A bucket of mass m is attached to a rope that is wound around the outside of a solid sphere (I = 2/5 M^2) of radius R. When the bucket is allowed to fall from rest, it falls with an acceleration of a down. What is the mass of the sphere in terms of m, R, a, and g?

Answer: what I know that the unit is farad

Explanation:

Hi there!

Part 1:

According to Newton's Third Law, every action has an EQUAL and OPPOSITE reaction.

For a collision, the objects involved exert an EQUAL and OPPOSITE impulse on each other, which means the forces exerted are equal as well.

Therefore, the school bus and Toyota Prius exert an EQUAL FORCE on each other.

Part 2:
The school bus has a greater mass.

Part 3:

Using Newton's Second Law:
[tex]\Sigma F = ma[/tex]

Using this relationship, the smaller the mass, the larger the acceleration. Since the forces are EQUAL, the Toyota Prius will experience a larger acceleration because it has a smaller mass.

Answer: a = 0.647 m/s^2

Explanation:

Acceleration = change in speed / time → a = 22 / 34 → a = .647 m/s^2

Answer:

Approximately [tex]1.1 \times 10^{4}\; {\rm m\cdot s^{-1}}[/tex] if air friction is negligible.

Explanation:

Let [tex]G[/tex] denote the gravitational cosntant. Let [tex]M[/tex] denote the mass of the earth. Lookup the value of both values: [tex]G \approx 6.67 \times 10^{-11}\; {\rm N\cdot m^{2}\cdot kg^{-2}}[/tex] while [tex]M \approx 5.697 \times 10^{24}\; {\rm kg}[/tex].

Let [tex]m[/tex] denote the mass of the meteor.

Let [tex]v_{0}[/tex] denote the initial velocity of the meteor. Let [tex]r_{0}[/tex] denote the initial distance between the meteor and the center of the earth.

Let [tex]r_{1}[/tex] denote the distance between the meteor and the center of the earth just before the meteor lands.

Let [tex]v_{1}[/tex] denote the velocity of the meteor just before landing.

The radius of planet earth is approximately [tex]6.371 \times 10^{6}\; {\rm m}[/tex]. Therefore:

Note the significant difference between the two distances. Thus, the gravitational field strength (and hence acceleration of the meteor) would likely have changed significant during the descent. Thus, SUVAT equations would not be appropriate.

During the descent, gravitational potential energy ([tex]\text{GPE}[/tex]) of the meteor was turned into the kinetic energy ([tex]\text{KE}[/tex]) of the meteor. Make use of conservation of energy to find the velocity of the meteor just before landing.

Initial [tex]\text{KE}[/tex] of the meteor:

[tex]\displaystyle (\text{Initial KE}) = \frac{1}{2}\, m\, {v_{0}}^{2}[/tex].

Initial [tex]\text{GPE}[/tex] of the meteor:

[tex]\displaystyle (\text{Initial GPE}) &= -\frac{G\, M\, m}{r_{0}}[/tex].

(Note the negative sign in front of the fraction.)

Just before landing, the [tex]\text{KE}[/tex] and the [tex]\text{GPE}[/tex] of this meteor would be:

[tex]\displaystyle (\text{Final KE}) = \frac{1}{2}\, m\, {v_{1}}^{2}[/tex].

[tex]\displaystyle (\text{Final GPE}) &= -\frac{G\, M\, m}{r_{1}}[/tex].
If the air friction on this meteor is negligible, then by the conservation of mechanical energy:

[tex]\begin{aligned}& (\text{Initial KE}) + (\text{Initial GPE}) \\ =\; & (\text{Final KE}) + (\text{Final GPE})\end{aligned}[/tex].

[tex]\begin{aligned}& \frac{1}{2}\, m\, {v_{0}}^{2} - \frac{G\, M\, m}{r_{0}} \\ =\; & \frac{1}{2}\, m\, {v_{1}}^{2} - \frac{G\, M\, m}{r_{1}}\end{aligned}[/tex].

Rearrange and solve for [tex]v_{1}[/tex], the velocity of the meteor just before landing:

[tex]\begin{aligned}{v_{1}} &= \sqrt{\frac{\displaystyle \frac{1}{2}\, m\, {v_{0}}^{2} - \frac{G\, M\, m}{r_{0}} + \frac{G\, M\, m}{r_{1}}}{(1/2)\, m}} \\ &= \sqrt{{v_{0}}^{2} - \frac{G\, M}{r_{0}} + \frac{G\, M}{r_{1}}} \\ &= \sqrt{{v_{0}}^{2} - G\, M\, \left(\frac{1}{r_{1}} - \frac{1}{r_{0}}\right)}\end{aligned}[/tex].

