The speeds and the direction of each after the collision:
The proton = -1.692 x 10⁷m/s to the left.
The carbon = 0.3076 x 10⁷ m/s to the right.
The law of conservation of momentumIf there are two object each with masses m₁ and m₂ move with speed v₁ and v₂, then the two objects collide, so after colliding the speed of each object becomes v₁’ and v₂'.
Since there are no external forces acting on the system, then the momentum of the system is conserved, meaning the momentum before and after the same collision.
The equation is:
(m₁)(v₁) + (m₂)(v₂) = (m₁v₁)' + (m₂v₂)'
We have,
velocity of the proton = 2.0 x 10⁷ m/s ⇒ v₁
Mass of the proton = m₁
The velocity of a carbon atom = 0 ⇒ v₂
The mass of the carbon atom = 12 m₁
So, the speeds of proton after the collision:
(m₁)(v₁) + (m₂)(v₂) = (m₁v₁)' + (m₂v₂)'
v₁’ = (m₁ - m₂) / (m₁ + m₂) (v₁)
= (m₁ - 12m₁) / (m₁ + 12m₁) (2.0 x 10⁷)
= (-11 m₁) / (13m₁) (2.0 x 10⁷)
= -1.692 x 10⁷m/s ⇒ it's negative, so to the left.
Now, the speed of the carbon atom after collision:
V₂’ = (2m₁) / (m₁ + m₂)v₁
= 2/13 (2 x 10⁷)
= 0.3076 x 10⁷ m/s ⇒ it's positive, so to the right.
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a truck is traveling east at 30 m/s. it makes a turn and 10.0 s later it is traveling 40 m/s south. what is the average acceleration while making the turn?
The average acceleration of the truck while making the turn is 5 m/s².
Average acceleration is defined as the change in velocity for a particular time interval.
Given that, initial velocity u = 30 m/s towards east = 30 m/s i
Final velocity v = 40 m/s towards south = 40 m/s j
We know the formula for average acceleration as the ratio of change in velocity upon time
⇒ (v - u)/t = (40 j - 30 i)/10 = 4 j - 3 i
The magnitude of average velocity | a'|
| a'| = √3²+4² =√(9 + 16) = √25 = 5 m/s²
Thus, the average acceleration of a truck while making the turn is 5 m/s².
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a fairground ride spins its occupants inside a flying saucer-shaped container. if the horizontal circular path the riders follow has an 8.90 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration 1.50 times that due to gravity? (you do not need to enter any units.)
There are 17.1 revolutions per minute will the riders be subjected to a centripetal acceleration 1.50 times that due to gravity
Acceleration is the rate at which velocity changes over time, both in terms of speed and direction. A point or object travelling in a straight path is accelerated if it accelerates or decelerates. Even if the speed is constant, motion on a circle is accelerated because the direction is always changing.
The centripetal acceleration can be written as: a =
r \sω \s²
Where is the angular velocity. Equating this to the question: r²= 2.25 g
7.00 2 = 2.25 9.81
When we solve for, we get: = 1.78
Angular velocity is defined as the rate of change of angle = 2 T.
Where T is the time span (time for one revolution)
As a result, we can solve for T.
= 3.5
As a result, it completes one rotation every 3.5 seconds. It will finish in one minute:
60 /3.5
= 17.1 rotations.
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A man whoe Ma i 40kg walk up a flight of 20 tep each 150mm height in 10ec. Find the average power developed. (g=10m-2)
A man whose mass is 40kg walk up a flight of 20 step each 150mm height in 10 sec. The average power developed is 12.0 W.
The average power developed by the man as he walks up the stairs, you need to know the work he does and the time it takes him to do it. First, you can find the work done by the man by multiplying his weight (which is equal to his mass multiplied by the acceleration due to gravity) by the distance he travels:
= Work = (40 kg) x (10 m/s^2) x (20 steps x 0.150 m/step)
= 120 J
Then, you can divide the work done by the time it takes to do it to find the average power developed:
= Power = Work / Time
= 120 J / 10 s
= 12.0 W
So, the average power developed by the man as he walks up the stairs is 12.0 W.
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how are radio communications usually affected by the charged particles that reach earth from solar coronal holes?
