Can anyone help with this?

Can Anyone Help With This?

Answers

Answer 1

Answer:

Explanation:

Add a horizontal line.  An object that is not moving has no change in distance with respect to time.


Related Questions

A man drags a 10.0 kg bag of mulch at a constant speed applying a 22.5 N force at a 32-degree angle. What is the friction force acting on the bag?

Answers

The

friction

force acting on the bag is 4.36µ.

What is friction force?

The

force

preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction.

Given,

Force =F=22.5 n

Mass=m= 10 kg

mu=µ=?                            

(1N= 1kg m/s²)

Gravitational force =g= 9.81 m/s²

As we know,

F= µ*m*g

µ= m*g/F

  = 10*9.81/ 22.5

µ= 4.36 .

Therefore, the friction force acting on the bag is 4.36.

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The bag is subject to a friction force of 4.36. A man applies a 22.5 N force at a 32° angle while dragging a 10.0 kilogram bag of mulch at a steady speed.

How much friction is there?

Friction refers to the force that resists hard surface, fluid layering, and materials ingredients from gliding past one another. Friction lessens a machine's mechanical advantage, or, to put it another way, friction decreases the output to input ratio.

Force = 22.5 N

Mass  = 10 kg

⇒ mu     = µ (1N= 1kg m/s²)

⇒ g        = 9.81 m/s²

As we know, F= µ × m × g

⇒ µ = (m × g)/F

⇒ (10 × 9.81)/ 22.5

⇒ µ = 4.36 .

Therefore, the friction force acting on the bag is 4.36.

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Which of the following is NOT a scientific hypothesis?
A. Neon atoms emit red light.
B. There is an attractive force between the earth and moon.
C. Halle Berry is attractive.
D. Summer days are hottest
E. The sky is blue.

Answers

The following statement is not a scientific hypothesis:

C. Halle Berry is attractive.

A scientific hypothesis is a proposed explanation for an observation or pattern in nature that can be tested through further investigation and experimentation. It should be testable, falsifiable, and based on evidence.

Neon atoms emit red light. This is a scientific hypothesis that can be tested and confirmed by looking at the spectrum of light emitted by neon atoms.

B. There is an attractive force between the earth and moon. This is a scientific hypothesis that can be tested and confirmed by measuring the force of gravity between the earth and moon.

D. Summer days are the hottest of the year. This is a scientific hypothesis that can be tested and confirmed by collecting temperature data during the summer months.

E. The sky is blue. This is a scientific hypothesis that can be tested and confirmed by observing the sky under different atmospheric conditions.

The statement "Halle Berry is attractive" is a subjective opinion that cannot be tested or confirmed through scientific investigation, hence it is not a scientific hypothesis. Attractiveness, as a concept, can vary widely based on personal, cultural, and social factors.

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A 4.51 kg object is placed upon an inclined plane which has an incline angle of 23.0*. The object slides down the inclined plane with a constant speed. Find the force of gravity and the parallel component of gravity along with the perpendicular component.

Answers

The force of gravity is 103.73N and the parallel component of gravity is 40.45N along with the perpendicular component is 95.43N.

How strong is the force of gravity?

The gravitational force, which pulls mass-containing objects in the same direction, is the force of gravity. The force of gravity from Earth is something we consider frequently. Your body is held firmly in place by this force. However, every mass-bearing object pulls everything else with mass toward it through gravity.

The force of gravity F = ma

F = 4.51×23

F = 103.73N

F parallel component = F sinθ

F parallel = 103.73 sin 23°

F parallel = 103.73 × 0.390

F parallel = 40.45N

F perpendicular component =  F cosθ

F perpendicular = 103.73 × cos 23°

F perpendicular = 103.73 × 0.920

F perpendicular = 95.43N.

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The heaviest train ever pulled by a single engine was over 2 km long. Suppose a force of 1.13 X 10^8 N is needed to overcome static friction in the train's wheels. If the coefficient of static friction is 0.741, what's the train's mass?

