

t=time

dP=small change in momentum

dt=small change in time

dP=Fdt  (multiplying both sides with dt)

To get change of momentum within a particular time interval, we have to integrate the above expression giving the necessary limits according to the problem.

Here, we have to calculate the change in momentum between 1.0s and 2.0s. So, the limit of integration is 1.0 to 2.0.

Thus,

[tex]\int\limits^P_p {} \, dP[/tex]=[tex]\int\limits^2_1 {F} \, dt[/tex]

where,

p=momentum at t=1s

P=momentum at t=2s

substituting F in the above equation,

[tex]\int\limits^P_p {} \, dP[/tex]=[tex]\int\limits^2_1 {26i-12jt^{2}} \, dt[/tex]

[tex]\int\limits^P_p {} \, dP[/tex] = P-p = Change in momentum between 1.0s and 2.0s

[tex]\int\limits^2_1 {26i-12jt^{2}} \, dt[/tex] = [tex]\int\limits^2_1 {26i} \, dt - \int\limits^2_1 {12t^{2}j } \, dt[/tex] (Since we can integrate each term of an expression separately)

[tex]\int\limits^2_1 {26i} \, dt - \int\limits^2_1 {12t^{2}j } \, dt[/tex] = [tex]26i(2-1) - 12j(\frac{2^{3} -1^{3} }{3} )[/tex]

=26i-28j

therefore the change in momentum between 1.0s and 2.0s is 26i-28j.

Note: the answer we got is a vector. Because momentum is a vector and therefore change in momentum is also a vector

To find the change in momentum of a particle under the force F=26i-12t2j from 1.0s to 2.0s, we first integrate the force over the given time interval. The change in the particle's momentum is found to be 26i - 20/3j kg*m/s.

The question involves calculating the change in momentum of a particle when a force F=26i-12t2j is applied from 1.0s to 2.0s. To find the change in momentum, we first need to integrate the force over the given time interval, because the change in momentum (Δp) is equal to the integral of the force over time, according to the impulse-momentum theorem, Δp = ∫t1t2 F dt.

For the i-component, the force is constant (26i), so its contribution to the change in momentum from 1.0s to 2.0s is simply 26i N multiplied by the time interval, which is 26i N * (2.0s - 1.0s) = 26i kg*m/s. For the j-component, the force varies with time (-12t2j), so we need to integrate this force from 1.0s to 2.0s. The integral of -12t2 from 1 to 2 gives us -∫12 12t2 dt = -[4t3/3]12 = -8 + 4/3 = -24/3 + 4/3 = -20/3. Thus, the change in momentum in the j-direction is -20/3 j kg*m/s.

Combining the i and j components, the total change in the particle's momentum between 1.0s and 2.0s is 26i - 20/3j kg*m/s.

Answer:

neutron is a subatomic particle of about the same mass as a proton but without an electric charge, present in all atomic nuclei except those of ordinary hydrogen.

Answer:

According to Oxford dictionary neutron is a subatomic particle of about the same mass as a proton but without an electric charge, present in all atomic nuclei except those of ordinary hydrogen.

Explanation:

Let east represent X axis and north represent Y axis.

We need to find what displacement would put the ball in the hole in one putt.

The first putt displaces the ball 6.50 m east

First displacement = 6.50 i m

The second putt displaces it 5.90 m south

Second displacement = -5.90 j m

Total displacement = 6.50 i - 5.90 j

[tex]\texttt{Magnitude = }\sqrt{6.50^2+(-5.90)^2}=8.78m\\\\\texttt{Direction = }tan^{-1}\left ( \frac{-5.9}{6.5}\right )=-42.23^0[/tex]

So displacement to hole from initial position is 8.78 m at direction 42.23° south of east.

Final answer:

The statement is true, as pus is composed of dead neutrophils, dead tissue, bacteria, and living white blood cells. It reflects the immune system's response to infection, with pus indicating an accumulation of these elements at the site of infection.

Explanation:

The statement "Pus is a mixture of dead neutrophils, dead tissue, bacteria, and living white blood cells" is true. Pus is indeed an accumulation of these components. When neutrophils, which are a type of leukocyte, respond to an infection, they engulf pathogens in a process called phagocytosis. The dead neutrophils, along with any other cellular debris, dead pathogens, and living immune cells, such as macrophages still fighting the infection, aggregate to form pus at the infection site.