Charged particle emissions interact with the magnetosphere of the earth to produce geomagnetic storms or disturbances.
Communication systems suffer harm from solar storms. Some radio frequencies are absorbed during geomagnetic storms while others are reflected, resulting in rapidly fluctuating signals and unexpected propagation patterns (reproducing or multiplying in unplanned directions). Amateur and public radio are frequently interfered with. The atmospheric circumstances that radio waves meet, like clouds and precipitation, reflect, absorb, scatter, refute, and diffract them. Importantly, different air conditions have distinct effects on radio waves. A different type of disturbance that might impact radio communications is a coronal mass ejection, or CME. Although in many ways superior to flares, CMEs were not identified until spacecraft were able to study the Sun from orbit.
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what is the frequency of an electromagnetic wave that has the same wavelength as a 3.5 khzkhz sound wave in water?
7.095 × 10⁵ KHz is the frequency of an electromagnetic wave that has the same wavelength as a 3.5 KHz sound wave in water.
What is the frequency?The pace at which current changes direction each second is known as frequency. One hertz (Hz), which is a unit of measurement used internationally, equals one cycle per second. One hertz (Hz) is one cycle every second. A full alternating current or voltage wave is referred to as a cycle.
The number of waves that pass a specific place in a predetermined period of time is known as the wave frequency. A wave passes a fixed point in one hertz (Hz), the SI unit for wave frequency, in one second. A wave with a higher frequency has more energy than a wave with a lower frequency of the same amplitude.
Given that,
frequency = 3.5 KHz
As we know,
V = fλ
As, the electromagnetic wave that has the same wavelength, thus
V/f = constant
Therefore,
V₁/V₂ = f₁/f₂
now, f₁ = (V₁/V₂)× f₂
or, f₁ = [(3 × 10⁸) / 1480] × (3.5 × 10³)
or, f₁ = 7.095 × 10⁸ Hz
or, f₁ = 7.095 × 10⁵ KHz.
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the cosmic microwave background is almost perfectly uniform in all directions, except for very small deviations in its temperature. what do scientists think these small deviations represent?.
a. varying redshift and blueshift due to motions of gas in the early universe
b. region of slightly higher helium abundance in the early universe
c. the warmer spots represent regular matter and the cooler spots represent dark matter
d. regions of slightly density that made it possible for galaxies form
In a case whereby cosmic microwave background is almost perfectly uniform in all directions, except for very small deviations in its temperature. what the scientists think these small deviations represent is d. regions of slightly density that made it possible for galaxies form.
What is the cosmic microwave background?The Cosmic Microwave Background can be descibed as the cooled remnant of the first light which could ever travel freely throughout the Universe it can be seen as the 'fossil' radiation, which an be considered as the furthest that any telescope can see.
It should be noted that the density i can be of two types, whereby one is absolute density, and the other is relative density hgowever the Relative density can be described as the specific gravity, and this is the ratio of the density of a material to the density of reference material.
Therefore, option D is correct.
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some time later, kid a was spinning with the same speed that kid c had originally. what would kid a's centripetal acceleration be if his distance from the center of the merry-go-round was r
Centripetal refers to “center-seeking” Quantifies the change in directionof the velocity The acceleration is directed toward the center of the circle of motion.
The magnitude of the centripetal acceleration is given by V^2/r, the direction is toward the center of the circle. The tangential component of the acceleration is due to changing speed. The centripetal component of the acceleration is due to changing direction.
When an object is rotating at a constant angular velocity, the whole object has a constant angular velocity. Therefore, every mint on the turntable has the same, constant angular velocity.
The acceleration which causes the tangential velocity to change direction is called Centripetal acceleration. Centripetal acceleration is always in toward the center of the circle.
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a rock is rolled in the sand. it starts at 5.0 m/s, moves in a straight line for a distance of 3.0 m, andthen stops. what is the magnitude of the average acceleration?
The magnitude of the average acceleration is [tex]4.2 m/s^{2}[/tex].
Acceleration is the rate of change of an object's velocity with respect to time. Acceleration is a vector quantity (as long as it has magnitude and direction). The direction of an object's acceleration is given by the direction of the net force acting on that object.
