You push a shopping cart full of groceries. The shopping cart has a mass of 32
kg.
a. What is the weight of your shopping cart?

b. How much force must you apply to give the cart an acceleration of 1.3 m/s2?

c. If you push with a force of 200 N, what is the acceleration of the cart?

d. You are driving home from the store. If your car has an acceleration of 4.1 m/s2 and its engine is applying a forward force of 7000 N, what is the mass of your car?

Answer: it is easier to read in bright light than dim light.

Explanation:

The ray of light is the direction that is used by light in travelling through a medium. Rays that pass through a lens very close to the principle axis are more sharply focused than those that are very far from the axis.

Because of the fact that the rays are close to the principle axis, the spherical aberration helps us to understand the reason why it is easier for people to read in bright light than readin iin dim light.

Answer:

Helium atoms compared to nitrogen atoms are moving faster and have a greater kinetic energy.

Explanation:

The molecular velocity of a gas at room temperature is inverse proportional to the square root of its molecular mass.

The greater the molecular mass of the gas the lesser the average speed of its molecules. Comparing the molecular masses of nitrogen and helium, helium is found to have a lower molecular mass and a corresponding greater velocity.

Hence helium moves faster than nitrogen and has a higher kinetic energy than nitrogen

Answer:

(a) aₓ = 1.33 m/s² and aᵧ = -0.770 m/s²

(b) x = 0.665 m and y = 4.62 m

(c) 3.61 s

Explanation:

(a) There are two ways we can solve this.  The first way is to sum the forces in the x and y direction, then use the relation tan 30° = -aᵧ/aₓ, where aᵧ is the acceleration in the +y direction (up) and aₓ is the acceleration in the +x direction (right).

The second way is to sum the forces in the parallel and perpendicular directions to find the acceleration parallel to the incline, a.  Then, use the relations aᵧ = -a sin 30° and aₓ = a cos 30°.

Let's try the first method.  Sum of forces in the +y direction:

∑F = ma

N cos 30° + Nμ sin 30° − mg = maᵧ

N cos 30° + Nμ sin 30° − mg = -maₓ tan 30°

Sum of forces in the +x direction:

∑F = ma

N sin 30° − Nμ cos 30° = maₓ

Substituting:

N cos 30° + Nμ sin 30° − mg = -(N sin 30° − Nμ cos 30°) tan 30°

N cos 30° + Nμ sin 30° − mg = -N sin 30° tan 30° + Nμ sin 30°

N cos 30° − mg = -N sin 30° tan 30°

N (cos 30° + sin 30° tan 30°) = mg

N = mg / (cos 30° + sin 30° tan 30°)

N = (10 kg) (10 m/s²) / (cos 30° + sin 30° tan 30°)

N = 86.6 N

Now, solving for the accelerations:

N sin 30° − Nμ cos 30° = maₓ

aₓ = N (sin 30° − μ cos 30°) / m

aₓ = (86.6 N) (sin 30° − 0.4 cos 30°) / 10 kg

aₓ = 1.33 m/s²

N cos 30° + Nμ sin 30° − mg = maᵧ

aᵧ = N (cos 30° + μ sin 30°) / m − g

aᵧ = (86.6 N) (cos 30° + 0.4 sin 30°) / 10 kg − 10 m/s²

aᵧ = -0.770 m/s²

Now let's try the second method.

Sum of forces in the perpendicular direction:

∑F = ma

N − mg cos 30° = 0

N = mg cos 30°

Sum of forces in the parallel direction:

∑F = ma

mg sin 30° − Nμ = ma

mg sin 30° − mgμ cos 30° = ma

a = g (sin 30° − μ cos 30°)

a = (10 m/s²) (sin 30° − 0.4 cos 30°)

a = 1.536 m/s²

Solving for the accelerations:

aₓ = a cos 30°

aₓ = 1.33 m/s²

aᵧ = -a sin 30°

aᵧ = -0.770 m/s²

As you can see, the second method is faster and easier, but both methods will give you the same answer.

