two blocks with masses 2 kg and 4 kg are pushed from rest by the same amount of fore for a distance of 100 m on a frictionless floor. the final kinetic energy of the 2 kg block after the 100 m distance is

Answer:  arrows

Explanation:

A vector quantity is usually represented by an arrow, with the direction of the vector being the direction in which the arrow points and the length of the arrow representing the vector's magnitude.

What is the vector quantity unit?

The meter is the only fundamental SI unit that is a vector. The rest are all scalars. Derived quantities might be scalar or vector, but all vector quantities require meters as part of their definition and measurement.

The term "vector quantities" refers to physical quantities whose magnitude and direction are well specified.

Arrows are used to depict vectors. An arrow has a direction and a magnitude (how long it is) (the direction in which it points).

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Answer:

Increases

Explanation:

Due to an increase in temperature, molecules within the medium will vibrate more vigorously, meaning that the rate of chemical reactions generally increases with temperature due to an increase in kinetic energy. Because sound is a form of kinetic energy, it is safe to assume that the speed of sound waves increases with temperature.

Answer:

A- increases because The particles bump into each other more often.

Explanation:

Just took the test

Answer:

Coefficient of kinetic friction = 0.146

Explanation:

Given:

Mass of sled (m) = 18 kg

Horizontal force (F) = 30 N

FInal speed (v) = 2 m/s

Distance (s) = 8.5 m

Find:

Coefficient of kinetic friction.

Computation:

Initial speed (u) = 0 m/s

v² - u² = 2as

2(8.5)a = 2² - 0²

a = 0.2352 m/s²

Nweton's law of :

F (net) = ma

30N - μf = 18 (0.2352)

30 - 4.2336 = μ(mg)

25.7664 =  μ(18)(9.8)

μ = 0.146

Coefficient of kinetic friction = 0.146

Answer:

Explanation:

 Time taken by sound waves to cover distance between politician and reporter = time taken by em waves to travel distance between politician and the television viewer.

5.5 / 343 = d / 3 x 10⁸ + 2.7 / 343

d is distance between politician and television set + time taken by sound to travel distance between television and its viewer.

.0160349 = d / 3 x 10⁸  + .0078717

d / 3 x 10⁸  = .0081632

d = 2448960 m

= 2448.96 km

= 2449 km .

Answer:

The height of the tower is 8.96 m.

Explanation:

We have, a visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 6.01 s.

It is required to find the height of the tower. Let it is l. The time period of a simple pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

l is length of pendulum, or height of tower

[tex]l=\dfrac{T^2g}{4\pi^2}\\\\l=\dfrac{(6.01)^2\times 9.8}{4\pi^2}\\\\l=8.96\ m[/tex]

So, the height of the tower is 8.96 m.

Answer:

The thermal conductivity of the insulated metal rod is [tex]202.92\,\frac{W}{m\cdot K}[/tex].

Explanation:

This is a situation of one-dimensional thermal conduction of a metal rod in a temperature gradient. The heat transfer rate through the metal rod is calculated by this expression:

[tex]\dot Q = \frac{k_{rod}\cdot A_{c, rod}}{L_{rod}}\cdot \Delta T[/tex]

Where:

[tex]\dot Q[/tex] - Heat transfer due to conduction, measured in watts.

[tex]L_{rod}[/tex] - Length of the metal rod, measured in meters.

[tex]A_{c,rod}[/tex] - Cross section area of the metal rod, measured in meters.

[tex]k_{rod}[/tex] - Thermal conductivity, measured in [tex]\frac{W}{m\cdot K}[/tex].

Let assume that heat conducted to melt some ice was transfered at constant rate, so that definition of power can be translated as:

[tex]\dot Q = \frac{Q}{\Delta t}[/tex]

Where Q is the latent heat required to melt the ice, whose formula is:

[tex]Q = m_{ice}\cdot L_{f}[/tex]

Where:

[tex]m_{ice}[/tex] - Mass of ice, measured in kilograms.

[tex]L_{f}[/tex] - Latent heat of fussion, measured in joules per gram.