This purulent or suppurative discharge is a typical sign of the body's defensive responses engaging with the invading microorganisms. While small amounts of pus can indicate a healthy immune response, in history, there were attempts to produce pus artificially under the misguided notion that it could aid in healing. We now know that inducing pus does not promote recovery and that a natural immune response is best in fighting infections.

Answer:

A) being influenced by equal amounts of gravity and air resistance.

Explanation:

B) slowing down because of an unbalanced force of air resistance.

False - if it was slowing down, then the velocity would go down.

D) on the ground and is not falling anymore.

False - This would be mistaken as the answer but it is not because if the person is not falling anymore the horizontal line should be at the x-axis, meaning that there is no more velocity.

C) accelerating because of an unbalanced force of gravity.

False - The line would otherwise be going up or down.

The shape of the graph of the magnitude of the acceleration versus time for a falling skydiver initially increases and then decreases towards zero as the skydiver reaches terminal velocity. The graph of the magnitude of the velocity versus time initially increases and then reaches a plateau at terminal velocity. The graph of the magnitude of the displacement versus time initially increases and then levels off as the skydiver experiences constant displacement.

In the case of a skydiver, the shape of the graph of the magnitude of the acceleration versus time will initially be positive and then decrease towards zero as the skydiver reaches terminal velocity. This is because the skydiver is initially accelerating due to the unbalanced force of gravity, but as they approach terminal velocity, the force of air resistance opposes the force of gravity and causes the acceleration to decrease.

Similarly, the shape of the graph of the magnitude of the velocity versus time for a falling skydiver will initially be positive and then reach a plateau at terminal velocity.

Lastly, the shape of the graph of the magnitude of the displacement versus time for a falling skydiver will initially be positive and then level off as the skydiver reaches terminal velocity and experiences constant displacement.

Answer:2.5

Explanation:

Answer:

Resistance is the opposition that a substance offers to the flow of electric current

Explanation:

resistance is the opposition and Resistivity is a measure of the resistance of a given size of a specific material to electrical conduction.

Final answer:

Resistance is the opposition to electric current flow in materials, measured in ohms, while resistivity is a fundamental property of the material itself, indicating how much it resists electric current flow.

Explanation:

Understanding Resistance and Resistivity in Physics

Resistance is a measure of the difficulty in passing an electric current through a wire or component. It has units of ohms and is calculated by the formula V = IR, where V is voltage, I is current, and R is resistance. Resistivity, represented by the symbol p, is a material property that quantifies how strongly a material opposes the flow of electric current. The resistance R of a cylindrical object like a wire can be calculated using the formula R = pL/A, where L is the length and A is the cross-sectional area.

The key difference between resistance and resistivity is that resistivity is an intrinsic property of a material, which means it does not change regardless of the shape or size of the material. In contrast, resistance is an extrinsic property that depends on both the material's resistivity and the physical dimensions of the object. Materials can generally be categorized into conductors, semiconductors, and insulators, based on their resistivity values.

150 g

From the question;

It means the mass is 15 cm from the pivot

Therefore;

Assuming the mass of half meter rule is m

Then;

m × 5 cm = 50 g × 15 cm

m = 150 g

Therefore;

Mass of the  half meter rule is 150 g

The mass of the half meter ruler is 150g

Answer:

one feels diffulcites to breath in a deep well while cleaning it because well has less amount of oxygen in it.

A fired paper piece can be thrown to check the amount of oxygen.

Answer:

Because usually oxygen is on the ground, and then if you dig a hole, all kinds of gases scramble to run in, then oxygen is naturally less, which is also because of the depth of the ground. The deeper the ground, the more gas will press on you. Simply put, the deeper the well, the greater the pressure. Most of the carbon dioxide you emit in that well is held down by other gases and cannot go out, so that there is less oxygen.

Answer:

a) 20 m/s

b) No

Explanation:

a)

Mr. G needs to run x= 200 m in t = 10 seconds to catch the bus.

Knowing the speed is computed as

[tex]\displaystyle v=\frac{x}{t}[/tex]

We have

[tex]\displaystyle v=\frac{200m}{10s}=20m/s[/tex]

b)

The fastest human can run 12 m/s, so Mr. G won't be able to catch the bus because he needs to run faster than that

Final answer:

Mr.G needs to run at 20 meters per second to catch the bus, but since the fastest human can run only at 12 meters per second, it is impossible for Mr.G to catch the bus on time.

