Let’s discuss some particle physics. In 1897, physicist J.J. Thomson conducted a seminalexperiment with a cathode ray tube. In the experiment, a beam of an unknown particle of chargeqandmassmis shot through the tube onto a fluorescent screen, at some speedvand in thex-direction. Uponimpact the beam leaves a bright spot on the screen. Sincevis very fast, effects of gravity are negligible andthe beam forms essentially a straight line normal to the screen.

To eliminate this deflection, an external uniform magnetic field of magnitudeBis turned on as well. What should be the direction and magnitudeBof this field such that ∆z= 0?

Answers

Answer 1

Answer:

The direction of the magnetic field should be in the x and y coordinates alone, and their should be no change towards the z coordinate. Also the magnitude of the magnetic field in the z direction would be zero if there is no magnetic field in that coordinate.

The coordinate should be:

B = bi + bj


Related Questions

a batsman deflects a ball by an angle of 45 without changing its initial speed which is equal to 54km/h.what is the impulse imparted to the ball? mass of the ball is 0.15kg​

Answers

Answer:

the impulse imparted to the ball is 4.158 kg.m/s

Explanation:

Please find attached image for diagram.

Given;

initial speed of the ball from point A, u = 54km/h = 15 m/s

angle of deflection of the ball along BOP, θ = 45⁰/2 = 22.5⁰

mass of the ball, m = 0.15 kg

the final speed of the ball along B,  = u (in reverse direction)

The initial momentum of the ball, P₁ = mucosθ

The final momentum of the ball is P₂ in reverse direction to P₁.

the impulse imparted to the ball = change in momentum of the ball

J = ΔP = P₂ - P₁

J = mucosθ - (-mucosθ)

J = mucosθ + mucosθ

J = 2mucosθ

J = 2(0.15)15cos(22.5⁰)

J = 4.158 kg.m/s

Thus, the impulse imparted to the ball is 4.158 kg.m/s

a batsman deflects a ball by an angle of 45 without changing its initial speed which is equal to 54km/h.what

A member of the software team recently got into LED art. They bought a couple of cheap LEDs and resistors and and wired them up. They expect all four to be the same brightness, but they're not. Why is that

Answers

It should be noted that the reason for the difference in brightness is that the resistance is lower on the right than on the left.

Solving the resistance.

From the complete information, the resistance that's given in the first two LED circuits is R. Also, the resistance that is given in the two LED circuits onto the right is R/2.

From Ohm's law, I = V/R. This implies that I is indirectly proportional to R. Therefore when the resistance is decreased, there will be an increase in current flow.

Therefore, the glow of the two LEDs on the right is more than those on the left because the resistance is lower on the right than on the left.

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robert brown discovery; doc brown; robert brown discovered the cell; robert brown discovery of nucleus; when did robert brown discovered nucleus; emmett brown; robert brown contribution to cell theory; emmett brown death

Answers

1) Robert Brown, a Scottish botanist who was born on December 21, 1773, is best known for his descriptions of cell nuclei and what is now known as Brownian motion—the continuous motion of tiny particles in solution.

2) Robert Brown found no cell. His discovery of Brownian motion—the haphazard movement of small particles in a surrounding solution—made him most famous. He also created a different classification system for plants.

3) Robert Brown discovered the existence of a structure within the cells of orchids and many other plants in 1831 while researching the fertilization processes of plants in the Orchidaceae and Asclepiadaceae families. He named this structure the "nucleus" of the cell.

4) Hooke observed cork under his microscope and noticed tiny box-like cavities, which he depicted and referred to as cells. He had stumbled across plant cells! Hooke's finding laid the groundwork for cell theory by revealing cells as the tiniest constituents of life.

5) Emmett Brown was an actor best remembered for his roles in St. Elmo's Fire, The Outsiders, and Rumble Fish from 1983. (1985). He passed away on April 12, 1989.

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Help ASAP Will mark BRainliest

Help ASAP Will mark BRainliest

Answers

Answer:

see explanation

Explanation:

beam balance

temperature degree celsius

newton meter per second

weight.

hope I was helpful to tou

List the two factors that create orbital motion and describe how each factor affects the motion.​

Answers

Answer:

The forward motion of a body in space, such as a planet or moon, and the pull of gravity on it from another body in space.