Answers

The overcoming force is equal to the friction. The train's mass is 15,560,880.5 Kg

What is Friction ?

Friction can simply be defined as a force that opposes the movement of an object in a plain surfaces.

Given that the heaviest train ever pulled by a single engine was over 2 km long. Suppose a force of 1.13 X 10^8 N is needed to overcome static friction in the train's wheels. If the coefficient of static friction is 0.741, what's the train's mass?

F = μN

Where

F = Frictional force = overcoming force = 1.13 X 10^8 Nμ = coefficient of static friction = 0.741N = Normal reaction = mg

Substitute all the necessary parameters

1.13 X 10^8 = 0.741N

N = 1.13 X 10^8/0.741

N = 152496626.2 N

N = mg

152496626.2 = 9.8m

m = 152496626.2/9.8

m = 15,560,880.5 Kg

Therefore, the mass of the train is 15,560,880.5 Kg.

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Which of the following best explains the cause and effect relationship between convection currents in the mantle and the movement of tectonic plates?

A. The tectonic plates will heat up the mantle due to being closer to the surface of the earth and sun. The less dense particles in the mantle fall and cool toward the core, driving the convection cycle.

B. The tectonic plates drive the convection cycles in the mantle. As the plates move apart or push together, particles in the mantle will be thrust toward the core.

C. The heat from the core will make the particles in the mantle more dense and rise, causing plates in the
lithosphere to move in the opposite direction of the convection current.

D. The heat from the core will make particles in the mantle less dense and rise, causing plates in the
lithosphere to move in the direction of the convection current.

Answers

C) The mantle's particles will become more dense and rise as a result of the core heat, causing the lithosphere's plates to move in the opposite direction of the convection current.

How does the mantle's density change as it heats up?

Convection Currents The lithosphere becomes denser than the surrounding magma and sinks back toward the core as the heated mantle transfers heat energy to it.

How does heat travel from the core to the crust in the mantle?

Conduction from the core directly heats the lower mantle. As atoms collide, heat is transferred in conduction. Convection is the movement of warm and cool materials upward and downward. Material that is hot rises to the surface through conduction.

When the mantle rises, what takes place?

“hot spots," which are non-plate tectonic volcanic regions, are probably caused by mantle plumes. A diapir is formed when a mantle plume reaches the upper mantle. Volcanic eruptions are sparked by the heat generated by this molten material in the asthenosphere and lithosphere.

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Maritza's school provides a laptop to each student to use in the classroom and for
homework. What is the BEST way for her to use the laptop in her science class?
A.to look up bands who are coming to town?
B.to take notes as her teacher talks?
C.to complete her English assignment?
D.to email her friend in another class?

Answers

The best way for her to use the laptop in her science class  is to take notes as her teacher talks

How can a laptop be used in a classroom?Fostering online collaboration with other students.Providing curriculum support and additional information to students.Promoting better organization: Laptops help students keep track of their assignments and utilize an online school calendar.Laptops allow students to collaborate with their classmates inside and outside the classroom. They can ask questions, compare notes and share what they have learned more readily. They can also work together on group projects even if they are not in the same locationIn the last several years, schools across the country have experimented with providing each student with a laptop to facilitate learning. In 2016, Michigan State University studied the results from a number of these programs to determine if providing laptops influenced academic performance. The researchers, led by Michigan State University’s Assistant Professor Binbin Zheng, looked at nearly 100 studies of the use of laptops in the classroom, known as “one-to-one computing environments.”

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A sample of copper (specific heat capacity of copper is 0.386J/g*C) absorbs 1200 J of heat and
the temperature of the water it is being heated in increases from 27*C to 95*C, what mass of
copper was heated?

Answers

The mass of copper heated from a temperature of 27°C to 95°C is 45.72 g.

What is mass?