As described in Newton's second law, the magnitude of an object's acceleration is the combined effect of two sources.
-The mass of this object is inversely proportional to the mass of the object.
-Depending on the material from which it is made.
Calculation :
Use the equation of linear motion:
[tex]v^{2} =( v_{0} )^{2} = 2a(x-x_{0} )[/tex]
Therefore
[tex]v = 0 m/s[/tex] - final velocity is zero
[tex]v_{0} = 5.0 m/s[/tex] - greater than initial Velocity
[tex]x - x_{0} = 3.0m[/tex] - this is the displacement.
now, a is what you are looking for.
[tex]0 = 5^{2} + 2a*3[/tex]
[tex]-25 = 6a[/tex]
[tex]a = \frac{-25}{6}[/tex]
[tex]a = -4.2 m/s^{2}[/tex]
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4. A 2.00 kg object is accelerated uniformly from rest to 3.00 m/s while moving 1.5 m across a
level frictionless surface. Calculate the power output.
The power output of 2.00 kg object is accelerated uniformly from rest to 3.00 m/s while moving 1.5 m across a level frictionless surface is 24.09 watts.
What is power?In science, power is the time required to do work or provide energy, expressed as work done W or energy transferred divided by the time interval t - or W/t. A fixed amount of work can be done for a long time with a low-powered engine, or for a short time with a high-powered engine. The unit of power is work (or energy) per unit of time. Such as foot pounds per minute, joules (or watts) per second, and ergs per second. Force can also be expressed as the product of the force required to move an object and the object's velocity in the direction of the force. If the magnitude of the force F is measured in pounds and the velocity ν is measured in feet per minute, then the power is equal to Fν foot pounds per minute.
Given,
Mass of object (m) = 2.00 kg
Distance covered (s) = 1.5 m
Velocity of object (v) = 3.00 m/s
For calculation of acceleration:
v² = u² + 2as
3² = 0 + 2 × a × 1.5
9 = 3a
a = 2 m/s²
For calculation of time:
s = ut + ¹/₂at²
1.5 = 0 × t + ¹/₂ × 2 × t²
1.5 = t²
t = 1.22 sec.
For calculation of gravitational force:
F = mg
F = 2 × 9.8
F = 19.6 N
For calculation of work done:
W = F × s
W = 19.6 × 1.5
W = 29.4 J
For calculation of power output:
P = W/t
P = 29.4/1.22
P = 24.09 watts
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you are raising a flag on a flagpole. you apply 2 kg of force to the rope to raise the flag 10 meters in 5 seconds. the amount of power you expend doing so is
Typically, pulleys are used to raise objects, particularly heavy objects. The load is the thing that a pulley lifts. The effort is the force delivered to the pulley.
The first weight to be lifted up, if the man exerts enough force (T), is the one whose force of gravity (mass times g) is exceeded by 2T. Weights do matter since the force of gravity is proportional to mass; the lightest weight rises first. To lift the bucket out of the well, pulley systems are used. Pulleys are essential to the operation of numerous forms of workout equipment. Heavy materials can be lifted and moved using construction pulleys.
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a proton is accelerated by a uniform 360 n/c electric field. find the kinetic eergy and the velocity of the proton after it has traveled 50
The kinetic energy is 2.88 × 10-17 J and the velocity of the proton will be 180 m/s
The kinetic energy of the proton is given by
KE = qV = (1.60217662 × 10-19 C) (360 N/C) (0.50 m)
= 2.88 × 10-17 J, The velocity of the proton is given by:
V = (360 N/C) (0.50 m) =0.360 x 0.50 = 0.180 m/s .
This means that after the proton has traveled 50 cm, it will have a kinetic energy of 2.88 × 10-17 J and a velocity of 180 m/s. This result is because the electric field is uniform and constant, and the proton is accelerated by the same amount throughout its journey. This means that the velocity and kinetic energy of the proton will increase linearly with the distance traveled. The electric field provides the proton with a constant acceleration, and as the proton travels further, it gains more kinetic energy and a higher velocity.
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a thin rod of mass m and length l is suspended vertically from a frictionless pivot at its upper end. a mass m of putty traveling horizontally with a speed υ strikes the rod at its cm and sticks there. Explain why the intial angular momentum is what it is?