The latent heat of fussion of water is equal to [tex]330000\,\frac{J}{g}[/tex]. Hence, the total heat received by the ice is:

[tex]Q = (6.15\,g)\cdot \left(330\,\frac{J}{g} \right)[/tex]

[tex]Q = 2029.5\,J[/tex]

Now, the heat transfer rate is:

[tex]\dot Q = \frac{2029.5\,J}{(10\,min)\cdot \left(60\,\frac{s}{min} \right)}[/tex]

[tex]\dot Q = 3.382\,W[/tex]

Turning to the thermal conduction equation, thermal conductivity is cleared and computed after replacing remaining variables: ([tex]L_{rod} = 0.75\,m[/tex], [tex]A_{c,rod} = 1.25\times 10^{-4}\,m^{2}[/tex], [tex]\Delta T = 100\,K[/tex], [tex]\dot Q = 3.382\,W[/tex])

[tex]\dot Q = \frac{k_{rod}\cdot A_{c, rod}}{L_{rod}}\cdot \Delta T[/tex]

[tex]k_{rod} = \frac{\dot Q \cdot L_{rod}}{A_{c,rod}\cdot \Delta T}[/tex]

[tex]k_{rod} = \frac{(3.382\,W)\cdot (0.75\,m)}{(1.25\times 10^{-4}\,m^{2})\cdot (100\,K)}[/tex]

[tex]k_{rod} = 202.92\,\frac{W}{m\cdot K}[/tex]

The thermal conductivity of the insulated metal rod is [tex]202.92\,\frac{W}{m\cdot K}[/tex].

Answer:

A

Explanation:

Fussion occurs when elements of lower atomic mass combines to form that of a larger atomic mass, releasing energy in the process .

Hydrogen has a lower atomic mass than Helium.

Answer:

v = 7.67 m/s

Explanation:

The equation for apparent weight in the situation of weightlessness is given as:

Apparent Weight = m(g - a)

where,

Apparent Weight = 360 N

m = mass passenger = 61.2 kg

a = acceleration of roller coaster

g = acceleration due to gravity = 9.8 m/s²

Therefore,

360 N = (61.2 kg)(9.8 m/s² - a)

9.8 m/s² - a = 360 N/61.2 kg

a = 9.8 m/s² - 5.88 m/s²

a = 3.92 m/s²

Since, this acceleration is due to the change in direction of velocity on a circular path. Therefore, it can b represented by centripetal acceleration and its formula is given as:

a = v²/r

where,

a = centripetal acceleration = 3.92 m/s²

v = speed of roller coaster = ?

r = radius of circular rise = 15 m

Therefore,

3.92 m/s² = v²/15 m

v² = (3.92 m.s²)(15 m)

v = √(58.8 m²/s²)

v = 7.67 m/s

Note: The complete question is attached as a file to this solution. The parallel plate mentioned can be seen in this picture attached.

Answer:

E = 225 N/C

Explanation:

Note: At any point on the parallel plates of a capacitor, the electric field is uniform and equal.

Therefore, Electric field at x = 14 cm equals the electric field at x = 7 cm

V(x) = 31.5 Volts

x = 14 cm = 0.14 m

The magnitude of the electric field at any point between the parallel plate of the capacitor is given by the equation:

E = V(x)/d

E(x = 0.14) = 31.5/0.14

E(x=0.14) = 225 N/C

E(x=0.14) = E(x=0.07) = 225 N/C

Answer:

a) emf = 0.01804 V

b) I = 0.03 A

Explanation:

a) The emf is calculated by using the following formula:

[tex]|emf|=|\frac{d\Phi_B}{dt}|=|\frac{d(A\cdot B)}{dt}|[/tex] [tex]=A|\frac{dB}{dt}|[/tex]

A: area of the loop = 0.0820m^2

B: magnitude of the magnetic field

dB/dt: change of the magnetic field, in time: 0.220 T/s

Where ФB is the magnetic flux, the surface vector and magnetic vector are perpendicular between them, and the area A is constant.

You replace the values of A and dB/dt in the equation (1):

[tex]|emf|=(0.082m^2)(0.220T/s)=0.01804V[/tex]

b) The current in the loop is:

[tex]I=\frac{emf}{R}[/tex]

R: resistance of the loop = 0.600Ω

[tex]I=\frac{0.01804V}{0.600\Omega}=0.03A=30mA[/tex]

a.  The emf induced in this loop is 18.04mV.

b. The current induced in the loop is 30.06mA.

a. We know that,

                        [tex]flux(\phi)=B*A[/tex]

Where B is magnetic field and A is the area.