Mass is the quantity of matter contained in a body, The units of mass are

Kilogram (kg)Gram (g)Milligram (mg) etc.

To calculate the mass of the copper, we use the formula below.

Formula:

m = Q/cΔt.................. Equation 1

From the question,

Given:

m = MassQ = Amount of heatc = Specific heat capacity of copperΔt = Change in temperature

From the question,

Given:

Q = 1200 Jc = 0.386 J/g°CΔt = 95-27 = 68°

Substitute these values into equation 1

m = 1200/(0.386×68)m = 45.72 g

Hence, the mass of copper is 45.72 g.

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A 30kg metal ball is dropped from a height of 12.5 m.  
a.  Find the final velocity when the ball  hits the ground.
b.  Find the time it takes for the ball to hit the ground.

Answers

From conservation of linear momentum, the final velocity is 15.7 m/s and the time taken is 1.6 s

What is Velocity ?

Velocity can be defined as a distance travel in a specific direction per time taken. It is a vector quantity.

Given that 30kg metal ball is dropped from a height of 12.5 m.  

a.  Find the final velocity when the ball  hits the ground.

The maximum K.E of the ball at it final velocity will be equal to its maximum P.E at height 12.5 m. That is,

K.E = P.E

1/2mv² = mgh

Where

m = 30 Kgg = 9.8 m/s²h = 12.5 mv = ?

Substitute all the parameters

1/2 × 30 × v² = 30 × 9.8 × 12.5

v² = 245

v = √245

v = 15.65 m/s

b. The time it takes for the ball to hit the ground can be found through

h = ut + 1/2gt²

but u = 0

h = 1/2gt²

Substitute all the necessary parameters

12.5 = 1/2 × 9.8 × t²

12.5 = 4.9t²

t² = 12.5/4.9

t² = 2.55

t = √2.55

t = 1.6 s

Therefore, the final velocity when the ball hits the ground is 15.65 m/s and the time it takes for the ball to hit the ground is 1.6 s

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What is electronic dispersion theory?

Answers

Dispersion in wave theory is the phenomena where a wave's phase velocity changes depending on its frequency. The article can explore different definitions. This is the typical definition for dispersion (waves).

When sinusoidal waves with various wavelengths propagate at various speeds, a wave packet with mixed wavelengths has a tendency to disperse in space. Dispersion in wave theory is the phenomena where a wave's phase velocity changes depending on its frequency.

The article can explore different definitions. This is the typical definition for dispersion (waves).

A full set of approximate solutions to the one-electron Schrödinger equation are found in a three-dimensional atomic lattice that is randomly filled with atoms of different kinds and has, on average, the periodicity of a Bloch wave.

Equations are provided that enable the calculation of each wave's energy, average behavior, absent a phase factor, close to any sort of atom, and damping parameter.

A comparison is made between a periodic lattice with a complicated, energy-dependent potential and a random A-B lattice. The dispersion relation of the system is obtained by solving the eigenvalue problem in this potential using any of the established techniques for periodic potentials.

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Gravity on earth is 9.8
Jaydens mass is 50 kilograms his weight is

Answers

The weight of an object is a measure of the force of gravity on that object. It is calculated using the formula weight = mass * acceleration due to gravity.

In this case, the mass of the object is 50 kilograms and the acceleration due to gravity on Earth is 9.8 m/s^2. Plugging these values into the formula, we get:

weight = 50 kg * 9.8 m/s^2
= 490 N

Therefore, the weight of Jayden, who has a mass of 50 kilograms, is 490 Newtons.

8:11
GCSE Science - Physics
22 of 25
14 67%
A cat accelerates from rest to 10 m/s
when it sees a dog. This takes 2
the cat?
seconds What is the acceleration of the cat ?

Answers

the acceleration of the cat is 5m/s square

To find the acceleration of the cat, you can use the formula a = (v-u)/t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the time it takes for the acceleration to occur.