Explanation:

Earth and many other bodies—including asteroids, comets, and the other planets—move around the sun in curved paths called orbits. Generally, the orbits are elliptical, or oval, in shape. Because of the sun’s relatively strong gravity, Earth and the other bodies constantly fall toward the sun, but they stay far enough away from the sun because of their forward velocity to fall around the sun instead of into it. As a result, they keep orbiting the sun and never crash to its surface. The motion of Earth and the other bodies around the sun is called orbital motion. Orbital motion occurs whenever an object is moving forward and at the same time is pulled by gravity toward another object.

What type of image can be larger or smaller than the object?
A. An expansion
B. A magnification
C. A reduction
D. An enlargement

Answers

it’s D. An enlargement (hope this helps!)

Mention 2 everyday applications each of conduction, convection and radiation​

Answers

Answer:

Conduction: Touching a stove and being burned. Ice cooling down your hand. .

Explanation:

Elvis and Noah want to move the piano in their living room. Elvis pushes from behind with a force of
400 N, and Noah pulls from the front using a rope with a force of 150 N. The piano has a mass of 225 kg,
and the friction force of the floor and the piano is 100 N.
Calculate the acceleration of the piano.
Round your answer to the nearest tenth.

Answers

Answer:

2.0 m/s

Explanation:

Remember that F = maF=maF, equals, m, a, where FFF is the net force, mmm is the mass of the object, and aaa is its acceleration. To solve this problem, we will need to first find the net force acting on the piano and then use F = maF=maF, equals, m, a to find the piano’s acceleration.

Hint #22 / 4

The net force is the sum of all of the forces on the piano. In this circumstance, Elvis's and Noah's forces are in the same direction, and the friction force is in the opposite direction. So, our net force equation would be:

=400 N+150 N−100 N

=450 N

Now, we can use F = maF=maF, equals, m, a and solve for the acceleration:

225 kg

450 N

=2.0

The acceleration of the piano is 2.0 m/s

The acceleration of the piano is 2m/s².

We know the formula for force is

F =ma

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

We need to calculate the total force used in moving the piano

F= Total force- Frictional force

F= 400N+150N-100N= 450N.

We have F=450N and m= 225kg

F=ma

450N= 225ˣ a

a= 450/225

a= 2m/s²

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90 V
R₁
60
R2
30
R3
30
Based on the circuit above, what would be the current through the R3 resistor?

Answers

In the parallel combination, the current through R3 is 3 A. In the series combination, the current through R3 is 0.75 A.

To determine the current through resistor R3 in both the parallel and series combinations, we need to apply Ohm's Law and the appropriate formulas for calculating total resistance and current in each configuration.

First, let's consider the parallel combination:

In a parallel combination, the voltage across each resistor is the same. Therefore, the voltage across R3 is also 90 V.

Using Ohm's Law (V = I × R), we can calculate the current flowing through R3 in the parallel combination:

I_parallel = V / R3

= 90 V / 30 Ω

= 3 A

So, in the parallel combination, the current through R3 is 3 A.

Now, let's consider the series combination:

In a series combination, the total resistance is the sum of the individual resistances:

R_total = R1 + R2 + R3

= 60 Ω + 30 Ω + 30 Ω

= 120 Ω

To find the current through the series combination, we can use Ohm's Law:

I_series = V / R_total

= 90 V / 120 Ω

= 0.75 A

Therefore, in the series combination, the current through R3 is 0.75 A.

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Note the complete questions is User

90 V R₁=60 R2=  30, R3 = 30

Based on the circuit above, what would be the current through the R3 resistor in parallel and in series combinantion.

How do atomic and molecular interactions explano the properties of matter that we see and feel?

Answers

Answer:

The atomic and molecular interactions unveil the bulk properties of matter in our environment by ways of the fact that everything in the whole universe is made of either atoms, molecules or even ions

How matter is made up of atoms and molecules?

It has been proven practically everything in the whole universe is matter and everything which interact with matter is also matter. This explains to us the reasons why matter could be atoms, molecules or ions.

That being said, some substances (matter) is made up of atoms of elements, some made up of molecules or atoms and molecules and others ions or both. However, matter is anything which has mass and occupies space.

In conclusion, we can now conclude from the explanation above that the properties of matter are as a result of the interaction which exists between matter at the atomic and molecular level.

A cheetah can accelerate from rest to a speed of 29.0 m/s in 5.75 s. What is its acceleration (in m/s2)?