  [tex]emf=\frac{d\phi}{dt}=A*\frac{dB}{dt}[/tex]

Given that,  Area , [tex]A=0.0820m^{2},B=3.80T,\frac{dB}{dt}=0.220T/s[/tex]

Substituting all values in above equation.

  [tex]emf=0.0820*0.220=0.01804V=18.04mV[/tex]

b. Resistance, [tex]R=0.600ohm[/tex]

  Current induced in the loop is,

                [tex]I=\frac{emf}{R}=18.04/0.6=30.06mA[/tex]

Hence, the emf induced in this loop is 18.04mV.

The current induced in the loop is 30.06mA.

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Answer:

The centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex]

Explanation:

It is given that, A carousel has a diameter of 6.0-m and completes one rotation every 1.7 s.

We need to find the centripetal acceleration of the traveler. It is given by the formula as follows :

[tex]a=\dfrac{v^2}{r}[/tex]

r is radius of carousel

[tex]v=\dfrac{2\pi r}{T}[/tex]

So,

[tex]a=\dfrac{4\pi ^2r}{T^2}[/tex]

Plugging all the values we get :

[tex]a=\dfrac{4\pi ^2\times 3}{(1.7)^2}\\\\a=40.98\ m/s^2[/tex]

So, the centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex].

Complete question is;

Assuming 100% efficient energy conversion how much water stored behind a 50 centimeter high hydroelectric dam would be required to charge the battery with power rating, 12 V, 50 Ampere-minutes

Answer:

Amount of water required to charge the battery = 7.35 m³

Explanation:

The formula for Potential energy of the water at that height = mgh

Where;

m = mass of the water

g = acceleration due to gravity = 9.8 m/s²

H = height of water = 50 cm = 0.5 m

We know that in density, m = ρV

Where;

ρ = density of water = 1000 kg/m³

V = volume of water

So, potential energy is now given as;

Potential energy = ρVgH = 1000 × V × 9.8 × 0.5 = (4900V) J

Now, formula for energy of the battery is given as;

E = qV

We are given;

q = 50 A.min = 50 × 60 = 3,000 C

V = 12 V

Thus;

qV = 3,000 × 12 = 36,000 J

E = 36,000 J

At a 100% conversion rate, the energy of the water totally powers the battery.

Thus;

(4900V) = (36,000)

4900V = 36,000

V = 36,000/4900

V = 7.35 m³

Answer:

C

Explanation:

Because everything on Earth falls at the same speed, the masses of the balls do not matter. Since the acceleration due to gravity is constant, their speeds will both be increasing at the same rate, and therefore the difference in speeds would remain constant until they hit the ground. Hope this helps!

Answer:

Explanation:

The man comes to halt due to reaction force acting on him in opposite direction . If R be the reaction force

impulse by net  force = change in momentum

Net force = R - mg , mg is weight of the man .

( R-mg ) x 2. 07 x 10⁻³ = 73 x 6.46 - 0

R - mg = 227.81 x 10³

Average net force = 227.81 x 10³ N .

Answer:

The answer is D)Theory

Explanation:

This is due because a theory is a scientific term and is a testable model that scientists seek to explain a phenomenon. You can also find out the answer by the process of elimination it can't be data because that would be something they already know and something they use to prove not explain. It can't be law because it isn't testable but can be used to explain. So that leaves you with two answers hypothesis and theory which are very similar but it isn't hypothesis because it isn't used to explain it to help the scientists come up with a theory and accumulate what might happen.

Answer:

Explanation:

Using the principle of moment to solve the problem. The principle states that the sum of clockwise moments is equal to the sum of anticlockwise moment.