In this case, the initial velocity (u) is 0 m/s (since the cat starts at rest), the final velocity (v) is 10 m/s, and the time (t) is 2 seconds. Plugging these values into the formula, we get:

a = (10 m/s - 0 m/s) / 2 s
= 10 m/s / 2 s
= 5 m/s^2

So the acceleration of the cat is 5 m/s^2.

A 4.51 kg object is placed upon an inclined plane which has an incline angle of 23.0*. The object slides down the inclined plane with a constant speed. Find the normal force, friction force and the coefficient of sliding friction

Answers

To find the normal force, we can use the equation: normal force = weight + friction force * cos(incline angle).

How to find the normal force ?The weight of the object is (4.51 kg) * (9.8 m/s^2) = 44.398 NTo find the friction force, we can use the equation: friction force = coefficient of friction * normal force.We can assume that the friction force is equal to the force of gravity acting against the object because it is moving down the inclined plane at a constant pace. As a result, the friction force is equal to the product of the object's weight and sin (incline angle)Friction force is equal to (9.927 N)*sin(23.0)*(44.398 N)We can use the following equation to determine the coefficient of sliding friction:friction coefficient is calculated as friction force divided by normal force.coefficient of sliding friction = 9.927 N /44.398 N = 0.224Therefore, the normal force is 44.398 N, the friction force is 9.927 N, and the coefficient of sliding friction is 0.224.

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4. How many excess electrons does a balloon that was rubbed on a child's hair and
now has a charge of 4.0 x 107 Coulombs?

Answers

The number of excess electrons in a balloon with a charge of 4.0 x 107 Coulombs is 4.0 x 10^7 electrons.

Hope this helps!

H
Question 12 of 15:
Select the best answer for the question.
12. A 150-lb block of ice has a temperature of 22 F. How much heat will the ice absorb before it begins to melt?
O A. 1500.0 Btu
O B. 1663.2 Btu
C. 756.0 Btu
OD. 2419.2 Btu

Answers

Answer:

I think it is A

Explanation:

It is A because if you calculate the weight minus the F, then you have to divide that by the amount of absorbation (the lb) before timsing it by 1000.

the angel between vector a A = 2.00i + 3.00i and vecto B is 45 degree , the scalar product of vectors A and B is 3.00 if the x component of vector B is positive , what is the vector B

Answers

I think the answer is b but im not really sure

a boy is swinging a toy on apiece of string in a vertical circle. the toy has mass 150g and the radius of circle is 0.8m. a) he swings the toy with a linear velocity 2m/s. will the top move in a circle? explain your answer.

Answers

The top move will in a circle because there is tension at the top which will add up with the weight of the toy to maintain equal centripetal force providing the circular motion.

What is tension of the top of the vertical circle?

The tension experienced by the top of the vertical circle is calculated by using the following formula.

T = Fc - W

where;

Fc is the centripetal force of the toyW is the weight of the toy

T = mv²/r - mg

where;

m is the mass of the toyv is the linear speed of the toyg is acceleration due to gravityr is the radius of the vertical circle

The tension experienced by the toy at the top of the vertical circle is calculated as follows;

T = ( 0.15 x 2² / 0.8 ) - ( 0.15 x 9.8 )

T = 0.75 - 1.47

T = -0.72 N

Thus, with the negative tension at the top of the vertical circle, the sum of the tension force and the weight of the toy will be equal to the centripetal force to maintain the orbit of the toy in a circular path.

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What will be the final temperature of a sample of water, if 32 kJ of heat is removed to lower 836
g of water starting with an initial water temperature of 25*C?

Answers

The final temperature of a sample of water is 15.89 ⁰C.

What will be the final temperature of the sample of water?

The final temperature of the sample of water is calculated by using the formula for heat capacity of water.

Q = mcΔθ

where;

Q is the heat capacity of the water = 32 kJm is the mass of the water = 836 gc is the specific heat capacity of water = 4200 J/kgCΔθ is the change in the temperature of the water = ?