Explanation:

To solve for how fast Mr.G needs to run to catch the bus on time, we need to find his required speed. Speed is calculated by dividing the distance by the time. Since Mr.G is 200 meters away from the bus and he has 10 seconds to reach it, his required speed is 20 meters per second (200m / 10s = 20m/s).

Regarding whether Mr.G can catch the bus, considering the fastest human can run at a speed of 12 meters per second, it is unfortunately impossible for Mr.G to catch the bus. The required speed to catch the bus is 20m/s, which exceeds the maximum human running speed.

Answer:

because mass of a matter never changes

on the other hand the weight of a matter changes due to gravity

for example the

on the moon the pull of gravity is less than it is on earth so the Weight of an object will be less on the moon but the mass of it will stay the same

Explanation:

I

Mass is more fundamental than weight because mass is a consistent measure of the quantity of matter, whereas weight is the gravity-dependent force acting on an object and can vary. The confusion between these terms occurs often in everyday language, especially since they are used interchangeably.

Physicists say that mass is more fundamental than weight because mass is an intrinsic property of an object that represents the quantity of matter, which does not vary in classical physics. Conversely, weight is the gravitational force acting on an object, which can vary depending on the location and gravity. Therefore, mass is a more consistent and universal characteristic of matter than weight, which can differ even on Earth depending on elevation or geographic location.

The confusion between mass and weight arises as the terms are used interchangeably in everyday language. For instance, our medical records may show our weight in kilograms, which is actually a unit of mass, instead of the correct unit of newtons, which is used to measure gravitational force. This interchangeability of terms has led to a common misunderstanding of these distinct physical quantities.

The relationship between mass and weight becomes particularly evident in space.

Answer:

11.48 m

Explanation:

initial velocity (u) = 15 m/s

acceleration due to gravity (g) = 9.8 m/s

final velocity (v) = 0 ( the ball's speed reduces gradually when thrown until    

                                   becomes 0 at maximum height)

find the height reached.

          we cannot apply this formula directly because we do no know the time        

          (t), so we first need to find the time

       0 = 15 + (-9.8 x t)   (the negative sign is because the ball is decelerating

         upwards)

         15 = 9.8t

         t = 1.53 s

       height (s) = (15 x 1.53)  + (0.5 x (-9.8) x 1.53^{2})

       height = 22.95 - 11.47 = 11.48 m

Answer:

Fuerza de roce = 15 N

Hacia la izquierda

Explanation:

Las leyes de Newton explican el comportamiento de cuerpos bajo efectos de fuerzas externas. La primera ley especifica que un cuerpo no cambiará su estado de movimiento mientras una fuerza desequilibrante no lo acelere. Es decir, un cuerpo que se mueve a velocidad constante, tiene cero fuerza desequilibrante.

Como el cuerpo se está moviendo a velocidad constante, no hay aceleración y por lo tanto la fuerza total es cero.

Dado que estamos aplicando una fuerza horizontal de 15N y aún así el cuerpo se mueve a velocidad constante, significa que esa fuerza está siendo contrarrestada por la fuerza de roce hasta producir un equilibro de fuerzas y por lo tanto, cero fuerza desequilibrante.

La fuerza de roce es entonces, en módulo igual a la fuerza aplicada, es decir, 15 N

Su dirección siempre es opuesta al movimiento, así que la fuerza de roce se dirige hacia la izquierda

Everyone has a different reaction time because not everyone reacts the same to situations. Some people may be faster or slower than others. It could be a result of age, health,  and how they take care of themselves physically.

Gender, age, physical fitness, level of exhaustion, distraction, alcohol usage, personality type, the limb utilized for the test, biological rhythm, health, and whether the stimulus is auditory or visual have all been found to have an impact on reaction time. Social and cultural factors on reaction time are irrelevant.

A reaction is a deliberate, free response to an outside stimulus. The reaction time is the amount of time between the administration of an external stimulus and the appropriate motor response.

The period between the introduction of the stimulus and the emergence of the subject's proper voluntary response is referred to as the reaction time.

Typically, it is measured in milliseconds. It depicts the rate at which stimuli operate on a person's sensory system to produce neurophysiological, cognitive, and informational processes.

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The electrical energy consumed by a toaster is 0.033 Kwh.

Explanation:

The power utilized by the toaster is 400 W.

[tex]\text { The power utilized by the toaster is } 400 \mathrm{W} \text { in kilo-watts is } \frac{400}{1000}=0.4 \mathrm{Kw}[/tex]

The toaster is operated for 5 Minutes.