Substitute in the values and evaluate:

[tex]\begin{aligned}v_{1} &= \sqrt{{v_{0}}^{2} - G\, M\, \left(\frac{1}{r_{1}} - \frac{1}{r_{0}}\right)} \\ &\approx \sqrt{\begin{aligned}(& 6.5 \times 10^{3}\; {\rm m \cdot s^{-1}}) \\ & - [6.67 \times 10^{-11}\; {\rm N \cdot {m}^{2}\cdot {kg}^{2} \times 5.697\; {\rm kg}}\\ &\quad\quad \times (1 / (6.371 \times 10^{6}\; {\rm m}) - 1 / (1.9371 \times 10^{7}\; {\rm m}))]\end{aligned}} \\ &\approx 1.1 \times 10^{4}\; {\rm m\cdot {s}^{-1}}\end{aligned}[/tex].

(Note that assuming a constant acceleration of [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] would give [tex]v_{1} \approx 1.7\times 10^{4}\; {\rm m\cdot s^{-1}}[/tex], an inaccurate approximation.

Answer:

5.98 kg

Explanation:

To solve this problem, let use the Linear Momentum Conservation Law:

Before collision: [tex]\sum p=p_{1}+p_{2}=m_{1}v_{1}+m_{2}v_{2}=(2.99v_{1})+0=2.99v_{1}[/tex]

After collision: [tex]\sum p'=p_{1}'+p_{2}'=(2.99+m_{2})(v_{1}/3)[/tex]

So, we obtain:

[tex]\sum p =\sum p' \rightarrow 2.99v_{1}=(2.99+m_{2})(v_{1}/3) \rightarrow 8.97 = 2.99 + m_{2}[/tex]

[tex]m_{2}=8.97-2.99=5.98 kg[/tex]

This question involves the concept of  Newton's law of gravitation.

The force of gravity between the two spaceships is "1355.78 N".

According to Newton's Law of Gravitation:

[tex]F=\frac{Gm_1m_2}{r^2}[/tex]

where,

Therefore,

[tex]F=\frac{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(500\ kg)(498\ kg)}{(35\ m)^2}\\\\[/tex]

F = 1355.78 N = 1.356 KN

Learn more about Newton's Law of Gravitation here:

https://brainly.com/question/9373839

Two space ships traveling next to each other. The first one is 500 kg and the second one is 498 kg. They are 35 meters apart, the Force of gravity between the two spaceships is 1355.78 N.

It is given that the First spaceship's weight ([tex]m_{1}[/tex]) is 500 kg,

The second spaceship's weight ([tex]\rm m_{2}[/tex]) is 498 kg.

The distance between spaceships (r) is 35 meters.

It is required to find the Force of gravity between these spaceships.

It is defined as the force which attracts any two masses in the universe.

By Newton's law of Gravitation:

[tex]\rm F= \frac{Gm_1m_2}{r^2}[/tex]  , Where

[tex]\rm F = The\ force \ of \ gravity \ between \ the \ spaceships\\\rm G= Universal\ Gravitational \ Constant = 6.67 \times 10^{-11} N.m^2/kg^2[/tex]

Putting values in the above formula:

[tex]\rm F = \frac{(6.67\times 10^{-11} N.m^2/kg^2)(500kg)(498kg)}{(35m)^2}[/tex]

F = 1355.78 N = 1.356  KN

Thus, Two spaceships travel next to each other. The first one is 500 kg and the second one is 498 kg. They are 35 meters apart, the Force of gravity between the two spaceships is 1355.78 N.

Learn more about Gravitational Force here:

https://brainly.com/question/3009841

If a person generates about 412005 joules of heat from the body,  the water temperature is mathematically given as

t=21.6296C

Question Parameter(s):

The person is submerged neck-deep into a tub containing 2124 kg of water at 20.9 °C

Generally, the equation for the Heat   is mathematically given as

Heat gained =Heat loess

Thereofore

mw*cw*(t-2160)=1.5*10^5

[tex]t=21.60+\frac{1.5*10^5}{mw*Cw}\\\\t=21.60+\frac{1.5*10^5}{1.2*10^3*4186}[/tex]

t=21.6296C

In conclusion, the tempreature

t=21.6296C

Read more about Temperature

https://brainly.com/question/13439286

Answer:

0.5 mega grams

Explanation:

Answer:

H = 1/2 g t^2    where t is time to fall a height H

H = 1/8 g T^2   where T is total time in air  (2 t  = T)

R = V T cos θ       horizontal range

3/4 g T^2 = V T cos θ       6 H = R    given in problem

cos θ = 3 g T / (4 V)           (I)

Now t = V sin θ / g     time for projectile to fall from max height

T = 2 V sin θ / g

T / V = 2 sin θ / g

cos θ = 3 g / 4 (T / V)     from (I)

cos θ = 3 g / 4 * 2 sin V / g = 6 / 4 sin θ

tan θ = 2/3      

θ = 33.7 deg

As a check- let V = 100 m/s

Vx = 100 cos 33.7 = 83,2

Vy = 100 sin 33,7 = 55.5

T = 2 * 55.5 / 9.8 = 11.3 sec

H = 1/2 * 9.8 * (11.3 / 2)^2 = 156

R = 83.2 * 11.3 = 932

R / H = 932 / 156 = 5.97        6 within rounding

With the use of first and third equation of motion, the distance covered by a T-Rex is 30.51 m

When a body is in linear motion, the body is moving in a straight line. some of the parameters to consider are:

Given that a T-Rex move from 0 m/s to 9 m/s in 6.78 seconds, the distance covered can be found by calculating the acceleration.

Let us use equation 1

V = U + at

9 = 0 + 6.78a

a = 9 / 6.78

a = 1.33 m/[tex]s^{2}[/tex]

Now let us use equation 3

[tex]v^{2}[/tex] = [tex]u^{2}[/tex] + 2as

[tex]9^{2}[/tex] = 2 x 1.33 x S

81 = 2.655S

S = 81/2.655

S = 30.51 m

Therefore, the distance covered by a T-Rex is 30.51 m.

Learn more about Linear Motion here: https://brainly.com/question/12721831

What the equation given?

Maximum velocity occurs at the equilibrium position

So

Now

Now

As we know the formula

[tex]\\ \rm\rightarrowtail V_max=A\omega[/tex]

These expressions can be used

The maximum speed of the oscillating object will be given by [tex]V_{max}=Aw[/tex]

An oscillation is defined as the repitative periodic motion of any object about its mean or equilibrium position.

The given equation is as follows:

x(t)=Acost

Maximum velocity occurs at the equilibrium position x=0

x(0)=Acos0

x(0)=A

Hence the maximum velocity will be  [tex]V_{max}=Aw[/tex]

To know more about Oscillation follow

https://brainly.com/question/26449711

Answer:

acceleration of the gravity

Explanation:

The weight of an object on the moon is less because the acceleration of the gravity on the moon is less.

Answer:

The answer should be choice B.

Answer:25

Explanation: because higher means less kinetic energ

The athlete can improve performance by building strength, coordination and balance.

This is an individual who is proficient in sports and other forms of physical exercise.

Improvement of performance based on the kinematic variable of speed and acceleration can be achieved by building strength, coordination and balance by performing plyometric exercises etc.

Read more about Athlete here https://brainly.com/question/1532968

The miniature circuit breaker should rather be fastned to a wall using nails and other neccessary tools.

A miniature circuit breaker is a circuit breaker that is used in homes as a means of guarding against damage to appliances due to a very high current.

This miniature circuit breaker is also harzardous in the sense that it could lead to an electrical fault related fire outbreak especially when it is being blown freely by wind as you tie it with a thread. Doing this a very bad idea because of the risk of a fire hazard.

The miniature circuit breaker should rather be fastned to a wall using nails and other neccessary tools.

Learn more about miniature circuit breaker: https://brainly.com/question/1298425

Answer:

If one wraps the fingers around the wire and points the thumb in the direction of the "conventional" current the fingers will point towards the North pole - the direction of the B-field.

In this case the B-field is pointed "West".

Answer:

The delicate balance between temperature and magnetic domains is destabilized when a magnet is subjected to high temperatures. If a magnet is exposed to this temperature for an extended length of time or heated over its Curie temperature, it will lose its magnetism and become irreversibly demagnetized.

Explanation:

the x- component of the vector is 36.86 m.

Vectors are quantities that have both magnitude and direcion

To calculate the x-component of the vector, we use the formula below.

Formula:

Where;

From the question,

Given:

Substitute these values into equation 1

Hence, the x- component of the vector is 36.86 m.