The rotating equivalent of linear momentum in physics is called angular momentum, also known as moment of momentum or rotational momentum.
Conservation of Angular Momentum m v (L/2) = I w => w^2 = m^2 v^2 L^2/(4 I^2)---------eq1
Conservation of Energy (1/2) I w^2 = (m + M)g h----------------eq2 where h = height of the center of mass
Relate h to h': h' = height from the bottom a= angle between rod and the normal
(L/2 -(L/2) cos(a)) = h (L - L cos(a))=h' => h=h'/2--------------------------eq3
Compute I=moment of inertia I=m(L/2)^2 + (1/12) M L^2 + M(L/2)^2 I= [(L^2)/4](m + 4M/3)------------------eq4
Plug eq1 and eq3 into eq2 (1/2) I m^2 v^2 L^2/(4 I^2) = (m + M)g h'/2 Solve for h' h'=m^2 v^2 /((m + M)g)
Then use eq4 to get the final result h'=m^2 v^2 /((m + 4M/3)(m + M)g)
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a 5.0 kg cat and a 2.0 kg bowl of tuna fish are at opposite ends of the 4.0-m-long seesaw of figure ex12.31. how far to the left of the pivot must a 4.0 kg cat stand to keep the seesaw balanced?
The 4.0-m-long seesaw has a 5.0-kg cat and a 2.0-kg bowl of tuna fish at either end. To keep the seesaw balanced, a 4.0 kg cat must stand 1.5m to the left of the pivot.
Given length of seesaw (l) = 4m
Mass of first cat (m1) = 5kg
Mass of tuna fish (m) = 2kg
Mass of second cat (m2) = 4kg
Let the second cat is at a distance to the left of pivot = d
To keep the seesaw balanced we apply net momentum or torque theorem at pivot.
Torque net about pivot = 0
The pivot is situated at middle of seesaw so the distance from first cat to seesaw and from fish to seesaw = 2m
Force acted on first cat (F1) = m1xg = 5x9.8 = 49N
Force acted on second cat (F2) = m2xg = 4x9.8 = 39.2N
Force acted on tuna fish (F3) = mxg = 2x9.8 = 19.6N
Tourque(T) = force x distance (perpendicular)
Tnet= 49X2 - 39.2Xd - 19.6x2 = 0
58.8 = 39.2d
d = 1.5m
Hence the distance from the left of pivot where the second cat to be situated is 1.5m
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Wwhat was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?
The speaker's power output is 785.398 W assuming uniform spherical spreading of the sound and neglecting absorption in the air.
Given the Sound Intensity = I and
the Loudspeaker Distance = r = 2.5m
Sound level produced(β) : 130 dB
The formula for calculating sound intensity is:
β = 10logI/I0
130 = 10logI/10-12
13 = logI/10-12
10^13x10^-12 = I
I = 10 W/m^
A = area, hence power (P) = IA = 4πr^2
P = 10X 4X 3.14X (2.5)^
P = 785.398W
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At a rock concert, a dB meter registered 130 dB when placed 2.5 m in front of a loudspeaker on stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?
an object in free fall has a speed of 60 m/s. one second later its speed is
An object in free fall has a speed of 60 m/s. One second later its speed is 70m/s.
We're asked to find the speed of an object in free fall one second after it has a speed of 60m/s. An object in free fall means that the only force affecting its motion is gravity. To do this, we can use the equation
vy=v°y+ayt
where:
vy is the velocity at time (what we're trying to find) voy is the initial velocity (60m/s in this case, because it's assumed to be travelling downward, which is taken to be the negative y- axis) ay is the acceleration, equal to -g, which is 9.81m/s is the time, which in this case is 1 second.Plugging in known values, we have Vy=60m/s(9.81m/s²)(1s) =-70m/s rounded to 2 (or 1, technically) significant figures.
This the velocity of the object (which is why it includes a sign). The speed is simply the magnitude of this, which is a positive quantity.
speed = 70m/s
You also could have solved this problem neglecting the signs of the initial velocity and acceleration in the above equation:
speed = 60m/s +(9.81m/s²)(1s) = 70m/s
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Disregarding air resistance, what is the speed of a ball dropped from 12 feet just before it hits the ground? (Use 1 ft = 0.30 m, and use g = 9.8 m/s2.)