Moment = force *perpendicular distance

Moment of Archimedes about the fulcrum = 75 * x  ... 1

x is the distance of Archimedes from the fulcrum

Moment of Heron about the fulcrum = 150 * 2 = 300kgm... 2

Equation 1 and 2 according to principle of moment to get x we have;

75x = 300

x = 300/75

x = 4metres

Archimedes need to sit 4m from the fulcrum

Answer:

Explanation:

Moment of inertia of the rod = 1/12 m L²

m is mass of the rod and L is its length

= 1/2 x 2.3 x 2 x 2

= 4.6 kg m²

Moment of inertia of masses attached with the rod

= m₁ d² + m₂ d²

m₁ and m₂ are masses attached , and d is their distance from the axis of rotation

= 5.3 x 1² + 3.5 x 1²

= 8.8 kg m²

Total moment of inertia = 13.4 kg m²

B )

Rotational kinetic energy = 1/2 I ω²

I is total moment of inertia and ω is angular velocity

= .5 x 13.4 x 2²

= 26.8 J .

C )

when mass of rod is negligible , moment of inertia will be due to masses only

Total moment of inertia of masses

= 8.8 kg m²

D )

kinetic energy of the system

= .5 x 8.8 x 2²

= 17.6 J .

(A) Total moment of inertia is 13.4 kgm²

(B) Total kinetic energy is 26.8J

(C) Moment of inertia is  8.8 kgm²
(D) Kinetic energy is 17.6J

(A) The moment of inertia of the rod is given by:

I = 1/12 mL²

where m is the mass of the rod

and L is the length

So,

I = (1/12) × 2.3 × 2²

I = 4.6 kgm²

Now, the moment of inertia of masses attached to the rod is given by:

I' = m₁ d² + m₂d²

where m₁ and m₂ are masses

and d is their distance from the axis of rotation

I' = 5.3 × 1² + 3.5 × 1²

I' = 8.8 kgm²

The total moment of inertia of the system is given by:

I(tot) = I + I'

I(tot) = 13.4 kgm²

(B) The rotational kinetic energy of an object with a moment of inertia I and angular velocity ω is given by:

KE = 1/2 I(tot)ω²

KE = 0.5 × 13.4 × 2²

KE = 26.8J

(C) If the mass of the rod is negligible, then the moment of inertia of the rod will be zero. So the total moment of inertia will be

I(tot) = I' = 8.8 kgm²

(D) the kinetic energy of the system when the mass of the rod is negligible and the angular speed is 2 rad/s is given by:

KE = 1/2 I'ω²

KE = 0.5 × 8.8 × 2²

KE = 17.6J

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B and D are both true statements. I'm not comfortable saying that either one is better than the other one.

The statement that best describes one way that molecules differ from atoms is a molecule can contain two atoms of the same element, and only a molecule can be broken down into two or more different elements. The correct options are b and d.

According to science, an atom is the smallest component of an element that can exist freely or not. A molecule, on the other hand, is the smallest component of a chemical and is made up of a group of atoms linked together by a bond.

A molecule is the smallest component of a substance that has the chemical properties of the compound.

The term "independent molecule" is not commonly used to refer to atoms and complexes linked by non-covalent interactions such as hydrogen or ionic bonds. Molecules are common constituents of matter.

Therefore, the correct options are b and d.

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Answer:

  0.365 cm³

Explanation:

The change in volume is found by multiplying the coefficient of expansion by the volume and the temperature change. The temperature change is in °F, but the expansion coefficient is per °C, so we need to convert the temperature scale in the computation.

  ΔV = V·Ce·ΔT

  = (π/6·d³)(1.5×10⁻⁶/°C)((5 °C)/(9 °F))(305 °F)

  = (1436.76 cm³)(1.5×10⁻⁶/°C)(169.44 °C)

  = 0.365 cm³ . . . . increase in volume

When you ride a bicycle, the direction of the angular velocity of the wheels is; Option A; to your left

Complete question is;

When you ride a bicycle, in what direction is the angular velocity of the wheels? A) to your left B) to your right C) forwards D) backwards

While an object rotates, each particle will have a different velocity:

the 'Speed' component will vary with radius while the 'Direction' component will vary with angle.

Now, all of the velocity vectors are aligned in the same plane and as such we can be solve this by choosing a single vector normal to ALL of the possible velocity vectors of the rotating object in that plane.

The convention that will be used to answer this question is known as "Right-hand rule". The angular velocity vector points along the wheel's axle.