Learn more about vector here: https://brainly.com/question/25705666

[tex]\text{Given that,}\\ \\\text{Power,} ~P=24~ KW = 24000~ W\\\\\text{Force,} ~F=600~N\\\\\text{We know that,}\\\\P=Fv\\\\\implies v = \dfrac{P}{F} = \dfrac{24000}{600}=40~ ms^{-1}\\\\\\\text{It travels at 40 m/s}[/tex]

Answer:

A. An unbalanced force.

Explanation:

There needs to be a net force in order for the nail to be driven into presumably the wall. Without the net force then the hammer and nail wouldn't move.

Answer:

Explanation:

Speed of light v = 3 x 10⁸ m/s

wavelength λ = 8.1 x 10⁻⁸ m

frquency f = v/λ = 3.7 x 10¹⁵ Hz

If a source of light emits photons with a wavelength of 8.1 x 10⁻⁸ meters, then the frequency of the light would be 3.7 × 10¹⁵ Hz, as the wavelength and the frequency of the photon are inversely proportional to each other.

It can be understood in terms of the distance between any two similar successive points across any wave for example wavelength can be calculated by measuring the distance between any two successive crests.

C = λν

As given in the problem if a source of light emits photons with a wavelength of 8.1 x 10⁻⁸ meters, then we have to find out the frequency of the light,

The frequency of the light = 3 × 10⁸ / 8.1 x 10⁻⁸

                                            =3.7 × 10¹⁵ Hz

Thus, the frequency of the light would be 3.7 × 10¹⁵ Hz

To learn more about wavelength, refer to the link given below ;

brainly.com/question/7143261

#SPJ5

The frequency of the 5 waves with a length of 4m hit the shore every 2 seconds is 2.5 Hz.

This is the number of cycles completed by a wave in one second. The s.i

unit of frequency is Hert (Hz).

From the question, to calculate the frequency of 5 waves with length of 4 m that hit the shores every 2 seconds, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The frequency of the wave is 2.5 Hz.

Learn more about frequency here: https://brainly.com/question/254161

[tex]\\ \rm\rightarrowtail F=-kx[/tex]

[tex]\\ \rm\rightarrowtail F=-20(0.03)[/tex]

[tex]\\ \rm\rightarrowtail F=-0.6N[/tex]

Step 1: Define an equation that relates the volume of a sphere to its radius.

V = 4/3*π*r3

Step 2: Take the derivative of each side with respect to time (we will define time as "t").

(d/dt)V = (d/dt)(4/3*π*r3)

dV/dt = 4πr2*dr/dt

Step 3: We are told in the problem statement that diameter is 100m, so therefore r = 50mm. We are also told the radius of the sphere is increasing at a rate of 2mm/s, so therefore dr/dt = 2mm/s. We are looking for how fast the volume of the sphere is increasing, or dV/dt.

dV/dt = 4π(50mm)2*(2mm/s)

dV/dt = 62,832 mm3/s

Answer:

See below.

Explanation:

According to the question, we know that,

work done is given by,  [tex]W=qV[/tex]

and change in kinetic energy is, Δ [tex]KE=W=1=1/2[mv^{2} ][/tex]

therefore equating both the equations we get,

[tex]qV=1/2[mv^{2} ][/tex] ⇒ [tex]V=\frac{mv^{2} }{2q}[/tex]

m= mass of electron =  [tex]9.1*10^{-31} kg[/tex]

q= charge on an electron = [tex]1.6*10^{-19} C[/tex]

v= speed of electron= 700000m/s

substituting the values in the above equation, we get

[tex]V=\frac{9.1*10^{-31} *(700000)^{2} }{2*1.6*10^{-19} } =1.39V[/tex]

(1).  the potential difference that stopped the electron is 1.39 volts.

now the kinetic energy equation is :  2 ways[tex]KE=1/2[mv^{2} ]=\frac{9.1*10^{-31} *700000^{2} }{2} =2.22*10^{-19} J\\[/tex]

or [tex]KE=\frac{2.22*10^{-19} }{1.6*10^{-19} } =1.39eV[/tex]

(2).  the initial kinetic energy of the electron is 1.39eV.

The amplitude of the wave on the given sinusoidal wave graph is 10 cm.

The amplitude of a wave is the maximum displacement of a wave. This is the highest vertical position of the wave from the origin.

Amplitude of the wave is calculated as follows;

From the graph, the amplitude of the wave or maximum displacement of the wave is 10 cm.

Thus, the amplitude of the wave on the given sinusoidal wave graph is 10 cm.

Learn more about wave amplitude here: https://brainly.com/question/25699025