Δθ = Q / mc

The change in the temperature of the sample of water is calculated as follows;

Δθ = ( 32,000 ) / ( 0.836 x 4200 )

Δθ = 9.11 ⁰C

The final temperature of the water when heat is removed  is calculated as follows;

T₂ = 25 ⁰C - 9.11 ⁰C = 15.89 ⁰C

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Please help with this

Answers

A unit vector must have length equal to 1. By calculating the length of (1, 1), we discover that (12 + 12) = 2 = 1.414, which is not the same as 1, is the length.

How do you write unit vector notation?I,J notation is a way to describe a vector. In Cartesian coordinates, a unit vector is a vector with length 1. The unit vectors along the axis are denoted by the letters I and j, respectively. The form ai+bj an I + b j can be used to represent any two-dimensional vector.Numerous operations, including addition, subtraction, and vector multiplication, can be carried out with the aid of the vector form of representation. A=xi+yj+zk is the vector form of the cartesian representation of the three points (x, y, and z). A is equal to x I y j, and z k.Vy = Vyj, Vz = Vz k, and Vx = Vxî. V = Vx + Vy + Vz = Vxî+ Vyj+ Vz k is the result of applying the triangle rule to vector addition twice. The unit vector notation is used in this situation.

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Why the specific heat of water changed as the water state changed?​

Answers

Answer:

Infinity. Yes, specific value of water during phase change is infinity. This is because, as long as water is present and it is changing phase (at boiling point or at any other constant temperature), the temperature of the water does not change no matter what amount of heat you are supplying to the water. Thus, its specific heat value is infinity.

A car accelerates from the rest at 1.5 m/s^2 for 10 sec. What made the car move?

Answers

Accelerating linearly is simple.

What is Acceleration?

When the velocity vector length of an object moving in a straight line changes in response to changes in the object's speed (speed being the magnitude of the velocity vector), we have acceleration. Increasing speed is frequently referred to as "positive acceleration" and decreasing speed as "negative acceleration."

A particle's acceleration is the rate at which its velocity changes over time. The term "constant acceleration" refers to the pace at which a particle's velocity changes.

We shall measure acceleration in metres per second per second because our basic units are metres and seconds.

Therefore, Accelerating linearly is simple.

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Ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A. Is the momentum conserved in the collision? Why?

Answers

The mass of ball B and the final velocity of ball A can complement the conservation of linear momentum. The answer is yes.

What is Momentum ?

Momentum can simply be defined as the product of mass and velocity. It is a vector quantity.

Given that ball A with a mass of 0.280kg makes an elastic head-on collision with ball B initially at rest. After collision, ball B moves off with half the original speed of ball A.

In an elastic head-on collision, momentum is mostly always conserved. That is, the sum of the momentum before collision will be equal to the sum of the momentum after collision.

Mathematically, MaUa = MaVa + MbVb

Is the momentum conserved in the collision?

The answer is yes!

Why?

Because we need to consider the mass of the ball B and the final velocity of the ball A.

Therefore, In consideration of the mass of the ball B and the final velocity of the ball A, we can say that the momentum is conserved.

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An object has 100 J of kinetic energy. If the object’s mass doubles, what is its kinetic energy?

Answers

An object has 100 J of kinetic energy. If the object’s mass doubles, then its kinetic energy will be 200J and is denoted as option C.

What is Kinetic energy?

This is referred to as the type of energy that it possesses due to its motion and can also defined as the work which is needed to accelerate a body of a given mass from rest to its stated velocity.

The unit is in Joules and the formula is 1/2mv² where m is the mass and v is the velocity of the body or object. In a scenario where the mass is doubled or tripled and the velocity is constant then the kinetic energy will also be doubled or tripled respectively.