(b) In the x direction:

Given:

x₀ = 0 m

v₀ = 0 m/s

aₓ = 1.33 m/s²

t = 1 s

Find: x

x = x₀ + v₀ t + ½ at²

x = 0 m + (0 m/s) (1 s) + ½ (1.33 m/s²) (1 s)²

x = 0.665 m

In the y direction:

Given:

y₀ = 5 m

v₀ = 0 m/s

aᵧ = -0.770 m/s²

t = 1 s

Find: y

y = y₀ + v₀ t + ½ at²

y = 5 m + (0 m/s) (1 s) + ½ (-0.770 m/s²) (1 s)²

y = 4.62 m

(c) In the y direction:

Given:

y₀ = 5 m

y = 0 m

v₀ = 0 m/s

aᵧ = -0.770 m/s²

Find: t

y = y₀ + v₀ t + ½ at²

0 m = 5 m + (0 m/s) t + ½ (-0.770 m/s²) t²

t = 3.61 s

Answer:

C) 8 m/s²

Explanation:

Given:

v₀ = 40 m/s

v = 0 m/s

Δy = 100 m

Find: a

v² = v₀² + 2aΔy

(0 m/s)² = (40 m/s)² + 2a (100 m)

a = -8 m/s²

Answer:

Explanation:

Kinetic energy is expressed as KE = 1/2 mv² where;

m is the mass of the body

v is the velocity of the body.

For the heavier shell;

m = 5kg

KE gained = 100J

Substituting this values into the formula above to get the velocity v;

100 = 1/2 * 5 * v²

5v² = 200

v² = 200/5

v² = 40

v = √40

v = 6.32 m/s

Note that after the explosion, both body fragments will possess the same velocity.

For the lighter shell;

mass = 2.0kg and v = 6.32m/s

KE of the lighter shell = 1/2 * 2 * 6.32²

KE of the lighter shell = 6.32²

KE of the lighter shell= 39.94m/s

Hence, the lighter one gains a kinetic energy of 39.94m/s.

The gain in the kinetic energy of the smaller fragment is 249.64 J.

The given parameters;

The velocity of the heavier fragment is calculated as follows;

[tex]K.E = \frac{1}{2} mv^2\\\\mv^2 = 2K.E\\\\v^2 = \frac{2K.E}{m} \\\\v= \sqrt{\frac{2K.E}{m} } \\\\v = \sqrt{\frac{2 \times 100}{5} }\\\\v = 6.32 \ m/s[/tex]

Apply the principle of conservation of linear momentum to determine the velocity of the smaller fragment as;

[tex]m_1 u_1 + m_2 u_2 = v(m_1 + m_2)\\\\-6.32(5) \ + 2u_2 = 0(7)\\\\-31.6 + 2u_2 = 0\\\\2u_2 = 31.6\\\\u_2 = \frac{31.6}{2} \\\\u_2 = 15.8 \ m/s[/tex]

The gain in the kinetic energy of the smaller fragment is calculated as follows;

[tex]K.E_2 = \frac{1}{2} mu_2^2\\\\K.E_2 = \frac{1}{2} \times 2 \times (15.8)^2\\\\K.E_2 = 249.64 \ J[/tex]

Thus, the gain in the kinetic energy of the smaller fragment is 249.64 J.

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Answer:

frequency =4125Hz

Explanation:

L = 4cm = 0.04m

f =v/2L

f = 330/2 x 0.04

f = 4125Hz

Answer:

a) 1764.71 ohms

b) 1.73 H

Explanation:

From the question, we can identify the following parameters;

Vo =12 V , i = 4.86 mA, t =0.700 ms, io =6.80 mA

(a) Indcued emf V = L di/dt =0

From ohms law Vo = ioR

R = 12/6.80*0.001

R=1764.71 ohms

(b) For LR circuit

i =io (1-e^-t/T)

Time constant T = L/R

4.86 = 6.80 (1-e^-0.7*10^-3/T)

divide both side by 6.8

0.715 = 0.0007/T

L/R = 0.0007/0.715

L/R = 0.000979020979

Substitute R from above

L = 0.000979020979 * 1764.71

L =1.73 H

Answer:

La piedra alcanza una rapidez de 196.14 metros por segundo y una distancia recorrida de 1961.4 metros en 20 segundos.