[tex]\text { The toaster is operated for } 5 \text { Minutes in hours is } \frac{5}{60}=0.083 \text { hours. (One minute is } 60 \text { seconds) }[/tex]

We know that,

[tex]\text {power}=\frac{\text {energy}}{\text {time}}[/tex]

Substitute the values in the above formula to obtain electrical energy,

[tex]0.4=\frac{\text { energy }}{0.083}[/tex]

Electrical energy = 0.4 × 0.083

Electrical energy is 0.033 Kwh.

Answer:

The answer is 120,000 Joules

Explanation:

Answer:#1 NEWTON’S THREE LAWS OF MOTION LAID THE FOUNDATION OF CLASSICAL MECHANICS    #2 HE WAS THE FIRST TO FORMULATE THE NOTION OF GRAVITY AS A UNIVERSAL FORCE

#3 NEWTON’S PRINCIPIA IS ONE OF THE MOST IMPORTANT WORKS IN THE HISTORY OF SCIENCE

#4 HE DISCOVERED THE GENERALISED BINOMIAL THEOREM IN 1665

#5 ISAAC NEWTON INVENTED CALCULUS

#6 HE INVENTED THE FIRST REFLECTING TELESCOPE

#7 HE DID GROUND BREAKING WORK IN OPTICS

#8 HE IDENTIFIED LIGHT AS THE SOURCE OF COLOUR SENSATION

#9 HE INFERRED CORRECTLY THE OBLATENESS OF EARTH’S SPHEROIDAL FIGURE

#10 SIR ISAAC NEWTON WAS THE SECOND SCIENTIST TO BE KNIGHTED

Answer:

Invented the reflecting telescope.

Proposed new theory of light and color.

Discovered calculus.

Developed three laws of motion.

Devised law of universal gravitation.

Advanced early modern chemistry.

Explanation:

Sir Isaac Newton had many great accomplishments. Here are some of his most notable achievements:

1. Newton's Three Laws of Motion: Newton formulated three fundamental laws that laid the foundation of classical mechanics. These laws describe how objects move and interact with each other. They are still widely used today to understand and predict the motion of objects.

2. Formulation of Gravity: Newton was the first to formulate the notion of gravity as a universal force. He explained that every object with mass attracts other objects towards it. His understanding of gravity helped explain why objects fall to the ground and why planets orbit the Sun.

3. Principia: Newton's book called "Mathematical Principles of Natural Philosophy" (commonly known as "Principia") is one of the most important works in the history of science. In this book, Newton presented his laws of motion and the law of universal gravitation. It revolutionized the field of physics and became the foundation for classical mechanics.

4. Generalized Binomial Theorem: In 1665, Newton discovered the generalized binomial theorem, which is a mathematical formula used to expand powers of binomials (expressions with two terms). This theorem is still studied and applied in various branches of mathematics.

5. Invention of Calculus: Newton independently developed calculus, a branch of mathematics that deals with rates of change and the accumulation of quantities. Calculus is widely used in many fields, including physics and engineering, and it provides a powerful tool for solving problems involving change and motion.

6. Invention of the Reflecting Telescope: Newton constructed the first reflecting telescope, which used mirrors instead of lenses to gather and focus light. This invention greatly improved the quality and clarity of images observed through telescopes and had a significant impact on the field of astronomy.

7. Groundbreaking Work in Optics: Newton conducted groundbreaking experiments and made important discoveries in the field of optics. He demonstrated that white light is composed of different colors, which led to the understanding of the color spectrum. His work on optics laid the foundation for future developments in this field.

8. Identification of Light as the Source of Color Sensation: Newton proposed that light is the source of color sensation. He demonstrated that the colors we perceive are a result of how light interacts with objects and our eyes. This understanding of light and color perception has had lasting effects in fields like art and design.

9. Inference of Earth's Oblateness: Newton correctly inferred that the Earth is not a perfect sphere but rather oblate, meaning it is slightly flattened at the poles and bulges at the equator. His understanding of the Earth's shape was based on his knowledge of gravity and the forces acting on the planet.

10. Knighthood: Newton was knighted by Queen Anne in 1705, becoming the second scientist to receive this honor. His contributions to science and mathematics were recognized and celebrated during his lifetime.

c. Ben is correct. According to Newton's 2nd law of motion objects with more mass require more force to accelerate.