2.4 m/s
8.4 m/s
10.8 m/s
15.3 m/s
Answer:
[tex]8.4\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
Let [tex]x[/tex] denote the displacement of the ball. It is given that [tex]x = 12\; {\rm ft}[/tex]. Apply unit conversion and ensure that the displacement [tex]x\![/tex] of the ball is measured in meters:
[tex]\begin{aligned}x &= (12\; {\rm ft})\, \frac{(0.30\; {\rm m})}{(1\; {\rm ft})} = 3.6\; {\rm m}\end{aligned}[/tex].
Let [tex]u[/tex] denote the initial velocity of the ball, and let [tex]v[/tex] denote the velocity of the ball right before it hits the ground. Note that since the question states the ball was "dropped", assume that the ball was initially at rest with initial velocity [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex].
Under the assumptions, the acceleration [tex]a[/tex] of the ball will be constantly [tex]a = g = 9.8\; {\rm m\cdot s^{-2}[/tex].
Rearrange the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] to find the final velocity [tex]v[/tex] of the ball right before landing:
[tex]\begin{aligned}v &= \sqrt{u^{2} + 2\, a\, x} \\ &= \sqrt{(0\; {\rm m\cdot s^{-1}})^{2} + 2\, (9.8\; {\rm m\cdot s^{-1}})\, (3.6\; {\rm m})} \\ &= 8.4\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Answer: B (8.4 m/s)
Explanation:
if you represented earth's history by a line that is 2 m long, how long a segment (in cm) would represent the 400 million years since life moved onto the land?
If you represented earth's history by a line that is 2 m long then, the segment length in 400 million years will be 43.2 cm.
The entire history of the Earth is represented by a line 5 meters long.
The age of the Earth is 4.6 billion years.
That means a length of 5 meters or 500 cm (1m = 100cm, so 5m = 5× 100 = 500 cm) represents 4.6 billion years, i.e 4600million years. (As 1 billion years = 1000 million years)
We have to calculate the length of the segment for 400 million years.
In 4600 million years, the segment length is = 500 cm
In 1 million years, the segment length will be = 500 / 4600 = 0.108 cm
In 400 million years, the segment length will be = 0.11 × 400 = 0.108 × 400 = 43.2 cm
Therefore, the segment length in 400 million years will be 43.2 cm.
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a falling coconut has a mass of 3.5 kg and an upward force of air resistance of 12 n. a) calculate the net force on the coconut as it falls
The coconut is subject to a downward force of 1.47 N from gravity. The gravitational pull of the tree causes a coconut to fall from it.
The gravitational pull is both an attracting and non-contact force. The coconut consequently falls from the tree. Given that palm trees may reach heights of up to 30 meters (98 feet) over, or the equivalent of an 8-story building, a coconut can fall at a rate of up to 85 kilometers per hour (53 mph). Accordingly, the force of the coconut as it lands on the ground is equal to a ton of weight.
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the gas in a cylynder absorbs 850 kj of heat, and the subsequent expansion does 455 kj of work on the surroundings. what is the change in the systems internal energy
The change in the systems internal energy is 400KJ.
ΔE = Q - W
but, Qin > 0
Win < 0
ΔE = 850 - 450 = 400KJ
As with the static rest mass energy of its constituent matter, the internal energy cannot be readily measured, and knowledge of all of its components is rarely interesting. In contrast to its absolute value, the internal energy is only primarily concerned with changes in thermodynamics. Instead, it is typical to specify a reference state and gauge how a thermodynamic process differs from this state. Matter is transferred, energy is released as heat, or thermodynamic work is performed to change the internal energy. The system's attributes, including changes in temperature, entropy, volume, and molar composition, are used to measure these processes. The system is referred to as closed when matter transfer is inhibited by impermeable containment walls. Neither matter if the confining walls fail.
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a traveller covers1.2km distance in 5 min calculate its average velocity
Answer: Average Velocity = Distance/Time
Average Velocity = 1.2km/5min
Average Velocity = 0.24km/min
Therefore, the average velocity of the traveller is 0.24km/min.
is there an angle of incidence between 0∘ and 90∘ such that all of the light will be reflected?
