Neil Armstrong dropped a hammer on the moon. If it took 4 seconds to fall and the final speed was 8 m/s, what is the acceleration due to gravity on the moon?

The gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.

Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.

Given data

Mass of object 1,m = 80 kg

Mass of object 2,M = 50 kg

Gravitational constant,G = 6.6 × 10⁻¹¹ kg⁻² m²

Distance of seperation,R = 0.2 m

The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.

[tex]\rm F = G\frac{mM}{R^ 2} \\\\ F = 6.6 \times 10^{-11 }\times \frac{80 \times 50 }{(0.2)^2} \\\\F = 6.6 \times 10^{-6 } \ N[/tex]

Hence the gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.

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The force constant of the spring is determined as 14,222.2 N/m.

Apply the principle of conservation of energy,

K.E = U

where;

¹/₂mv² = ¹/₂kx²

mv² = kx²

k = mv²/x²

Where;

k = (2000 x 8²)/(3²)

k = 14,222.2 N/m

Thus, the force constant of the spring is determined as 14,222.2 N/m.

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The free body diagram showing the forces acting on block A is diagram 3; option C.

Free body diagrams are simple diagrams which are used to illustrate the magnitude and direction of the forces acting on the body.

The diagram of the crane and boxes as well as the free body diagrams are shown in the attached image.

Three forces are acting on A as follows:

Therefore, diagram 3 is correct.

In conclusion, free body diagram shows the forces acting on a body as well as their direction of action.

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Answer:

I think C is the correct answer

Explanation:

Answer:

6.39 × 10^23 kg

.........

Answer:

76.52

Explanation:

the density of gas is 1.775kg/m^3 at 27 degree celcius and pressure of 10^-5n/m^2. if the specific heat capacity at constant pressure is 846 jkg^-1k^-1, the ratio of specific heat capacity at constant pressure to tht constant volume​ is 76.52

Density is  the mass of a unit volume of a material substance. The formula for density is represented by d = M/V, where d is density, M is mass, and V is volume.

It is commonly represented in units of grams per cubic centimeter. Density can also be expressed as kilograms per cubic meter .

Density can used to define how different materials interact when mixed together. For example Wood floats in water because it has a lower density, while an anchor sinks because the metal has a higher density.

density can be applied in pipe design, shipbuilding, helium balloons, weight distribution in the aeroplane, and the fact that ice floats on water.

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The magnitude is 13.12 mV.

The steps are attached below.

The standard SI unit of the magnetic field is the tesla (T). As an end result, we can use these equations and the equation for an induced emf due to changes in magnetic flux, ϵ=−NΔϕΔt ϵ = − N Δ ϕ Δ t, to calculate the importance of a precipitated emf in a solenoid.

The magnitude of the precipitated contemporary depends on the rate of trade of magnetic flux or the fee of reducing the magnetic area strains.

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The period or time duration of these waves is 0.16 sec. While the wave velocity is 18m/sec.

Wavelength may be defined as the space between equivalent points in the contiguous cycles of a waveform signal propagated in the area or along a wire.

The time duration of these waves is calculated by the given formula:

T = [tex]\frac{1}{F}[/tex] = [tex]\frac{1}{6}[/tex] = 0.16 seconds.

The velocity is calculated by the given formula:

V= Wavelength × Frequency = 6Hz × 3m = 18m/sec.

Therefore, it is well described above.

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Answer:

Given,

Frame rate = 25 frames per second

To find,

Time interval between one frame and the next.

Solution,

We can simply solve this numerical problem by using the following process.

Now,

Number of frames = 25

Total time taken to display the given number of frames (ie. 25 frames) = 1 second

To calculate the time interval between one frame and next, we need to divide the time taken to display total number of frames by total number of frames.

So,

Time interval between one frame and next :

= Time taken to display total number of frames / Total frames

= 1/25

= 0.04 second

Hence, time interval between one frame and next is 0.04 second.

The design that would be used to make an efficient commercial vehicle chassis that has many realistic truck components is:

This refers to the main vehicle structure of a car that bears all the main stress that other components are attached to.

