(a) The frequency of the motion after the collision is 0.71 Hz.
(b) The maximum angular displacement of the motion after the collision is 16.3⁰.
Speed of the 2.2 kg ball when it collides with 2.7 kg ballThe speed of the 2.2 kg ball which was initially 10 cm higher that 2.7 kg ball is calculated as follows;
K.E = P.E
¹/₂mv² = mgh
v² = 2gh
v = √2gh
v = √(2 x 9.8 x 0.1)
v = 1.4 m/s
Final speed of both balls after collisionThe final speed of both balls after the collision is determined from the principle of conservation of linear momentum.
Pi = Pf
m₁v₁ + m₂v₂ = vf(m₁ + m₂)
2.2(1.4) + 2.7(0) = vf(2.2 + 2.7)
3.08 = 4.9vf
vf = 3.08/4.9
vf = 0.63 m/s
Maximum displacement of the balls after the collisionP.E = K.E
[tex]mgh_f = \frac{1}{2} mv_f^2\\\\h_f = \frac{v_f^2}{2g} \\\\h_f = \frac{(0.63)^2}{2(9.8)} \\\\h_f = 0.02 \ m[/tex]
Maximum angular displacementThe maximum angular displacement of the balls after the collision is calculated as follows;
[tex]cos \theta = \frac{L - h_f}{L} \\\\cos\theta = \frac{0.5 - 0.02}{0.5} \\\\cos\theta = 0.96\\\\\theta = cos^{-1}(0.96)\\\\\theta = 16.3 \ ^0[/tex]
Frequency of the motion[tex]f = \frac{1}{2\pi} \sqrt{\frac{g}{L} } \\\\f = \frac{1}{2\pi } \sqrt{\frac{9.8}{0.5} } \\\\f = 0.71 \ Hz[/tex]
Learn more about maximum angular displacement here: https://brainly.com/question/13665036
6. A spring is originally 1.5 m long. It is stretched so that it is 1.8 m long. The spring constant is 50 N/m.
Find the potential energy stored in the spring.
Answer:
PE = 1/2 K X^2
K = 50 N/m
X = .3 m
PE = 1/2 * 50 * .3^2 = 2.25 Joules
Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 105 kg·m2. When one person is standing at a distance of 1.57 m from the center, the carousel has an angular velocity of 0.512 rad/s. However, as this person moves inward to a point located 0.507 m from the center, the angular velocity increases to 0.795 rad/s. What is the person's mass?
For one person standing at a distance of 1.57 m from the center, the carousel has an angular velocity of 0.512 rad/s, the person's mass is mathematically given as
m = 24.2 kg
What is the person's mass?Generally, the equation for the conservation angular momentum is mathematically given as
(I + m * r0^2) * w0 = (I + m * r^2) * w^2
Therefore
(105 + m * 1.78^2) * 0.517 = (105 + m * 0.524^2) * 0.841
m = 24.2 kg
In conclusion, the mass
m = 24.2 kg
Read more about Mass
https://brainly.com/question/4931057
Which point on the graph would have the most kinetic energy?
-Which point on the graph would have the least kinetic energy?
-What point on the graph would have just a little less potential energy than point E?
-What point on the graph would have just a little more potential energy than point F?
-What point on the graph would have just a little less potential energy than point G?
The total mechanical energy is kinetic energy + potential energy, so we can look at the object's potential energy to determine the place where it has maximum and minimum kinetic energy.
Potential energy is determined by the equation PE = mgh, where the height is the only changing variable here. Therefore, we look at the height to answer these questions.
Which point on the graph would have the most kinetic energy?
The point where the object's potential energy is the lowest, aka where its height is the lowest. Point D would have the most kinetic energy.Which point on the graph would have the least kinetic energy?
The point where the object's potential energy is the highest, aka where its height is the highest. Point A would have the least kinetic energy.What point on the graph would have just a little less potential energy than point E?
Look at the point that is just below point E. Point D has just a little less potential energy than point E.What point on the graph would have just a little more potential energy than point F?
Look at the point that is just above point F. Point B has just a little more potential energy than point F.What point on the graph would have just a little less potential energy than point G?
Look at the point that is just below point G. Point B has just a little less potential energy than point E.The two basic properties of all matter are ______ and ______.
options for first blank
a. length B. volume
options for second blank
a. density B. mass
Answer:
volume , mass
Explanation:
the 3 basic properties of a matter is volume, mass and shape.
PLEASE HELP I WILL MARK BRAINLIEST
A 0.14 kg baseball is dropped from rest. It has a momentum of 0.78 kg.m/s just before it lands on the ground. For what amount of time was the ball in the air?