For instance, lets assume initial mass is 50kg and the v² is 50m/s then the kinetic energy is  1/2mv²  which is 1/2 × 50 × 50 = 1250J. When the mass is doubled it becomes 100kg which 1/2 × 100 × 50 = 2500J which depicts that  it was also doubled.


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The options are:

A.  50 Joules.

B.  100 Joules.

C.  200 Joules.

D.  400 Joule

Assuming an object has 100 Joules of kinetic energy. If the object’s mass doubles, its kinetic energy would be equal to: C. 200 Joules.

What is kinetic energy?

In Science, kinetic energy can be defined as a type of energy that's possessed by a physical object or body, especially due to its motion or a change in velocity (acceleration).

This ultimately implies that, a physical object or body would gain more of kinetic energy as it falls back toward the Earth because it is in motion.

How to calculate kinetic energy?

Mathematically, kinetic energy can be calculated by using this formula:

K.E = 1/2 × mv²

Where:

K.E represents the kinetic energy.m represents the mass.v represents the speed or velocity.

Since the mass of the object doubles, its kinetic energy would be twice that of its initial kinetic energy;

Kinetic energy = 2 × initial kinetic energy

Kinetic energy = 2 × 100

Kinetic energy = 200 Joules.

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Complete Question:

A.  50 Joules.

B.  100 Joules.

C.  200 Joules.

D.  400 Joules.

Periodic motion
This question is about the stretching of springs
The diagram below shows an unblocked spring of length 100 mm
hanging suspended from a clamp. When an object of mass 50g is
hung on the spring, it becomes 180 mm long.
The spring constant K=50N/m
100 mm
50g
1- Calculate x in (mm) then convert it to meter
X is the distance that the spring is stretched from its
equilibrium position.
2- Use Hooke's law to calculate the restoring force of the spring

Answers

Springs are elastic devices used to absorb shock, store energy, and provide support in a variety of applications.

1- The distance the spring is stretched from its equilibrium position is x = 180 - 100 = 80 mm. This can be converted to meters by dividing by 1000, so x = 0.08 m.

2- The restoring force of the spring can be calculated using Hooke's law, which states that F = kx, where F is the restoring force, k is the spring constant, and x is the distance the spring is stretched from its equilibrium position. In this case, F = 50 N/m × 0.08 m = 4 N.

What is Hooke's law?

Hooke's law is a basic law of physics that states that the force applied to a spring is proportional to the amount of displacement (or stretching) of the spring. In other words, the more you stretch a spring, the more force is needed to keep it stretched. This law is expressed mathematically as F = -kx, where F is the force, k is a constant known as the spring constant, and x is the displacement.

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helpp tyy



Which of the following is a way to make magnets?

heating
freezing
pressure

Answers

heating or pressing but heating is most appropriate, so the answer is heating.

A 25 kg box of roofing shingles is lifted 15 meters vertically to the top of a roof. How much work is done on the box?

Answers

Important Formulas:

[tex]F=ma[/tex]

force(measured in newtons) = mass(measured in kg) * acceleration(measured in m/s^2)

[tex]w=Fd[/tex]

work(measured in joules) = force(measured in newtons) * distance(measured in meters)

__________________________________________________________

Given:

[tex]m=25kg[/tex]

[tex]d=15m[/tex]

[tex]w=?[/tex]

We know that the acceleration due to gravity is 9.8 m/s^2.

__________________________________________________________

Finding force:

[tex]F=ma[/tex]

[tex]F=25\times9.8[/tex]

[tex]F=245N[/tex]

__________________________________________________________

Finding work:

[tex]w=Fd[/tex]

[tex]w=245\times15[/tex]

__________________________________________________________

[tex]\fbox{w = 3675 Joules}[/tex]

A lawnmower is pushed with a force of 72 Newtons at an angle of 40 degrees from the horizontal. How much work is done to the mower if it moves 740 meters?

Answers

The work done to the mower is the product of the external force applied on the object and the distance covered by the object which is equal to 40,811 Joules.