Answers

Answer:

Hi

The acceleration in m/s 2 is:

a= (v-u)/t

a= (29.0-0)/5.75

a= 5.043478261

a= 5.04 (3s.f)

3.) A boat is moving south at 15.0, a passenger is walking north along the boat deck at 4.0 and throws a
rock north at 3.0, what is the velocity of the rock when viewed from the boat and the shore? (2)

Answers

When viewed from the boat, the velocity of the rock will be equal to the sum of the velocity of the rock relative to the passenger (3.0 m/s north) and the velocity of the passenger relative to the boat (4.0 m/s south).

Therefore, the velocity of the rock when viewed from the boat will be:

Vrock (boat) = Vrock (passenger) + Vpassenger (boat)

Vrock (boat) = 3.0 m/s north + (-4.0 m/s south)

Vrock (boat) = -1.0 m/s south

So, when viewed from the boat, the velocity of the rock will be 1.0 m/s south.

When viewed from the shore, the velocity of the rock will be equal to the velocity of the boat relative to the shore (15.0 m/s south) plus the velocity of the rock relative to the boat (which we calculated as -1.0 m/s south).

Therefore, the velocity of the rock when viewed from the shore will be:

Vrock (shore) = Vrock (boat) + Vboat (shore)

Vrock (shore) = -1.0 m/s south + (-15.0 m/s south)

Vrock (shore) = -16.0 m/s south

So, when viewed from the shore, the velocity of the rock will be 16.0 m/s south.

How are work and power different

Answers

Work is defined as the process of energy transfer to the motion of an object through the application of force. Power is defined as the amount of energy transferred in unit time.

What is energy anything that takes up space and has mass a change in the position of an object a push or pull the ability to cause change in matter

Answers

Energy is that which has the ability to cause change in matter.

What is energy?

Energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed.

So in simple definition we can say that energy is that which has the ability to cause change in matter.

Based on the given statements we can classify them as;

anything that takes up space and has mass - matter.cause a change in the position of an object through push or pull - forcethe ability to cause change in matter - energy.

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Convert .00016 to scientific notation

Answers

Answer:

\(1.6 \,\,\,10^{-4}\)

Explanation:

Recall that scientific notation involves expressing the number in powers of ten, and using a multiplicative factor whose value is larger than or equal to 1 (one) and strictly smaller than 10 in the form:

\(a\,\,\,10^n\\with\,\,\,1\leq a<10\)

and with n an integer value.

in our case, notice that 0.00016 = 16 / 100000 = 1.6 / 10000

and that denominator can be expressed as: 10^4, and can also be brought to the numerator as a negative power of ten:

1.6 / 10000 = 1.6 / 10^4 = 1.6 * 10^(-4)

\(\frac{16}{100000} =\frac{1.6}{10000}=\frac{1.6}{10^4}=1.6\,\,\,10^{-4}\)

why does sound travel faster in metal than in air

Answers

Sound travel faster in metal than air becoz molecules of metal i.e solid are closely packed and it will take less time for sound waves to travel from one molecule to another whereas in air i.e in gas,molecules are far apart so it will take more time for sound waves to travel.In case of vacuum there are no molecules at all so sound is not there.that is why in space we cannot hear anything.

HOPE THIS HELP<3

N4M.6 A board has one end wedged under a rock having a mass of 380 kg and is supported by another rock that touches the bottom side of the board at a point 85 cm from the end under the rock. The board is 4.5 m long, has a mass of about 22 kg, and projects essentially horizontally out over a river. Is it safe for an adult with a mass of 62 kg to stand at the unsupported end of the board

Answers

Answer:

it is safe to stand at the end of the table

Explanation:

For this exercise we use the rotational equilibrium condition

         Στ = 0

         W x₁ - w x₂ - w_table x₃ = 0

         M x₁ - m x₂ - m_table x₃ = 0

where the mass of the large rock is M = 380 kg and its distance to the pivot point x₁ = 850 cm = 0.85m

the mass of the man is 62 kg and the distance

            x₂ = 4.5 - 0.85

            x₂ = 3.65 m

the mass of the table (m_table = 22 kg) is at its geometric center

            x_{cm} = L/2 = 2.25 m

            x₃ = 2.25 -0.85

            x₃ = 1.4 m

let's look for the maximum mass of man

            m_{maximum} = \(\frac{ M x_1 -m_{table} x_3}{ x_2}\)

let's calculate

             m_{maximum} = \(\frac{ 380 \ 0.85 - 22 \ 1.4}{3.65}\)(380 0.85 - 22 1.4) / 3.65

             m_{maximum} = 80 kg

we can see that the maximum mass that the board supports without turning is greater than the mass of man

             m_{maximum}> m

consequently it is safe to stand at the end of the table

A ray of light is incident on a plane mirror and the angle of reflection is 50 degrees. What is the angle between the incident ray and the normal?