For instance, if you Imagine wrapping your right hand around the axle so that your fingers point in the direction of rotation, with your thumb sticking out. You will notice that your thumb points to the left.

Thus;

In conclusion, by right-hand rule, a wheel rotating on a forward - moving bicycle has an angular velocity vector pointing to the rider's left.

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Answer: Around 0:35 Pm or 12:35 Am

Explanation:

The equation that describes the cooling of objects can be written as:

T(t) = Ta + (Ti - Ta)*e^(k*t)

Where Ta is the ambient temperature, here Ta = 25°C.

Ti is the initial temperature of the body, we have Ti = 37°C.

t is the time.

k is a constant.

So our equation is:

T(t) = 25°C +12°C*e^(k*t)

at 2pm, the temperature was 33°C

at 3pm, the temperature was 31°C.

we want to find the hour where we have our t = 0, suppose this hour is X.

then we can write our times as:

2pm ---> 2 - X

3pm ----> 3 - X

and our equations are:

33°C = 25°C + 12°C*e^(k2 - k*X)

31° = 25°C + 12°C*e^(k3 - k*X)

So we have two equations and two variables, let's solve the system.

first, simplify it a bit, for the first eq:

33 - 25 = 12*e^(k2 - k*X)

8/12 = e^(k2 - k*X)

ln(8/12) = k*2 - k*X

for the second equation we have:

31 - 25 = 12*e^(k3 - k*X)

6/12 = e^(k3 - k*X)

ln(6/12) = k*3 - k*X

So our equations are:

1) ln(2/3) = 2*k - X*k

2) ln(1/2) = 3*k - X*k

First, let's isolate one of the variables in one of the equations. let's isolate k in the first equation.

ln(2/3)/(2-X) = k

now we can replace it in the second equation:

ln(1/2) = 3*ln(2/3)/(2 - X) - X*ln(2/3)/(2-X)

now let's solve it for X, i will take a = ln(1/2) and b = ln(2/3) so it is easier to read.

a = 3*b/(2 - X) - X*b/(2 - X)

a*(2 - X) = 3*b - X*b

2a - aX = 3b - Xb

X(a - b) = 2a - 3b

X = (2*ln(1/2) - 3*ln(2/3))/(ln(1/2) - ln(2/3)) = 0.590

now, knowing that one hour has 60 minutes, then this is:

0.59*60m = 35 minutes

So the hour of death is 0:35 Pm or 12:35 Am

Answer: A chemical change results from a chemical reaction, while a physical change is when matter changes forms but not chemical identity. Examples of chemical changes are burning, cooking, rusting, and rotting. Examples of physical changes are boiling, melting, freezing, and shredding. Often, physical changes can be undone, if energy is input.

Explanation: hope this helps have a good day

Answer:

If the reaction is a chemical change, new substances with different properties and identities are formed. This may be indicated by the production of an odor, a change in color or energy, or the formation of a solid.

Answer:

1. The Universe is Expanding

2. It’s temperature is it’s uniform

3. Cosmic background radiation

4. I will give a hint for this one, since I don’t know, the hint is the universe is cooling.

5. It provides evidence of universe expansion.

6. Sorry I don’t know the rest

Explanation:

The universe is the collection of every item in space and time as well as the contents of those items

The correct options are as follows;

1. The universe is expanding

2. Its temperature is uniform

3. Composition of matter in the universe, cosmic background radiation

4. The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses

5. It provides evidence of universe expansion

6. Nuclear fission involves one large atom splitting into two smaller atoms

Nuclear fission takes place in the nucleus of an atom

7. A distant object travels rapidly towards an observer

8. The fuel in nuclear fusion is often uranium

Nuclear fusion is used to generate electricity at nuclear power plants

9. The universe began as a very high density singularity

Dark matter makes up majority of the universe

10.  Acceleration expansion — Dark energy

Structure forming in the early universe — Dark matter

11. It causes the expansion of the universe to accelerate

The reasons for selecting the above options are as follows;

1. The universe is expanding

The redshift of light from galaxies indicates that that are moving away

2. Its temperature is uniform

The uniform temperature of the microwave background suggest a common source

3. Composition of matter in the universe, cosmic background radiation

The matter present in the universe are characteristically similar in their origins