Hence, we can see that to make a good design for an efficient commercial vehicle chassis that has many realistic truck components, we would have to consider various factors such as handling maximum stress, maximum equilateral stress, and deflection.

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Answer:

5 m /s^2

Explanation:

Change in velocity = 35 - 10 = 25 m/s

change in time = 5 s

decelleration = 25/5 = 5 m/s^2

The best way to arrange the salon to best use what he has is:

This refers to the change in direction of a wavefront between two different media so that the wavefront returns to its originating medium.

Hence, we can see that from our knowledge of shadows and reflection, we can note that mirrors reflect and light helps to bring detail in a dark area and the chairs should be facing the mirrors directly so the customer can see his hair and how it is being cut by the barber.

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Behaviorism approach centers on giving absolute prominence to the outside characters of individuals

Psychoanalysis approach centers on fact the fact that the unconscious has the potential to drive our behavior

Interestingly, the behaviorists and psychoanalysts share some common norms and values in such away that

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c. Sodium and potassium

Perspiration, water given off by the intact skin, either as vapor by simple evaporation from the epidermis or as sweat, a form of cooling in which liquid actively secreted from sweat glands evaporates from the body surface.

When our body is sweating sodium and potassium is lost from the body along with water.

In order to maintain the integrity of the cells in the body ,Sodium and potassium are very important.

Sweat is also known as perspiration.

So,

By maintaining  the proper cell functioning and cell vitality optimum level of sodium and potassium should be maintained in the body.

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For an emf source with a magnitude of E = 120.0 V, is mathematically given as

Q=136.63uC

Parameters

Generally, the equation for voltage on the resistor is mathematically given as

Vr=IR

Therefore

Vr=71*0.95

Vr=67.45V

voltage on capacitor

Vc=120-67.45

Vc=52.55V

In conclusion,

Q=CVc

Therefore

Q=52.55*2.60

Q=136.63uC

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From the calculation, the banking angle is obtained as 11.5°.

The banking angle refers to the angle at which the vehicle must be inclined so that it does not skid off the road.

Now we have;

θ = ?

v =  61.0 m/s

r = 1860 m

g = 9.8 m/s^2

θ = tan-1(61^2/ 1860 * 9.8)

θ = tan-1(3721)/18228

θ = 11.5°

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Answer:

35000 KJ

Explanation:

The equation for the kinetic energy is given by the formula :

[tex]E_{k} = \frac{1}{2} mv^{2}[/tex]

[tex]E_{k} = \frac{1}{2} (700)(10)^{2}[/tex]

[tex]E_{k} = \frac{1}{2} (700)(100)[/tex]

[tex]E_{k} = (350)(100)[/tex]  OR [tex]E_{k} = \frac{1}{2} (70000)[/tex]

[tex]E_{k} = 35000[/tex]

Units will be kilojoules since the units of mass was kilograms .

Our final answer is 35000 KJ

Hope this helped and have a good day

Answer:

See below

Explanation:

speed = freq * wavelength

          =  5 Hz    * .6 m = 3 m/s

speed = freq * wavelength

   3      =   freq  *  .4 m         freq = 7.5 hz

1. The speed of the waves is 3 m/s. 2. for a wavelength of 0.4 m, the frequency would be 7.5 Hz.

To find the speed of the waves, we can use the equation:

[tex]\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \][/tex]

Given that the frequency is 5 Hz and the distance between successive crests (wavelength) is 60 cm, we need to convert the wavelength to meters:

[tex]\[ \text{Wavelength} = 60 \, \text{cm} = 0.6 \, \text{m} \][/tex]

Plugging in the values, we have:

[tex]\[ \text{Speed} = 5 \, \text{Hz} \times 0.6 \, \text{m} = 3 \, \text{m/s} \][/tex]

Therefore, the speed of the waves is 3 m/s.

Now, to find the frequency at which the wavelength is 0.4 m, we rearrange the equation:

[tex]\[ \text{Frequency} = \frac{\text{Speed}}{\text{Wavelength}} \][/tex]

Substituting the given values:

[tex]\[ \text{Frequency} = \frac{3 \, \text{m/s}}{0.4 \, \text{m}} = 7.5 \, \text{Hz} \][/tex]

Thus, for a wavelength of 0.4 m, the frequency would be 7.5 Hz.