Answers


The angle of incidence is equal to the angle of reflection. As a result, the angle formed by the incidence and reflected rays is 100°.

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A particle’s position is ~r = (ct2 − 2dt3 )iˆ+ (2ct2 − dt2 )jˆ, where c and d are positive constants. Find the expressions for times t > 0 when the particle is moving in (a) x-direction (b) y-direction

Answers

The velocity of the particle is given by the derivative of the position vector:

\(\vec v = \dfrac{\mathrm d\vec r}{\mathrm dt} = (2ct-6dt^2)\,\vec\imath + (4ct-2dt)\,\vec\jmath\)

(a) The particle is moving in the x-direction when the y-component of velocity is zero:

\(4ct-2dt = 2t (2c - d) = 0 \implies t=0\)

But we want t > 0, so this never happens, unless 2c = d is given, in which case the y-component is always zero.

(b) Similarly, the particle moves in the y-direction when the x-component vanishes:

\(2ct-6dt^2 = 2t (c - 3dt) = 0 \implies t=0 \text{ or }c-3dt = 0\)

We drop the zero solution, and we're left with

\(c-3dt = 0 \implies c=3dt \implies \boxed{t = \dfrac c{3d}}\)

In the case of 2c = d, this times reduces to t = c/(6c) = 1/6.

Which of these statements is not correct?


The electrostatic interactive force between electrical charges is exactly the same as the gravitational interaction between them


A charged body is attracted to an uncharged body due to electrostatic induction


The charge on a neutral body is the algebraic sum of charges at different points in the body


Any physically existing charge is an integral multiple of an elementary or electronic charge, e.

Answers

The electrostatic interactive force between electrical charges is exactly the same as the gravitational interaction between them is referred to as the incorrect statement and is denoted as option A.

What is Electrostatic force?

This is defined as the force of attraction or repulsion which exists in a charged body and it is different from the gravitational force interaction between two bodies.

This is because gravitational force is the force of objects as a result of its mass while  electrostatic force is the force of an object due to charge which is therefore the reason why option A was chosen.

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Solve for the mass of a planet with an orbital radius of 4 AU and an orbital period of 4 Earth years,
orbiting a star whose mass is 3 solar masses.

Answers

The mass of the planet orbiting through the path can be calculated using its period of orbit, and radius . Here, the mass of the planet be 7.11 × 10³⁰ kg.

What is orbital period ?

The orbital period of a spatial object is the time taken to revolve around a star or another spatial object through out an elliptical orbit.

The mass of the star can be calculated using the formula :

m = 4 π r³/G T²

given,

r = 4 Au = 4 × 1.5 × 10¹¹ m

T = 4 years = 12.6 × 10⁷ seconds.

G = gravitational constant 6.67 × 10⁻¹¹ m³/kg s²

Then M = 4 × 3.14 × (4 × 1.5 × 10¹¹ m)³/ 6.67 × 10⁻¹¹ m³/kg s² × ( 12.6 × 10⁷ s)²

             = 7.11 × 10³⁰ kg.

Therefore, the mass of the planet is 7.11 × 10³⁰ kg..

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What does the cosmological principle allow cosmologists to assume?

A. Exactly what the specific fate of the universe will be and when

B. The galaxies are organized clusters of billions of stars, gas, dust, and matter in all other forms.

C. That the small portion of the space we can see is truly representative of all the rest of the universe that we cannot see.

D. How the helium clouds impact human health and life expectancy.

Answers

Answer:

C. That the small portion of the space we can see is truly representative of all the rest of the universe that we cannot see.

Explanation:

The Cosmological Principle assumes that the small portion of the universe that we can see is representative of the entire universe, even though we can only directly observe a tiny fraction of it. It's an assumption used by Cosmologists to simplify their models of the universe.

Questions:
1. Clara drives 250 km West to play a gig in Colombia City. After the gig he drives 450 km
east to jam with some musicians in Columbia. What distance did he cover? What was his
displacement?