The cosmic background provides evidence of the existence of a singularity

4. The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses

Based on the Big Bang Theory, the temperature of the universe is reducing as the universe expands, compared to the initial temperature

5. It provides evidence of universe expansion

The background radiation coming from a single source as the rest of the universe is expected to spread throughout the universe

6. Nuclear fission involves one large atom splitting into two smaller atoms

Nuclear fission takes place in the nucleus of an atom

Nuclear fusion involves the joining of small atoms to form a larger atom

7. A distant object travels rapidly towards an observer

The redshift is the opposite, indicating that the object is moving further away

8. The fuel in nuclear fusion is often uranium

Nuclear fusion is used to generate electricity at nuclear power plants

Nuclear fusion usually consists of joining small atoms together. It has not been used for commercial energy production

9. The universe began as a very high density singularity

According to the Big Bang Theory, the universe started from the dense, high temperature singularity

Dark matter makes up majority of the universe

10.  Acceleration expansion — Dark energy

Dark energy causes expansion

Structure forming in the early universe — Dark matter

Dark matter is instrumental to the formation of structures in the universe

11. It causes the expansion of the universe to accelerate

Dark energy is seen as the cause of the accelerating expansion of the universe

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' A ' looks like the best choice.

Answer:

B.  inverse plot, 0.51 kilograms/meter3

Explanation:

Answer:

19.872 degrees

Explanation:

Mathematically;

Using Snell’s law

n1 sin A = n2 sinB

Where ;

n1 = refractive index in air = 1

n2 is refractive index in water = 1.33

A = ?

B = 45

Substituting the values in the equation;

1 sin A = 1.33 sin45

Sin A = 1.33 sin 45

A = arc sin (1.33 sin 45)

A = 70.12

Thus, the actual direction of the Sun with respect to the horizon = 90-A = 19.872 degrees

Answer:

correct answer is c

v = -0.8 m / s

Explanation:

This is a problem of quantity of movement, for this we must define a system formed by the two cars, so that the forces during the collision are internal and therefore the quantity of movement is conserved

initial

    p₀ = m₁ v₁ - m₂ v₂

final

    = (m₁ + m₂) v

We have taken the direction to the right as positive

    p₀ =p_{f}

    m₁ v₁ - m₂ v₂ = (m₁ + m₂) v

    v = (m₁ v₁ - m₂ v₂) / (m₁ + m₂)

we calculate

    v = (2  4 - 8  2) / (2 + 8)

    v = (8 -16) / 10

     v = -0.8 m / s

the negative sign indicates that the set is moving to the left

correct answer is c

Answer:

13.9 kJ

Explanation:

Given that

Length of the side, l = 1.8 m

Drag coefficient, C(d) = 1.4

Distance of run, d = 200 m

Velocity of run, v = 5 m/s

Density, ρ = 1.23

Using the Aerodynamics Drag Force formula. We have

F(d) = 1/2.ρ.A.C(d).v²

The Area, A needed is 1.8 * 1.8 = 3.24 m². So that,

F(d) = 1/2 * 1.23 * 3.24 * 1.4 * 5²

F(d) = 139.482/2

F(d) = 69.74

recall that, energy =

W = F * d

W = 69.74 * 200

W= 13948

W = 13.9kJ

Therefore, the thermal energy added to the air by the drag force is 13.9kJ

Answer:

9.05 m/s ,   -14.72°  (respect to x axis)

Explanation:

To find the final velocity of the bowling ball you take into account the conservation of the momentum for both x and y component of the total momentum. Then, you have:

[tex]p_{xi}=p_{xf}\\\\p_{yi}=p_{yf}\\\\[/tex]

[tex]m_1v_{1xi}+m_2v_{2xi}=m_1v_1cos\theta+m_2v_{2}cos\phi\\\\0=m_1v_1sin\theta-m_2v_2sin\phi[/tex]

m1: mass of the bowling ball = 5.50 kg

m2: mass of the bowling pin = 0.850 kg

v1xi: initial velocity of the bowling ball = 9.0 m/s

v2xi: initial velocity of bowling pin = 0m/s

v1: final velocity of bowling ball = ?

v2: final velocity of bowling pin = 15.0 m/s

θ: angle of the scattered bowling pin = ?