Answer:
0.568
Explanation:
velocity = -9.8 (t) + Vo
Vo= 0 so v= 9.8(t)
Momentum = mass x velocity
v * 0.14 kg = 0.78 kg m/s
v = 5.571 m/sec
v= 9.8(t) , so substituting v we get , 5.571 = 9.8 * t
t = 5.571/9.8 = 0.568 seconds
A DJ is setting up their equipment and measures the sound level near a speaker to be 55.65dB. They decide to add two more speakers next to the first. What would they measure the new sound level to be?
For a DJ is setting up their equipment and measures the sound level near a speaker to be 55.65dB, the new sound level is mathematically given as
L=50.470dB
What would they measure the new sound level to be?Generally, the equation for the sound level is mathematically given as
l=10logl/io
Therefore
logl/io=5.57
Hence
I=3.715*10^−8
In conclusion
L'=10log(3*3.715*10^−8)/10^{-12}
L=50.470dB
Read more about Energy
https://brainly.com/question/13439286
6. When can you say that an object is accelerating?
A. when the speed remains the same
B. When the speed is changing
C. when the instantaneous velocity is the same
D. When there is a uniform motion
give explanation
Answer:
When the speed is changing is the correct answer
Explanation:
Because acceleration is rate of change of velocity
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
If the intensity of radiation from an x-ray tube at 2 feet is 100 mR/min, the intensity at a distance of 5 feet will
be?
Answer:
100 mR
Explanation:
[tex]Question: $x_{1}=\frac{5}{2}[\sin (2 \pi t)+\cos (2 \pi t)], x_{2}=5\left[\sin \left(2 \pi t+\frac{\pi}{4}\right)\right]$[/tex]
Find the ratio of the amplitude of the given motion?
Options:
[tex](a) $\sqrt{2}: 1$\\(b) $2: 1$\\(c) $1: \sqrt{2}$\\(d) $1: 2$[/tex]
Condense x₁ to get
sin(2πt) + cos(2πt) = √2 • (sin(2πt) + cos(2πt))/√2
… = √2 (cos(2πt) cos(π/4) + sin(2πt) sin(π/4))
… = √2 cos(2πt - π/4)
So the amplitude of x₁ is (5/2) • √2 = 5/√2, while the amplitude of x₂ is 5. The ratio between them is then 5/√2 : 5, or equivalently 1/√2 : 1 or 1 : √2.
The surface of a lake has an area of 15.5 km2. What is the area of the lake in m2?
Answer:
1.55 x 10⁷ m²
Explanation:
Unit conversion
km² → m² 1 km² = 10⁶ m²Solving
15.5 km² = 10⁶ x 15.5 m²155 x 10⁵ m²1.55 x 10⁷ m²What is the cycle of a breaststroke?
Answer:
Breaststroke can be divided up into 4 distinct phases, which consists of the out sweep, in sweep, breathing phase, and lunge, extension, or recovery phase.
Explanation:
pa follow po
The force of a hammer drives a nail into wood. This is an example of. A. An unbalanced force. B. Gravitational force. C. Friction. D. Balanced forces
Answer:
What i got was A. An unbalanced force.
Hope This Helps
1. A person walks 20 meters toward the east and then walks 30 meters toward the west. What is the total distance covered? What is the displacement? with explaination
2. What is the average speed of a car that travels 2000 meters in 5 minutes in meters/second? with explaination
Answer:
1.) 30 m is the total distance covered 10m is the displacement you
2.)24,000m/h (24km/h or 6.67m/s) Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance
Explanation:
The diagram shows a heating curve for water.
Which statement best describes what is happening at
segment W-X?
Heating Curve for Water
O Water is absorbing heat.
O Water is releasing heat.
O Aliquid is changing to a gas.
O A gas is changing to a liquid.
z
110
100
90
x
х
Y
80
Temperature (Cº)
70
60
50
40
w
Heat (J)
Answer:
a water is heating up
Explanation:
the water's temperature is inceasing
For the statements based on whether they are described as outcomes of results from thermal energy being added or removed particles move faster particles move slower temperature increases temperature decreases kinetic energy increases kinetic energy decreases thermal energy added thermal energy removed
Which statement about the interference behavior of electromagnetic radiation seen in the double-slit test experiment is true? (1 point)
O Waves that make up the radiation collide with each other so that they add together or cancel each other out.
O Particles that make up the radiation collide with each other so that they add together or cancel each other out.