Explanation:

We can answer this question by using Newton's second law of motion, which states that the net force applied on an object is equal to the product between the mass of the object and its acceleration. Mathematically:

[tex]F=ma[/tex]

where

F is the net force

m is the mass of the object

a is its acceleration

From the equation, we notice that:

- The force is directly proportional to the mass of the object --> so if the mass increases, the force needed to accelerate the object will increase too

Therefore, the correct answer is

c. Ben is correct. According to Newton's 2nd law of motion objects with more mass require more force to accelerate.

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1) Work done by the force: 8.3 J

2) Work done by gravity: -19.6 J

3) Normal force: 16.3 N

Explanation:

1)

The work done by a force pushing an object is given by

[tex]W=Fd cos \alpha[/tex]

where

F is the magnitude of the force

d is the displacement of the object

[tex]\alpha[/tex] is the angle between the direction of the force and of the displacement

First of all, we need to find the magnitude of the force F. Since the block is moving vertically at constant velocity (= zero acceleration), the equation of motion of the block along the vertical direction is:

[tex]F sin \theta - \mu N - mg = 0[/tex] (1)

Where

[tex]\theta=27.0^{\circ}[/tex]

[tex]\mu N[/tex] is the force of friction, where

[tex]\mu=0.40[/tex] is the coefficient of friction

N is the normal reaction of the wall

(mg) is the weight of the block, where

m =2.0 kg is the mass of the block

[tex]g=9.81 m/s^2[/tex] is the acceleration of gravity

Along the horizontal direction, the equation of motion is:

[tex]F cos \theta = N[/tex] (2)

Substituting (2) into (1),

[tex]F sin \theta - \mu F cos \theta - mg =0[/tex]

And solving for F,

[tex]F(sin \theta - \mu cos \theta) = mg\\F=\frac{mg}{sin \theta - \mu cos \theta}=\frac{(2.0)(9.81)}{sin 27^{\circ} - 0.40 cos 27^{\circ}}=18.3 N[/tex]

Now we can calculate the work done by the force. Here we have

d = 1.0 m is the displacement

[tex]\alpha = 90^{\circ} - 27^{\circ} = 63^{\circ}[/tex] is the angle between the direction of the force and the displacement

Substituting,

[tex]W=(18.3)(1.0)(cos 63^{\circ})=8.3 J[/tex]

2)

The work done by gravity is equal to:

[tex]W_g = mg d cos \alpha[/tex]

where

m = 2.0 kg is the mass of the block

[tex]g=9.81 m/s^2[/tex]

d = 1.0 m is the displacement

[tex]\alpha=180^{\circ}[/tex], since the direction of gravity is downward while the displacement of the block is upward

Substituting,

[tex]W=(2.0)(9.81)(1.0)(cos 180^{\circ})=-19.6 J[/tex]

3)

Equation (2) found in part 1) tells that

[tex]N=F cos \theta[/tex]

which means that the normal force between the wall and the block is equal to the horizontal component of the pushing force on the block.

Here we have:

F = 18.3 N is the magnitude of the pushing force

[tex]\theta=27.0^{\circ}[/tex] is the angle of the force with the horizontal

Substituting, we find the normal force:

[tex]N=(18.3)(cos 27^{\circ})=16.3 N[/tex]

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The work done by the force on the block is 22.3 J. The work done by gravity is 19.6 J and the normal force between the block and the wall is 18.1 N.

Firstly, we need to calculate the force that is applied (Force Applied) by taking the cosine of the angle (27.0◦) which is the force applied horizontally. Using the formula F_applied = m*g/cos(θ), where m=2.0 kg and g=9.81 m/s^2, we find that Force Applied = 22.3 N.

Next, the work done by the force on the block (Work Done) can be calculated by multiplying the Force Applied by the distance it moved (Force Applied x distance). Here, Work Done = 22.3 N x 1.0 m = 22.3 J.

The work done by gravity is obtained by multiplying the weight of the block by the distance it moves vertically (Work Done by Gravity). Here, Work done by Gravity = m*g*d = 2.0 kg * 9.81 m/s^2 * 1.0m = 19.6 J.

Finally, we calculate the magnitude of the normal force by multiplying the weight of the block by the cosine of the angle (m*g*cos(θ)) which equals to Normal Force = 2.0 kg * 9.81 m/s^2 * cos(27.0◦) = 18.1 N.

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The efficiency of the machine is 0.53 (53%).