Φ: angle of the scattered bowling ball = 85.0°

Where you have used that before the bowling ball hits the pin, the y component of the total momentum is zero.

First you solve for v1cosθ in the equation for the x component of the momentum:

[tex]v_1cos\theta=\frac{m_1v_{1xi}-m_2v_2cos\phi}{m_1}\\\\v_1cos\theta=\frac{(5.50kg)(9.0m/s)-(0.850kg)(15.0m/s)cos85.0\°}{5.50kg}\\\\v_1cos\theta=8.79m/s[/tex]

and also you solve for v1sinθ in the equation for the y component of the momentum:

[tex]v_1sin\theta=\frac{(0.850kg)(15.0m/s)sin(85.0\°)}{5.50kg}\\\\v_1sin\theta=2.3m/s[/tex]

Next, you divide v1cosθ and v1sinθ:

[tex]\frac{v_1sin\theta}{v_1cos\theta}=tan\theta=\frac{2.3}{8.79}=0.26\\\\\theta=tan^{-1}(0.26)=14.72[/tex]

the direction of the bawling ball is -14.72° respect to the x axis

The final velocity of the bawling ball is:

[tex]v_1=\frac{2.3m/s}{sin\theta}=\frac{2.3}{sin(14.72\°)}=9.05\frac{m}{s}[/tex]

hence, the final velocity of the bawling ball is 9.05 m/s

Answer:

a. 900 J

b. 0.383

Explanation:

According to the question, the given data is as follows

Horizontal force = 150 N

Packing crate = 40.0 kg

Distance = 6.00 m

Based on the above information

a. The work done by the 150-N force is

[tex]W = F x = \mu N x = \mu\ m\ g\ x[/tex]

[tex]W = 150 \times 6[/tex]

= 900 J

b. Now the coefficient of kinetic friction between the crate and surface is

[tex]\mu = \frac {F}{m\timesg}[/tex]

[tex]= \frac{150}{40\times 9.8}[/tex]

= .383

We simply applied the above formulas so that each one part could calculate

We want to find the work and kinetic friction for the given situation. The solutions are:

Here we have a horizontal force of 150N pushing a 40.0 kg packing crate a distance of 6.00m at a constant speed.

a) First we want to find the work, it is given by the force applied times the distance moved, so the work is just:

W = 150N*6.00m = 900 N*m

b) Now we want to find the coefficient of kinetic friction, it must be such that the kinetic friction force is equal to the pushing force, in this way there is no net force, and then there is no acceleration.

Remember that the friction force is:

F = m*g*μ

Where:

Then we must solve:

150N = 40kg*(9.8 m/s^2)*μ = 392N*μ

150N/392N = 0.38

So the coefficient of kinetic friction between the crate and the surface is 0.38

If you want to learn more about forces, you can read:

https://brainly.com/question/13370981

Answer:

Explanation:

According to newton's secomd law, ∑F = ma

∑F is the summation of the force acting on the body

m is the mass of the body

a is the acceleration

Given the normal force when the elevator starts N1 = 592N

Normal force after the elevator stopped N2 = 400N

When the elevator starts, its moves upward, the sum of force ∑F = Normal (N)force on the elevator - weight of the person( Fg)

When moving up;

N1 - Fg = ma

N1 = ma + Fg ...(1)

Stopping motion of the elevator occurs after the elevator has accelerates down. The sum of forces in this case will give;

N2 - Fg = -ma

N2 = -ma+Fg ...(2)

Adding equation 1 and 2 we will have;

N1+N2 = 2Fg

592N + 400N = 2Fg

992N 2Fg

Fg = 992/2

Fg = 496N

The weight of the person is 496N

\b) To get the person mass, we will use the relationship Fg = mg

g = 9.81m/s

496 = 9.81m

mass m = 496/9.81

mass = 50.56kg

c) To get the magnitude of acceleration of the elevator, we will subtract equation 1 from 2 to have;

N1-N2 = 2ma

592-400 = 2(50.56)a

192 = 101.12a

a = 192/101.12

a = 1.90m/s²