O Particles that make up the radiation collide with each other and scatter randomly.
O Waves that make up the radiation do not interact with each other.
Waves that make up the radiation collide with each other so that they add together or cancel each other out.
What is Interference?This is the phenomenon which occurs when two waves meet while traveling along the same medium.
In the double-slit test experiment, bright and dark fringes was observed which was caused by the superposition of overlapping light waves originating from the two slits which is why option A was chosen as the most appropriate choice.
Read more about Interference here https://brainly.com/question/9655287
Spring
The pulling force acting on an object is 350.0 N. It also is being affected by a 50.0 N
kinetic friction force. As a result, its acceleration is 3.0 m/s?, what is its mass?
A. 67 kg
B. 83 kg
C. 100 kg
D. 600 kg
E. 0.0 kg
If the gravitational force of the Farth nulling you"down" in th
Answer:
100 kg
Explanation:
Net force = 350 - 50 = 300 N
F= ma
300 N = m * 3 m/s^2
100 kg = mass
The sound intensity at a distance of 19 m from a noisy generator is measured to be 0.24 W/m2. What is the sound intensity at a distance of 27 m from the generator
Answer:
0.1111 W/m²
Explanation:
If all other parameters are constant, sound intensity is inversely proportional to the square of the distance of the sound. That is,
I ∝ (1/r²)
I = k/r²
Since k can be the constant of proportionality. k = Ir²
We can write this relation as
I₁ × r₁² = I₂ × r₂²
I₁ = 0.25 W/m²
r₁ = 16 m
I₂ = ?
r₂ = 24 m
0.25 × 16² = I₂ × 24²
I₂ = (0.25 × 16²)/24²
I₂ = 0.1111 W/m²
Loosing weight without diet require moving to the top of a mountain explain using weight and gravitational force
Answer:
You would weigh very slightly more at sea level than at the top of a mountain, not enough for you to notice, but a measurable amount. Weight, which really means gravitational force, is proportional to the product of the masses of two objects acting on each other, in this case the giant earth and the minuscule you.
Explanation:
A 3 Hz wave has a wavelength of 0.4 m. Calculate the speed of the wave (in m/s).
The speed of the wave with the given frequency and wavelength is 1.2m/s.
Given the data in the question;
Wavelength of the wave; [tex]\lambda = 0.4m[/tex]Frequency; [tex]f = 3Hz = 3s^{-1}[/tex]Speed of the wave; [tex]v = \ ?[/tex]WavelengthWavelength is the distance over which the shapes of waves are repeated. It is the spatial period of a periodic wave.
It is expressed as;
[tex]\lambda = \frac{v}{f}[/tex]
Where v is velocity/speed and f is frequency.
Now, we can easily get the speed of the wave by substituting our given values into the expression above.
[tex]\lambda = \frac{v}{f} \\\\0.4m = \frac{v}{3s^{-1}}\\ \\v = 0.4m * 3s^{-1}\\\\v = 1.2ms^{-1}\\\\v = 1.2m/s[/tex]
Therefore, the speed of the wave with the given frequency and wavelength is 1.2m/s.
Learn more about Speed, Frequency and Wavelength here: brainly.com/question/27120701
The Empire State Building is about 381m high. If you threw a baseball downward at 25 m/s from the top of the building how fast would it be traveling just before it landed?
Answer:
Explanation:
You can use that [tex]v = v_{o}+gt[/tex] or [tex]v^{2}=v_{o}^{2}+2gh=(25)^{2}+(2)(10)(381)=8245 \rightarrow v \approx 90.8[/tex] m/s.
The measured value of mass M in an experiment is M = 0.743 ± 0.005kg. The error in 2M is
Select one:
dM
3dM
2.5 dM
2dM
Given the measured value of mass M in the experiment the error in 2M is ; dM
Given data :
Measured value of mass M = ( 0.743 ± 0.005 ) kg
The error in 2M in the measured valueThe error in 2M in the measured value M = 0.743 ± 0.005 kg is dM while the error in M² will be 2dM
Hence we can conclude that the measured value of mass M in the experiment the error in 2M is ; dM.
Learn more about error in 2M : https://brainly.com/question/6650225
the dimensions of a cuboidal block are 2.5 m * 2m * 1.2m its weight 900 n what is the minimum presseure exerted by the block on the surface of its support.?
Answer:
your answer is here 180
Explanation:
900/2.5 * 2 = 180
Answer:
The answer is 180 Pa.