Explanation:

The efficiency of a machine is given by:

[tex]\eta = \frac{W_{out}}{W_{in}}[/tex]

where

[tex]W_{out}[/tex] is the output work

[tex]W_{in}[/tex] is the work in input

The output work is:

[tex]W_{out}=F_L d_L = (2000)(2)=4000 J[/tex]

where

[tex]F_L = 2000 N[/tex] is the load

[tex]d_L = 2 m[/tex] is the distance covered by the load

The input work is:

[tex]W_{in}=F_E d_E = (1250)(6)=7500 J[/tex]

where

[tex]F_E = 1250 N[/tex] is the effort force

[tex]d_E = 6 m[/tex] is the distance from the effort to the pivot

Solving for the efficiency,

[tex]\eta=\frac{4000}{7500}=0.53[/tex]

So, the efficiency of the machine is 0.53 (53%).

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Answer:

2. 0.27 N/kg

3a. 210 N

3b. 23.3 N

Explanation:

The acceleration due to gravity is:

g = GM / r²

where G is the gravitational constant, M is the mass of the planet, and r is the distance from the planet's center.

2. At the surface of the Earth (r = R), the acceleration due to gravity is 9.8 N/kg.

9.8 = GM / R²

At r = 6R, the acceleration due to gravity is:

g = GM / (6R)²

g = (GM / R²) / 36

g = 9.8 / 36

g = 0.27 N/kg

3a. Weight is mass times acceleration due to gravity:

W = mg

W = (20 kg) (10.5 N/kg)

W = 210 N

3b. Find the new value of g:

g = GM / (3R)²

g = (GM / R²) / 9

g = 10.5 / 9

g = 1.17 N/kg

Now find the weight:

W = mg

W = (20 kg) (1.17 N/kg)

W = 23.3 N

The mass of the cannonball is 75 kg

Explanation:

We can solve this problem by using the law of conservation of momentum: in fact, the total momentum of the ball-cannon system before and after the shot must be equal.

Before the shot, the total momentum is zero, since both objects are at rest:

[tex]p=0[/tex] (1)

After the shot, the total momentum is: given by:

[tex]p=mv+MV[/tex] (2)

where :

m kg is the mass of the cannonball

v = 100 m/s is the velocity of the ball

M = 2500 kg is the mass of the cannon

V = -3 m/s is the recoil velocity of the rifle  (in the opposite direction to the ball

Since the toal momentum is conserved, (1) = (2), therefore we can solve for m, the mass of the cannonball:

[tex]0=mv+MV\\m=-\frac{MV}{v}=-\frac{(2500)(-3)}{100}=75 kg[/tex]

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Answer:electric field

Explanation:Because in an electric field, positive charge is directed away and negative charge is directed towards the electric field.

Answer:

an electric field

Explanation:

this field is what is direted to a negative charge

given,

constant velocity = 9.50 m/s

acceleration = 0

distance = 16 m

the time of flight

 s = so + ut + 1/2at²

16 = 9.50 × t

t = 1.68 s

a) to catch the can the truck he must throw it  straight up, at 0° to the vertical.

b) now,

yf = Yi + UyT + 1/2at²

0 = 0 + Uy * 1.68 - 1/2 * 9.8 * 1.68²

Uy = 8.23 m/s

Answer:

Mean: 114.8

Median: 112

Explanation:

The mean is the average of the numbers so you add them all together and divide by the number of terms. The median is the middle value when the terms are in order from least to greatest.

Answer:

Mean of the sample set = 114.8  

Median of the sample set = 112

Explanation:

To calculate mean, add value of all samples and then divide with number of samples.

Mean of the sample set = (100+103+112+120+139)/5 = 114.8

To calculated median, arrange the values in ascending order then take the value which is at middle.

100, 103, 112, 120, 139

“112” is at the middle so,

Median of the sample set = 112  

Answer:

The minimum angle of incidence is, ∅  = 56° 18' 35'' to the normal

Explanation:

Given data,

The distance between the two plane mirror, d = 5 cm

The length of the plane mirror, L = 30 cm

According to the laws of reflection, the angle of incidence is equal to the angle of reflection.

If the laser beam touches each mirror only twice, then the base of the triangle formed is not less than L/2.

Let ∅ be the angle of incidence to the normal. The normal divides the triangle into two equal halves where base becomes L/4.

Therefore,

                        tan ∅ = opp / adj

                                  = (L/4) / d

                                   = (30/4) / 5

                        tan ∅  = 1.5

                               ∅  = tan ⁻¹ (1.5)

                                    = 56° 18' 35''

Hence, the minimum angle of incidence is, ∅  = 56° 18' 35'' to the normal.