What is Work done?

Work done on an object can be defined as the product of external force applied on the object and the distance over which the force is being applied on the object. Work is done on an object when a force is applied to an object and the object is moved through certain distance.

From this we can see that the horizontal component of the force:

X-Component (horizontal component):

cos(θ) = x/F

Then,

X= F cos(θ).…..(1)

Now putting the values of F and θ in equation (1) we get,

X = 72 N × cos(40)

X = 72 N × 0.766

X= 55.15 N this is the x-component force

The work done to the mower is:

W = F × d

W = 55.15 × 740

W = 40,811 Joules

The work done to the mower is 40811 Joules.

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What is the equivalent resistance of a 3.0 Ω resistor and a 6.0 Ω resistor connected in parallel?

Answers

Answer:

The equivalent resistance of a 3.0 Ω resistor and a 6.0 Ω resistor connected in parallel is 2.0 Ω.

Explanation:

A man is attempting to train his dog. He is pulling on the dog with a force of 52.4 Newtons at an angle of 35.1 degrees above the horziontal. Fimd the X and Y component of the applied Force

Answers

The formula for the horizontal component (Fx), which is the angle the force makes with the horizontal, is Ftens•cosine(). Ftens• sine() can be used to compute the upward component (Fy), where is the angle that the force produces with the horizontal.

What is the force's horizontal component?

The portion of a force that works horizontally with regard to a body is known as its horizontal component. Its vertical component is known as its vertical component.

Why is moving the box with the rope horizontal easier?

The pulling of the box is with the rope horizontal. When the rope is angled Because Is less than, the horizontal component (= F cos ) is less. As a result, it is the proper response.

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Which of the following does NOT take place at the mission control center?
Doing contracting work for government agencies of private businesses
International Space Center
Sending signals to the space craft
Planning the details of the mission

Answers

MISSION CONTROL CENTER

Doing contracting work for government agencies of private businesses

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While skiing in Jackson, Wyoming, your friend Ben (of mass 63.2 kg) started his de- scent down the bunny run. 11.5 m above the bottom of the run. If he started at rest and converted all of his gravitational potential energy into kinetic energy, what is Ben's kinetic energy at the bottom of the bunny run? Use g = 9.8 m/s Answer in units of J.​

Answers

Answer:

Approximately [tex]7.1 \times 10^{3}\; {\rm J}[/tex] (given: [tex]g = 9.8\; {\rm m\cdot s^{-2}}[/tex].)

Explanation:

To find the change in the gravitational potential energy ([tex]\text{GPE}[/tex]), use the formula:

[tex]\begin{aligned}& (\text{change in GPE}) \\ &= (\text{mass})\, (g)\, (\text{change in height})\end{aligned}[/tex].

Assume that gravitational field strength [tex]g[/tex] is constant (e.g., [tex]g = 9.8\; {\rm m\cdot s^{-2}}[/tex].) For an object of mass [tex]m[/tex], if the altitude of the object changes by [tex]\Delta h[/tex], the [tex]\text{GPE}[/tex] of that object would change by [tex]m\, g\, \Delta h[/tex].

In this question, the mass of Ben is [tex]m = 63.2\; {\rm kg}[/tex]. It is given that [tex]g = 9.8\; {\rm m\cdot s^{-2}} = 9.8\; {\rm N\cdot kg^{-1}}[/tex] and is constant. Since change in the altitude of Ben is [tex]\Delta h = 11.5\; {\rm m}[/tex], the change in the ([tex]\text{GPE}[/tex]) of Ben would be:

[tex]\begin{aligned} m\, g\, \Delta h &= (63.2\; {\rm kg}) \, (9.8\; {\rm N\cdot kg^{-1}})\, (11.5\; {\rm m}) \\ &\approx 7.1\times 10^{3}\; {\rm N\cdot m} = 7.1\times 10^{3}\; {\rm J} \end{aligned}[/tex].

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