Explanation:

Si se excluye los efectos del arrastre por la viscosidad del aire, la piedra experimenta un movimiento de caída libre, es decir, que la piedra es acelerada por la gravedad terrestre. La distancia recorrida y la rapidez final de la piedra pueden obtenerse con la ayuda de las siguientes ecuaciones cinemáticas:

[tex]v = v_{o} + g\cdot t[/tex]

[tex]y - y_{o} = v_{o}\cdot t + \frac{1}{2}\cdot g \cdot t^{2}[/tex]

Donde:

[tex]v[/tex], [tex]v_{o}[/tex] - Rapideces final e inicial de la piedra, medidas en metros por segundo.

[tex]t[/tex] - Tiempo, medido en segundos.

[tex]g[/tex] - Aceleración gravitacional, medida en metros por segundo al cuadrado.

[tex]y[/tex]. [tex]y_{o}[/tex] - Posiciones final e inicial de la piedra, medidos en metros.

Si [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex], [tex]y_{o} = 0\,m[/tex], entonces:

[tex]v = 0\,\frac{m}{s} +\left(-9.807\,\frac{m}{s^{2}} \right) \cdot (20\,s)[/tex]

[tex]v = -196.14\,\frac{m}{s}[/tex]

[tex]y-y_{o} = \left(0\,\frac{m}{s} \right)\cdot (20\,s) + \frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right) \cdot (20\,s)^{2}[/tex]

[tex]y-y_{o} = -1961.4\,m[/tex]

La piedra alcanza una rapidez de 196.14 metros por segundo y una distancia recorrida de 1961.4 metros en 20 segundos.

Answer:

   K_A = 32.2 10⁶ J

Explanation:

In this exercise we must relate the quantities given to find the kinetic energy

Asteroid A data

              m_A = 3.5 m_B

               v_A = 2.0 v

they also give the value of the kinetic energy of asteroid A

              K_B = 2.3 10⁶ J

the expression for scientific energy is

               K = ½ m v²

let's replace

              K_A = ½ m_a V_a2

               K_A = ½ 3.5 m_B (2.0 v_B)^2

                K_A = 3.5 2² (½ m_B v_B²)

                K_A = 14 K_B

               K_A = 32.2 10⁶ J

Answer:

processes are competitive and reach a thermal equilibrium where the absorbed energy is equal to the energy emitted, this is the equilibrium temperature of the planet.

Explanation:

The temperature of planet Earth is due to two main types of process, internal and external.

Internal processes are all chemical processes that occur that release heat into the environment or due to gases that trap heat on the planet, greenhouse effect

External processes is heating due to energy coming from the Sun. This includes direct heating of the surface by the absorption of energy and reflects of energy in different atmospheric layers.

These are the two terms that heat the Earth

In addition there are several processes so the planet loses energy,

* energy radiation to outer space that is a few degrees kelvin, for which there is a permanent emission

* endothermic processes that need to absorb heat to perform, this lowers the temperature of the system

* liquid (water) system that absorbs large amounts of heat to change state and temperature.

These processes are competitive and reach a thermal equilibrium where the absorbed energy is equal to the energy emitted, this is the equilibrium temperature of the planet.

Therefore it is impossible for the temperature to increase indefinitely since the emission would increase by decreasing the value

Answer:

Explanation:a 1

Correct answer is 2.7 x 10^-3 J/m3

I hope that helps ! <33

The maximum energy density of the capacitor is closest to: 2.7 x 10^-3 J/m3.

Energy density is defined as the total energy per unit volume of the capacitor. Since, Now, for a parallel plate capacitor, A × d = Volume of space between plates to which electric field E = V / d is confined. Therefore, Energy is stored per unit volume.

All Answers (14) Energy density is equal to 1/2*C*V2/weight, where C is the capacitance you computed and V should be your nominal voltage (i.e 2.7 V). Power Density is V2/4/ESR/weight, where ESR is the equivalent series resistance.