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The angular frequency of the oscillation is determined as 2.7 rad/s.

ω = √k/m

With respect to spring constant k1 and k2

k1 + k2 = 9.5 N/m + 5 N/m = 14.5 N/m

ω = √14.5/2 = 2.7 rad/s

Thus, the angular frequency of the oscillation is determined as 2.7 rad/s.

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The Sketch  of the figure will bear the parameters of the charge that lies   at (4,0,0)

Generally, the equation for is  mathematically given as

1)

Since both of the other points, "q1"<"q2," are on the x-axis, the third one must also be on the x-axis, and it must be close to the charge of lesser magnitude. off q1 by x cm

Now, forces on q3 due to q1

[tex]\vec{F}_{1}=\frac{k q_{1} q_{3}}{x^{2}} \hat{x}[/tex]

Force on q3 due to q2

[tex]\vec{F}_{2}=\frac{k q_{2} q_{3}}{(6+x)^{2}}(-\hat{x})[/tex]

[tex]\quad \vec{F}_{1}+\vec{G}_{2}=0$[/tex]

[tex]&\frac{k q_{1} q_{3}}{x^{2}}-\frac{k q_{2} q_{3}}{(x+6)^{2}}=0 \\&\frac{2}{x^{2}}=\frac{8}{(x+6)^{2}} \Rightarrow \frac{x+6}{x}=\sqrt{\frac{8}{2}}=2 \\&x+6=2 x \Rightarrow x=6 \mathrm{~cm}[/tex]

In conclusion, the charge lies at (4,0,0)

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For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive

Kinetic energy can be defined as the ability assumed by an object in motion.

Kinetic energy is also said to be a form of mechanical energy that is possessed by an object to be in motion.

In conclusion, For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive

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The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other.

We know that graphite is composed of layers. These hexagonal layers are held together by weak Van Der Walls forces and as such are able to slide over each other. The carbon atom in each layer are held together by strong covalent bonds.

The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other and as such make the graphite fluid.

Thus, the image that shows these layers of graphite is attached to this an answer

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Answer:it’s B

Explanation:

Answer:

Southwest. The electric force on this electron would point southwest (opposite to the direction of the electric field.)

Explanation:

Consider a position in an electric field. A positive point charge placed at that position would experience an electric force from this field. By definition, the direction of this field at that position would be the same as the direction of electric force that the field exerts on the positive point charge placed at that position.

It is given that the electric field in this question points to the northeast in this region. Thus, a positive point charge placed in this region would experience an electric force in the same direction- to the northeast.

Electrons are negatively charged. The direction of electric force on an electron would be opposite to that on a positive point charge placed at the same position. The electric force on a positive point charge in this region points to the northeast (same as the direction of the electric field). The opposite of northeast is southwest. Hence, the electric force on an electron at this position would point to the southwest.

The emf of the battery will be 2.955 V. The rate of change of magnetic flux linked with the coil is responsible for generating emf.

Electromagnetic induction is what causes the induced voltage. Electromagnetic induction generates emf (induced voltage) by subjecting a conductor to a magnetic field.

Given data;

Voltage,v = 200 v

Resistance, r=600 ohms

Internal resistance,R = 3 ohms

The EMF of the battery is found as follows;

E = {vR}/{R+r}

E = 200×3/(3 + 200)

E = 2.955 V

Hence, the emf of the battery will be 2.955 V.

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Hi there!

1.

Let's use the rotational equivalent of Newton's Second Law.

[tex]\Sigma \tau = I\alpha[/tex]

τ = Torque (Nm)

I = Moment of Inertia (1/2mR² for solid cylinder)

α = Angular acceleration (rad/sec²)

The torque is equivalent to:
[tex]\tau = r \times F[/tex]

r = distance from lever arm to pivot point, aka the radius for this cylinder (0.111 m)
F = applied force (7.161 N)

We are already given various values, so let's create a working equation and solve.