Answers

Answer:

700km

Explanation:

going was 250km and leaving was 450

250+450=700

The times in this problem are given using metric prefixes on the base SI unit of time: the second (s). Give the times without the metric prefixes. For example, the metric prefix T (tera) stands for 1012, so 47 Ts would be written as 4.7×1013s.

a) 966 Ps
b) 966 fs
c) 48 ns
d) 640 μs

Answers

( a ) 966 Ps is expressed in SI unit as 9.66 x 10⁻¹⁰ s

( b ) 966 fs is expressed in SI unit as 9.66 x 10⁻¹³ s

( c ) 48 ns is expressed in SI unit as 4.8 x 10⁻⁸ s

( d ) 640  μsis expressed in SI unit as 6.4 x 10⁻⁴ s

What is the expression of the SI unit in standard form?

A standard way of expressing a derived quantity or fundamental quantity in terms of the SI unit is always in power of 10.

The standard form of the given quantity is calculated as follows;

( a ) 966 Ps = 966 x 10⁻¹² s = 9.66 x 10⁻¹⁰ s

( b ) 966 fs =  966 x 10⁻¹⁵ s = 9.66 x 10⁻¹³ s

( c ) 48 ns = 48 x 10⁻⁹ s = 4.8 x 10⁻⁸ s

( d) 640  μs = 640 x 10⁻⁶ s = 6.4 x 10⁻⁴ s

Thus, the standard form of a quantity in SI unit involves the power of 10.

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A person standing at the edge of a seaside cliff kicks a rock horizontally of the cliff from a
height of 52 m and it lands a distance of 35 m from the base of the cliff. What is the speed at
which the rock was initially kicked?

Answers

The time will be the same for both horizontal and vertical component. The initial speed is 10.7 m/s

What is Speed ?

Speed is a distance travel per time taken. It is a scalar quantity and it is measured in m/s

Given that a person standing at the edge of a seaside cliff kicks a rock horizontally of the cliff from a height of 52 m and it lands a distance of 35 m from the base of the cliff.

The rock will move vertically downward with initial velocity = 0. The time taken will be constant. That is, same horizontally.

Let us first calculate the time by using the formula

h = ut + 1/2gt²

Where

h = 52 mu = 0Range R = 35 mg = 9.8 m/s²

Substitute all the necessary parameters into the formula

52 = 0 + 1/2 × 9.8 × t²

52 = 4.9t²

t² = 52/4.9

t² = 10.6

t = √10.6

t = 3.26 s

The speed at which the rock was initially kicked can be found by

R = Ut

35 = U × 3.26

U = 35/3.26

U = 10.7 m/s

Therefore, rock was initially kicked at a speed of 10.7 m/s

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A small block, with a mass of 4 kg. starts from rest at the top of the apparatus. It then slides without friction down the incline, across the level section on the right. It then colides with a spring and compresses it, which momentarily brings the block to a stop. The maximum height of the incline is 5 m and the spring constant is 120 N/mA.Find the intial potential energy of the block at point AB.Find the velocity of the block at the bottom of the incline at point b C.How much will the block compress the spring before coming at a stop at point b

Answers

Given:

The mass of the block, m=4 kg

The initial height of the block, h=5 m

The spring constant of the spring, k=120 N/m

To find:

A. Initial potential energy of the block.

B. Velocity of the block at the bottom of the incline.

C. The compression in the spring.

Explanation:

A.

The gravitational potential energy is the energy possessed by an object due to its height.

Thus the initial potential energy of the block is given by,

\(PE=mgh\)

Where g is the acceleration due to gravity.

On substituting the known values,

\(\begin{gathered} PE=4\times9.8\times5 \\ =196\text{ J} \end{gathered}\)

B.

From the law of conservation of energy, the total energy of an isolated system always remains constant. As the block slides down the apparatus, it loses its potential energy. And as there is no friction, the potential energy lost will be converted completely into the kinetic energy of the block.

Thus, when the block is at the bottom of the incline,

\(PE=\frac{1}{2}mv^2\)

Where v is the velocity of the block when it is at the bottom of the incline.

On substituting the knwon values,

\(\begin{gathered} 196=\frac{1}{2}\times4\times v^2 \\ \Rightarrow v=\sqrt{\frac{196\times2}{4}} \\ =10\text{ m/s} \end{gathered}\)

C.

From the law of conservation of energy, the total energy of the system remains the same.

Thus, when the block is stopped, the kinetic energy of the block is completely converted into the elastic potential energy of the spring. Thus the initial potential energy of the block is equal to the spring potential energy stored in the spring when it is compressed and the block is stopped.

Thus,

\(PE=\frac{1}{2}kx^2\)

Where x is the compression in the spring.