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Answer:

10 kgm/s

Explanation:

Change in momentum: This can be defined as the product of mass and change in velocity. The S.I unit of change in momentum is Kgm/s.

From the question,

ΔM = m(v-u)...................... Equation 1

Where ΔM = change in momentum, u = initial velocity, v = final velocity.

Note: Let upward direction be negative, and downward direction be positive.

Given: m = 0.2 kg, v = -20 m/s, u = 30 m/s

Substitute into equation 1

ΔM = 0.2(-20-30)

ΔM = 0.2(-50)

ΔM = -10 kgm/s.

The negative sign shows that the change in momentum is Upward

The magnitude of the change in momentum of the ball as a result of the collision with the sidewalk is -10 kg-m/s.

Given data:

The mass of rubber ball is, m = 0.2 kg.

The initial speed of ball is, u = 30 m/s.

The final rebounding speed of ball is, v = - 20 m/s ( Negative sign shows that during the rebounding, the ball changes its direction)

The momentum of any object is defined as the product of mass and change in velocity. The S.I unit of momentum is Kg-m/s. And the expression for the change in momentum is given as,

[tex]p= m ( v-u)[/tex]

Solving as,

[tex]p= 0.2 \times ( -20-30)\\\\p=-10 \;\rm kg.m/s[/tex]

Thus, we can conclude that the magnitude of the change in momentum of the ball as a result of the collision with the sidewalk is -10 kg-m/s.

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Answer:

Explanation:

a )

Moment of inertial of four masses about axis that coincides with one side :

Out of four masses . location of two masses will lie on the axis so their moment of inertia will be zero .

Moment of inertia of the two remaining masses

= m L² + m L²

= 2 mL²

b )

Axis that bisects two opposite sides

Each of the four masses will lie at a distance of L / 2 from this axis so moment of inertia of the four masses

= 4 x m x ( L/2 )²

= 4 x  mL² / 4

= m L² .

Answer:

a) true.

b) True

c) False. In the equation above the mass does not appear

d) True

e) False. Mass does not appear in the equation

f) False. The load even when distributed in the space can be considered concentrated in the center

Explanation:

1. The electric force is given by the relation

           F = k Q e / r2

where k is the Coulomb constant, Q the charge used, e the charge of the electron and r the distance between the two.

 The strength depends on:

a) true.

b) True

c) False. In the equation above the mass does not appear

d) True

e) False. Mass does not appear in the equation

f) False. The load even when distributed in the space can be considered concentrated in the center

two.

a) True

b) Treu

c) Fail

f) false

For a single electron located at a distance from a positive charge, we have:

1. The force on the electron depends on the distance between it and the positive charge (option a) and the charge of both particles (option b and d).      

2. The electric field at the electron's position depends on the distance between the positive charge and it (option a) and the charge of the positive particle (option d).    

The force on a single electron at a distance from the point charge is given by Coulomb's law:

[tex] F = \frac{Kq_{1}q_{2}}{r^{2}} [/tex]    (1)

Where:

As we can see in equation (1), the force on the electron by the positive charge depends on both charges q₁ and q₂, and the distance, so the correct options are:

a. The distance between the positive charge and the electron

b. The charge on the electron

d. The charge of the positive charge

The other options (c, e, f, and g) are incorrect because the electric force does not depend on the particles' masses or their radii.

The electric field (E) at a distance "r" from a point charge is given by:

[tex] E = \frac{Kq_{1}}{r^{2}} [/tex]   (2)

From equation (2), we can see that the electric field is directly proportional to the charge and inversely proportional to the distance of interest (r).  

The electric field at the electron's position is given by the one produced by the positive charge, so the correct options are:

a. The distance between the positive charge and the electron

d. The charge of the positive charge

The other options (b, c, e, f, and g) are incorrect because the electric field is independent of the mass of the charges involved and their radii.

Therefore, the correct options for part 1 are a, b, and d and for part 2 are a and d.

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I hope it helps you!