[tex]rF = I\alpha \\\\\alpha = \frac{rF}{I}[/tex]
[tex]\alpha = \frac{(0.111)(7.161)}{\frac{1}{2}(2.15)(0.111^2)} = \boxed{60.013 \frac{rad}{sec^2}}[/tex]

2.

So, let's begin by doing a summation of forces acting on the block.

We have its force of gravity downward(+), and the tension from the string upward. (-), assigning signs based on the path of the falling block.

[tex]\Sigma F = F_g - T\\\\\Sigma F = m_b g - T\\\\m_b a = m_b g - T[/tex]

Solving for 'T':

[tex]T = m_b g - m_b a[/tex]

Let's now do a summation of torques on the cylinder. We only have the torque caused by the tension in the string connected to the block.

[tex]\Sigma \tau = rT\\\\I\alpha = r(T = m_b g - m_b a)[/tex]

Using the relationship between angular and translational acceleration:

[tex]a = \alpha r\\\\alpha = \frac{a}{r}[/tex]

And the equation for the moment of inertia:
[tex]I = \frac{1}{2}Mr^2[/tex]

Simplify the expression.

[tex]\frac{1}{2}Mr^2(\frac{a}{r}) = r( m_b g - m_b a)\\\\\frac{1}{2}Ma = ( m_b g - m_b a)[/tex]

Solve for 'a':
[tex]\frac{1}{2}ma + m_b a= m_b g \\\\a = \frac{m_b g}{\frac{1}{2}M + m_b} = \frac{0.730(9.81)}{\frac{1}{2}(2.15) + 0.730} = \boxed{3.97 \frac{m}{s^2}}[/tex]

3.

This is just a case of kinematics since we have a constant acceleration. To solve for this instance, however, let's use calculus.

We know that:
[tex]a(t) = 3.97[/tex]

v(t) is the integral. There is no initial velocity (block starts from rest), so:
[tex]v(t) = 3.97t + C\\C = 0 m/s \\\\v(t) = 3.97t[/tex]

Now, we can take the integral of the velocity/time equation to find the displacement between the interval.

[tex]\int\limits^{0.590}_{0.390} {3.97t} \, dt = \boxed{0.389 m}[/tex]

4.

So, let's now find the translational acceleration produced by the new cylinder. Use the kinematic equation:
[tex]\Delta x = v_0 t + \frac{1}{2}at^2[/tex]

Since the block starts from rest, we can do some simplifying and rearranging:
[tex]2\Delta x = at^2\\\\a = \frac{2\Delta x}{t^2} = \frac{2(0.450)}{0.490^2} = 3.748 \frac{m}{s}^2[/tex]

So, let's go back to our summation of torques equation. This time, however, we cannot simplify 'I'.

[tex]I(\frac{a}{r}) = r( m_b g - m_b a)[/tex]

Solving for 'I':
[tex]I = \frac{r^2( m_b g - m_b a)}{a} = \frac{(0.111^2)(7.161 - .730(3.748))}{3.748}\\\\ = \boxed{0.0145 kgm^2}[/tex]

The net force on the canoe is obtained as 65.0 N [forward]

The frictional force is the force that opposes motion. We know that the net force is the actual force that moves the canoe in a given direction.

Hence, the total force acting in the forward direction = 60.0N + 90.0N = 150 N and the total backwards force =  85.0N

Net force =  150 N - 85.0N = 65.0 N [forward]

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It reasonable to expect that anyone would be able to make good sense of a filing system as it reduces the overall storage space occupied by the records.

This is the process of keeping document safely and being able to easily retrieve them.

The new filing system is based on their volume which is why the space is reduced thereby reducing the ambiguity.

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(a)The acceleration of the ball, while it is in flight, will be 9.81 m/s².

(b) The velocity of the ball when it reaches its maximum height will be 0 m/sec.

(c) The initial velocity of the ball is 20.30 m/s upward.

(d) The maximum height it reaches will be 21.00 m

The change of displacement with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.

The given data in the problem is;

u is the initial velocity of fall = ? m/sec

h is the distance of fall = ? m

g is the acceleration of free fall = 9.81 m/sec²

a.