A beam of light in the air encounters a transparent block with index of refraction n=1.53. Some of the light is reflected and some is refracted. There will be no such angle of incidence between [tex]$0^{\circ}$[/tex] and [tex]$90^{\circ}$[/tex] such that all of the light will be reflected.
In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the normal, or line perpendicular to the surface at the point of incidence. Any type of wave, including microwave, X-ray, optical, and acoustic, may create a ray.
The refractive index of an optical medium is a dimensionless quantity that indicates how well that medium bends light in optics. The refractive index controls how much light is refracted or twisted when it enters a substance.
[tex]\begin{aligned}\mu & =\frac{1}{\sin c} \\c & =\sin ^{-1}\left(\frac{1}{\mu}\right) \\& =\sin ^{-1}\left(\frac{1}{1.53}\right) \\& =40.83\end{aligned}[/tex]
First condition it should be remembered that if the incident angle is from denser medium to rarer medium at or greater than [tex]$40.33^{\circ}$[/tex], all light will be reflected but in this Question, the condition is the opposite.
Hence, there should not be such an angle.
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The complete question should be:
A beam of light in the air encounters a transparent block with index of refraction n=1.53. Some of the light is reflected and some is refracted.
Is there an angle of incidence between [tex]$0^{\circ}$[/tex] and [tex]$90^{\circ}$[/tex] such that all of the light will be reflected?
(a) Yes, at an angle greater than [tex]50^{\circ}[/tex]
(b) Yes, at an angle less than [tex]50^{\circ}[/tex]
(c) No.
A table tennis ball is dropped onto the flour from a height
€ 4m and It rebounds to a height of 3m. If the time of
ontact with the floor is o.ols, what is the magnitude and
irection of the acceleration during the contact.
The acceleration of the ball during the contact is 1652 m/s^2 in upward direction.
What is acceleration?
Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
The velocity of the ball before hitting the floor in downward direction:
u = √(2gs)
= √(2×9.8×4) m/s
= 8.85 m/s.
The velocity of the ball after hitting the floor in upward direction:
v = √(2gs)
= √(2×9.8×3) m/s
= 7.67 m/s.
Hence, the acceleration of the ball during the contact in upward direction is: a = change in velocity/time duration
= (7.67 - (-8.85))/0.01 m/s^2
= 1652 m/s^2
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A man wishes to throw two darts one by one at the target at B with same speed so that they arrive at the same time. Mark the correct statements about the two projections.
If the darts are thrown at the same speed then (b) Projectile that travels along trajectory B was projected earlier and (c) Second dart must be projected at angle, such that 0 + 0,8 = 90° is correct.
Initial speed of dart A = u'
Angle of dart A = θ'
Initial speed of dart B = u''
Angle of dart B = θ''
The initial speed of both the darts is same,
Thus, u' = u'' = u
The darts are projected from same point A but not at same time; they are thrown one by one. But they travel same horizontal distance and reach B at the same time.
Since the horizontal range of both darts are same,
= [ u²sin(2θ') / g ] = [ u²sin(2θ'') / g ]
= sin(2θ') = sin(2θ'')
Now, θ' is not equal to θ'', through the figure we can assume that θ'' > θ'
Since both are acute angles,
= sinθ'' > sinθ'
Multiplying both sides by 2u/g, we get,
= [ 2u X sinθ'' / g ] > [ 2u X sinθ' / g ]
which means, trajectory T of both the darts is as:
= T'' > T'.
Thus, statement B and C are correct options.
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The complete question:
A man wishes to throw two darts one by one at the target at B with same speed so that they arrive at the same time. Mark the correct statements about the two projections. Trajectory B Trajectory A А. B (A) Projectile that travels along trajectory A was projected earlier (B) Projectile that travels along trajectory B was projected earlier. (C) Second dart must be projected at angle e, such that 0 + 0,8 = 90° (D) Second dart must be projected at angle , >, STA
a solid sphere of mass m and radius r rolls without slipping along a table at speed v. what is its kinetic energy? (given for solid sphere i
The kinetic energy of a solid sphere is (1/2)mv² + [(2/5)mr²] × ω² × r for having mass m and radius r rolls without slipping.