Answer:

If the magnitude of the field is decreasing with time the direction of the induced magnetic field is CLOCKWISE

Explanation

This is because If the magnetic field decreases with time, the electric field will be produced in order to oppose the change in line with lenz law. Thus The right hand rule can be applied to find that the direction of electric field is in the clockwise direction.

Answer:

Magnitude of the magnetic field inside the solenoid near its centre is 1.293 x 10⁻³ T

Explanation:

Given;

number of turns of solenoid, N = 269 turn

length of the solenoid, L = 102 cm = 1.02 m

radius of the solenoid, r = 2.3 cm = 0.023 m

current in the solenoid, I = 3.9 A

Magnitude of the magnetic field inside the solenoid near its centre is calculated as;

[tex]B = \frac{\mu_o NI}{l} \\\\[/tex]

Where;

μ₀ is permeability of free space = 4π x 10⁻⁷ m/A

[tex]B = \frac{4\pi*10^{-7} *269*3.9}{1.02} \\\\B = 1.293 *10^{-3} \ T[/tex]

Therefore, magnitude of the magnetic field inside the solenoid near its centre is 1.293 x 10⁻³ T

Answer:

Peak current= 84.86 A

Area of each turn = 0.029 m^2

Explanation:

The peak value of current can be obtained from Irms= 0.707Io. Where Io is the peak current.

Hence;

Irms= 60.0A

Io= Irms/0.707

Io = 60.0/0.707

Io= 84.86 A

Vrms= 0.707Vo

Vo= Vrms/0.707= 170/0.707 = 240.45 V

From;

V0 = NABω

Where;

Vo= peak voltage

N= number of turns

B= magnetic field

A= area of each coil

ω= angular velocity

But ω= 2πf = 2×π×95= 596.9 rads-1

Substituting values;

A= Vo/NBω

A= 240.45/550×0.025×596.9

A= 0.029 m^2

Answer:

4.41 m/s^2

Explanation:

(v_f)^2 - (v_i)^2 = 2a * change in distance

(21)^2 - (0)^2 = 2a * 50

a = (21^2)/(2*50)

a = 4.41 m/s^2

Explanation:

Let x and y are two unknown resistors. When they are connected in series their equivalent resistance is 15 Ω. When they are connected in parallel, their equivalent resistance is 3.3 Ω.

For series combination,

[tex]x+y=15[/tex] ......(1)

For parallel combination,

[tex]\dfrac{1}{x}+\dfrac{1}{y}=3.3[/tex] ....(2)

We need to find the resistances of these resistors. Solving equation (1) and (2) we get :

x = 0.29 and y = 14.7

Hence, the resistances of these resistors are 0.29 ohms and 14.7 ohms.

Answer:

F= 3.56e22N

Explanation:

Using the force of radiation acting on the earth which is

force = radiation pressure x area = (intensity/c)xpi R^2

force = 1370W/m^2 x pi x( 6.37x10^6m)^2/3x10^8m/s

force = 5.82x10^8 N

But the sun's gravitational attraction means the magnitude of the solar gravitational force on earth: If that's the case, the answer is approx 10^22 N:

F=GMm/r^2

G=6.67x10^(-11)=6.67e-11

M=mass sun = 2x10^30kg=2e30

m=mass earth = 6x10^24kg

r=earth sun distance = 1.5x10^11m

F=(6.6e-11)(2e30)(6e24)/(1.5e11)^2 =

F= 3.56e22N

Answer:

Ethnomethodology theory

Explanation:

Take note of the fact that we are told Kevin worries that the police will stop and question him even though he has not done anything wrong.

This statement shows us that Kevin already understood his society from past experiences, and thus he tries to avoid social interactions with particular member of his society (the police) who may be show discrimination towards him.

Answer:

Different surfaces have different impact force during collision which depends on the time it takes the person to come to rest after collision.

Explanation:

Given;

speed on concrete = 12 m/s (27 mi/h)

speed on soil = 15 m/s (34 mi/h)

speed on water = 34 m/s (76 mi/h)

The impact force on this person during collision is rate of change of momentum;

[tex]F = \frac{\delta P}{\delta t}[/tex]

During collision, the force exerted on this person depends on how long the collision lasts; that is, how long it takes for this person to come to rest after collision with each of the surfaces.