On substituting the known values,

\(\begin{gathered} 196=\frac{1}{2}\times120\times x^2 \\ x=\sqrt{\frac{196\times2}{120}} \\ x=1.81\text{ m} \end{gathered}\)

Final answer:

A. The initial potential energy of the block is 196 m

B. The velocity of the block at the bottom of the incline is 10 m/s

C. The compression in the spring 1.81 m

A system consists of two uncharged metal spheres, each suspended on an insulating string and connected to the other by a thin
conducting wire. A positively charged rod is brought near, but does not touch, the left sphere, and the sphere is attracted to the rod. Which
of the following is correct about the net charge on the right sphere as a result?

Answers

The right sphere will acquire an equal and opposite net positive charge to balance the negative charge on the left sphere.

Electrostatic attraction

Since the left sphere is attracted to the positively charged rod, it means that the left sphere acquires a temporary negative charge due to induction.

The positive charge on the rod repels electrons in the left sphere, causing them to move away from the rod side and accumulate on the opposite side, resulting in a net negative charge on the left sphere.

According to the principle of charge conservation, the net charge on the system must remain zero. Therefore, the right sphere acquires an equal and opposite net positive charge to balance the negative charge on the left sphere.

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What is the displacement of a student who walks 12 m North, 5 m West, 3 m South,
and finally 6 m West to get to his next class?

Answers

When you draw all 4 of those moves, you see that he winds up 9m North and 11m West of where he started.

So the magnitude of his displacement is

D = √(9² + 11²)  m²

D = √(81 + 121)  m²

D = √(202)  m²

D = 14.2 m

The direction is arctan(-11/9) = 50.7° west of North

a piece of iodine is heated from 50 celcius to 197 celcius. what state of matter would we expect it to be in

Answers

Answer:

liquid

Explanation:

Cho places a letter from Cedric in a box and pushes the now 1.5 kg box against a 25 N/m spring and compresses it leftwards 0.5 m pver a rough patch of scarring on the table with a coefficient of friction of 0.2. She then releases the box so it slides against the table for 2.30 until it launches off at 75 degrees, to the horizontal. It lands in a pile of boxes 3.5 m away from the base of the table. fi the box can withstand a maximum fall from 2,5 m high, will the box land safely or will her letter be ruined?

Answers

In compressing the spring by 0.5 m, Cho stores

1/2 (25 N/m) (0.5 m)² = 3.125 J

of potential energy. As the spring relaxes, some of this potential energy is converted into kinetic energy K in the box and the rest is lost to heat H due to friction:

K - H = 3.125 J

By the work-energy theorem, the total work W performed on the box during this process is equal to the change in the box's kinetic energy. It starts at rest when the spring is compressed, so

W = K - 0 = 1/2 (1.5 kg) v²

By Newton's second law,

• the net vertical force on the box is

∑ F (ver) = n - mg = 0

where n is the magnitude of the normal force from contact with the table, and mg is the weight of the box. It follows that

n = mg = (1.5 kg) (9.8 m/s²) = 14.7 N

• the net horizontal force is

∑ F (hor) = r - f = ma

where r is the mag. of the restoring force, f = 0.2 n is the mag. of kinetic friction, and a is the resulting acceleration of the box. Friction exerts an opposing force of

f = 0.2 (14.7 N) = 2.94 N

The work done by the spring as it relaxes is 3.125 J. The work done by friction is (2.94 N) (0.5 m) = 1.47 J. Therefore the total work done on the box is

W = 3.125 J - 1.47 J = 1.655 J

Find the speed of the box v when it returns to the equilibrium position:

1/2 (1.5 kg) v² = 1.655 J

v² = (3.31 J) / (1.5 kg)

v ≈ 1.49 m/s

I assume the rest of the table is not scarred. (If it is, the box would come to a stop well before 2.30 seconds have passed, or before the box can slide for 2.30 m.) Then the box leaves the table with speed v at an angle of 75°, so that the horizontal distance x that it covers in the air after t seconds is

x = v cos(75°) t

and its tolerable height y is

y = 2.5 m + v sin(75°) t - g/2 t²

(if y turns out negative for some t, that means it has fallen more than 2.5 m and cannot land safely)

The pile is 3.5 m away from the table, so with its launch speed the box travels this distance in time t such that

v cos(75°) t = 3.5 m

t = (3.5 m) / ((1.49 m/s) cos(75°)) ≈ 9.1 s

After such time, the box would have height

2.5 m + v sin(75°) (9.1 s) - g/2 (9.1 s)² ≈ -390.51 m

i.e. it would be nearly 400 m underground! So no, the box will not land safely.

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