We know that if property of sphere is defined, it means that linear and rotational kinetic energy is possible.
For rotational energy, we need to know about moment of inertia and angular acceleration.
For solid sphere moment of inertia is given by the expression=(2/5)mr² where m is the mass and r is the radius of the sphere
Now, we know that for angular acceleration we need angular velocity which can be calculated by the linear velocity which can be calculated by the formula
v=ω×r where v is the linear velocity ,ω is angular velocity and r is the radius of the object.
So,ω=v/r
Now we know that angular acceleration(α)=ω² × r
Therefore, rotational energy is =I × α = [(2/5)mr²] × ω² × r
Now, we know that kinetic energy is given by =(1/2)mv² where m is the mass and v is the velocity of a solid sphere.
So, kinetic energy of sphere is =linear kinetic energy + rotational kinetic energy
=>kinetic energy = (1/2)mv² + [(2/5)mr²] × ω² × r
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Determine how much heat needs to be transferred to 1 kg of ice at -10C to turn it into water at 15C. The specific heat capacities of ice and water are 2.1 and 4.2 kJ, respectively, the specific heat of melting of ice is 330 kJ/kg
Answer: If you drop ice into hot water will result in the ice melting
Explanation:
the system moves upward with a constant velocity of 10 ft/s. what is the reading on the bathroom scale (in pounds)
The reading on the bathroom scale is W = 230 lbs.
Solution:
Since acceleration is zero, so weight remains the same on scale
W = 230 lbs
Acceleration is the rate of change of velocity over time, both in terms of velocity and direction. A point or object moving in a straight line accelerates as it accelerates or decelerates. Circumferential motion is accelerated because it always changes direction even at constant velocity.
Acceleration is the change in velocity over time. Whenever a change in velocity or acceleration in the direction of movement occurs. At constant velocity, acceleration is zero. Deceleration is called negative acceleration or deceleration.
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SOMEONE PLEASE HELP ME!!!
The velocity-time graph for an object is shown. How can the total displacement of the object be determined?
Answer:
Below
Explanation:
The area under the graph will represent the displacement .
Remember displacement = velocity * time
so the total displacement will be Area 1 - Area 2
what produces the retrograde motion of mars, and what geometric arrangements did ptolemy use to explain this motion?
Due of Earth's far bigger orbit than Mars', as Earth passes it, Mars seems to be going backwards. Ptolemy postulated that planets orbited on epicyles that revolved around deferents to explain this.
Mars experiences retrograde motion when Earth, which moves more quickly than Mars, passes it. Due to this, Mars seems to move westward in retrograde motion, which is the real or apparent travel of a body in a direction that differs from that of the majority of solar system members' (direct) movements or the motion of other astronomical systems with a preferred direction of motion. All of the planets, with the exception of Venus and Uranus, rotate counterclockwise on their own axes as seen from a location in space north of the solar system (from a large distance above the North Pole of the Earth). Venus and Uranus, therefore, exhibit retrograde rotation. Fewer than half of the known satellites of the planets exhibit retrograde rotation.
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a thin nonconducting rod with a uniform distribution of positive charge q is bent into a circle of radius r. the central perpendicular axis through the ring is a z axis, with the origin at the center of the ring.
Answer:
E max
=3.46×10
7
N/C
Explanation:
If the radius and charge are R and Q. We need to calculate the electric field due to the rod. Using formula of electric field. Where, Q = charge. z = distance. If z = 0, Then, The electric field is (b). If z = ∞, z>>R. So, R = 0. Then, the electric field is (c). In terms of R, We need to calculate the positive distance. If . Then, Taking only positive distance (d).
what happens if the woman suddenly slides closer to the hub by 0.400 m? (select all that apply.)
The new net torque is in the opposite direction and hhas greater magnitude than that of previous.
What is torque?The force that can cause an object to rotate along an axis is measured as torque. Similar to how force accelerates an item in linear kinematics, torque accelerates an object in an angular direction.
A vector quantity is a torque. The force acting on the axis determines the direction of the torque vector.
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