The longer the time of collision, the smaller the force exerted by each.

It takes shorter time for the person to come to rest on concrete surface than on soil surface, also it takes shorter time for the person to come to rest on soil surface than on water surface.

As a result of the reason above, the force exerted on the person during collision by the concrete surface is greater than that of soil surface which is  greater than that of water surface.

Answer:

They are cooler and wetter

Explanation:

Highland areas have lower temperatures compared to low lying areas. The climate is more wetter because of more rainfalls compared to low lying areas and the wind carries moist air over the highlands.

Answer:

The rejected by the air conditioning system is 1.75 kilowatts.

Explanation:

A air conditioning system is a refrigeration cycle, whose receives heat from cold reservoir with the help of power input before releasing it to hot reservoir. The First Law of Thermodynamics describes the model:

[tex]\dot Q_{L} + \dot W - \dot Q_{H} = 0[/tex]

Where:

[tex]\dot Q_{L}[/tex] - Heat rate from cold reservoir, measured in kilowatts.

[tex]\dot Q_{H}[/tex] - Heat rate liberated to the hot reservoir, measured in kilowatts.

[tex]\dot W[/tex] - Power input, measured in kilowatts.

The heat rejected is now cleared:

[tex]\dot Q_{H} = \dot Q_{L} + \dot W[/tex]

If [tex]\dot Q_{L} = 1\,kW[/tex] and [tex]\dot W = 0.75\,kW[/tex], then:

[tex]\dot Q_{H} = 1\,kW + 0.75\,kW[/tex]

[tex]\dot Q_{H} = 1.75\,kW[/tex]

The rejected by the air conditioning system is 1.75 kilowatts.

Complete Question

The complete question is shown on the first uploaded image  

Answer:

a

 [tex]a_{max} = 0.00246 \ m/s^2[/tex]

b

   [tex]k =722.2 \ N/m[/tex]

Explanation:

From the question we are told that

     The  amplitude is [tex]A = 1.8 \ cm = 0.018 \ m[/tex]

     The period is [tex]T = 17 \ s[/tex]

    The test weight is  [tex]W = 13 \ N[/tex]

Generally the radial acceleration is mathematically represented as

        [tex]a = w^2 r[/tex]

at maximum angular acceleration

       [tex]r = A[/tex]

So  

       [tex]a_{max} = w^2 A[/tex]

Now [tex]w[/tex] is the angular velocity which is mathematically represented as

      [tex]w = \frac{2 * \pi }{T}[/tex]

Therefore

       [tex]a_{max} = [\frac{2 * \pi}{T} ]^2 * A[/tex]

substituting values

       [tex]a_{max} = [\frac{2 * 3.142}{17} ]^2 * 0.018[/tex]

       [tex]a_{max} = 0.00246 \ m/s^2[/tex]

Generally this test weight is mathematically represented as

     [tex]W = k * A[/tex]

Where k is the spring constant

Therefore

        [tex]k = \frac{W}{A}[/tex]

substituting values        

      [tex]k = \frac{13}{0.018}[/tex]

     [tex]k =722.2 \ N/m[/tex]

Answer:

Explanation:

Using the law of gravitation of force to solve this question. The law states that the Force of attraction between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distances between them.

Mathematically, F = GMaMb/R² ... 1

G is the gravitational constant

Ma and Mb are the masses of the balls

R is the distance between the balls

If the mass of ball B is tripled and the magnitude of the separation of the balls is increased to 3R, the force between them will be;

F₂ = GMa(3Mb)/(3R)²

F₂ = 3GMaMb/9R² ... 2

Dividing equation 1 by 2 we will have;

F₂/F = (3GMaMb/9R²)/GMaMb/R²

F₂/F =  3GMaMb/9R² * GMaMb/R²

F₂/F = 3/9

F₂/F = 1/3

F₂ = 1/3 F

This shows that the magnitude of the new attractive force is one-third that of the initial attractive force

Answer:

Explanation:

d

Answer:

a. Bx is positive

Explanation:

See attached file