The acceleration of the ball, while it is in flight, is equal to the acceleration due to gravity,g=9.81 m/s².

b.

The ball's velocity will be zero when it has reached its highest point.

c.

The initial velocity of the ball is;

v=u-gt

0=u-gt

u=gt

u=9.81 m/s² × 2.07 sec

u=20.30 m/s

d.

The maximum height it reaches is found by the formula as;

[tex]\rm u^2 = - 2gh \\\\ (20.30)^2 = -2 \times (-9.8) \times h \\\\ 412.09 = 19.6 \times h\\\\ h = 412.09/19.6\\\\ h = 21.00 m[/tex]

Hence the acceleration of the ball,s the velocity of the ball when it reaches its maximum height, the initial velocity of the ball, and the maximum height it reaches will be 9.81 m/s²,0 m/sec,20.30 m/s, and 21.00 m respectively.

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The length of the filament is 0.2 m.

To find the answer, we need to know about the Stefan - Boltzmann law.

L= power/(π×d×e×σ×T⁴)

= 40/(π×0.0001×0.35×5.67×10^(-8)×2500⁴)

= 0.2m

Thus, we can conclude that the length of the filament is 0.2 m.

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The frictional force of air resistance is; 949N while the force of friction underwater is; 1859N.

The frictional force on the action rock can be evaluated as follows;

F - W = ma

However, the acceleration of fall a can be evaluated as follows;

a = (12² -0²)/2× 15

a = 144/30 = 4.8m/s².

a) Hence, the air resistance, frictional force, F = (65×9.8) + (65 ×4.8)

F = 949N.

b) When reaches a depth of 2.5m, it follows that the acceleration is;

a = (0²-12²)/(2×2.5)

a = 144/5 = 28.8m/s².

On this note, the force balance is;

F + 650 = 65(9.8 + 28.8)

F = 2509 - 650

F = 1859N.

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Answer:

Approximately [tex](-4.9\times 10^{2}\; {\rm N})[/tex] (rounded to two significant figures.)

Explanation:

The impulse [tex]\mathbf{J}[/tex] on an object is equal to the change in the momentum [tex]\mathbf{p}[/tex] of this object. Dividing impulse by duration [tex]\Delta t[/tex] of the contact would give the average external force that was exerted on this object.

If an object of mass [tex]m[/tex] is moving at a velocity of [tex]\mathbf{v}[/tex], the momentum of that object would be [tex]\mathbf{p} = m\, \mathbf{v}[/tex].

Let [tex]m[/tex] denote the speed of this ball. Let [tex]\mathbf{v}_{0}[/tex] denote the velocity of this ball before the contact, and let [tex]\mathbf{v}_{1}[/tex] denote the velocity of the ball after the contact.

Momentum [tex]\mathbf{p}_{0}[/tex] of this ball before the contact: [tex]\mathbf{p}_{0} = m\, \mathbf{v}_{0}[/tex].

Momentum [tex]\mathbf{p}_{1}[/tex] of this ball after the contact: [tex]\mathbf{p}_{1} = m\, \mathbf{v}_{1}[/tex].

Impulse, which is equal to the change in momentum:

[tex]\mathbf{J} = \mathbf{p}_{1} - \mathbf{p}_{0} = m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}[/tex].

Since the velocity of the ball after the contact is in the [tex](-x)[/tex] direction, [tex]\mathbf{v}_{1} = -20.0\; {\rm m\cdot s^{-1}}[/tex]. The average external force on this ball would be:

[tex]\begin{aligned} \mathbf{F} &= \frac{\mathbf{J}}{\Delta t} \\ &= \frac{m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}}{\Delta t} \\ &= \frac{m\, (\mathbf{v}_{1} - \mathbf{v}_{0})}{\Delta t} \\ &= \frac{0.145\; {\rm kg} \times ((-20.0\; {\rm m\cdot s^{-1}}) - 14\; {\rm m\cdot s^{-1}})}{0.010\; {\rm s}} \\ &\approx -4.9 \times 10^{2}\; {\rm N}\end{aligned}[/tex].

(Rounded to two significant figures.)