Explanation:
Given;Here, weight = thrust = 900 N,
dimensions are 2.5 m × 2 m × 1.2 m
To Find;Pressure exerted by the block on the surface of its support.Formula;Pressure = Thrust ÷ AreaWe know that, Pressure is inversely proportional to area. For the minimum pressure the area must be more.
So, if the block is resting with 2.5 m × 2 m surface on the support, the pressure will be minimum.
Pressure = 900 N ÷ 2.5 × 2.0 m² = 180 Pa
Thus, The pressure exerted by the block on the support is 180 Pa.
.
Which of the following is not true about the lymphatic system?
it drains white blood cells away from tissue
it brings nutrients to the tissue
it builds muscle cells
it fights infection
Answer:
it builds muscle cells
Explanation:
took test
If electromagnetic radiation acted like particles in the double-slit experiment, what would be observed? (1 point)
O A series of light and dark bands would appear on the screen.
O Two bright bands would appear on the screen in line with the slits.
O The screen would remain dark because no radiation would reach the screen.
O One bright band would appear in the center of the screen.
If electromagnetic radiation acted like particles in the double-slit experiment, we would observe one bright band would appear in the center of the screen.
Bahavior of particles in double-slit experimentIn a double-slit experiment, single particles, such as photons, pass one at a time through a screen containing two slits.
The photons behave like wave and the constructive interfernce of the waves of these photons will generate a high amplitude wave seen as a bright band in the center of the screen.
Thus, if electromagnetic radiation acted like particles in the double-slit experiment, we would observe one bright band would appear in the center of the screen.
Learn more about double slit experiment here: https://brainly.com/question/4449144
If a→=3i^-2j^-k^ and b→=i^+4j^+k^, find a unit vector n^ normal to the plane containing a→ and b→ such that a→, b→ and n^, in this order, form a right-handed system.
The unit vector normal to the plane is ; n = [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]
Given data :
The unit vectors
a→=3i^-2j^-k^ and b→=i^+4j^+k^
Determine the unit vector normal to the planeThe unit vector normal to the plane is calculated as
n = [tex]\frac{a*b}{|b*b|}[/tex] ---- ( 1 )
where ; a→ * b→ = 2i - 4j + 14k and |b * b| = [tex]\sqrt{216}[/tex]
back to equation ( 1 )
n = ( 2i - 4j + 14k ) / [tex]\sqrt{216}[/tex]
= [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]
Hence we can conclude that The unit vector normal to the plane is ; n = [tex]\frac{i}{\sqrt[3]{6} } - \frac{2j}{\sqrt[3]{6} } + \frac{7k}{\sqrt[3]{6} }[/tex]
Learn more about unit vector : https://brainly.com/question/1615741
Can someone help with this
Hi there!
A.
We can use the work-energy theorem to solve.
Initially, both blocks have gravitational potential energy, which is then converted to kinetic energy.
Recall:
[tex]U = mgh \\[/tex]
U = Potential Energy (J)
m = mass (kg)
g = acceleration due to gravity (m/s²)
h = height (m)
And at the end, block 2 has both kinetic and potential energy. Kinetic is defined as:
[tex]KE = \frac{1}{2}mv^2[/tex]
v = velocity (m/s)
We can do a summation of initial and final forces.
Initial:
[tex]E_i = m_2g\frac{h}{2} + m_1gh[/tex]
Final:
[tex]E_f = \frac{1}{2}m_2 v^2 + m_2g\frac{3h}{2} + \frac{1}{2}m_1 v^2[/tex]
Set the two equal (no energy loss in this situation) and solve for velocity.
[tex]m_2g\frac{h}{2} + m_1gh = \frac{1}{2}m_2 v^2 + m_2g\frac{3h}{2} + \frac{1}{2}m_1 v^2\\\\m_2g\frac{h}{2} + m_1gh - m_2g\frac{3h}{2} = \frac{1}{2}m_2 v^2 + \frac{1}{2}m_1 v^2\\\\v^2 = \frac{gh(\frac{m_2}{2} + m_1 - \frac{3m_2}{2})}{\frac{1}{2}m_2 + \frac{1}{2}m_1}\\\\v = \sqrt{\frac{gh(\frac{m_2}{2} + m_1 - \frac{3m_2}{2})}{\frac{1}{2}m_2 + \frac{1}{2}m_1}}\\\\v = \boxed{3.704 \frac{m}{s}}[/tex]
**This can be solved in a simpler way using a summation of forces.
B.
Now, we can do a summation of forces to solve. First, we must solve for the acceleration of the system now that we have found the velocity. Use the kinematic equation:
[tex]v_f^2 = v_i^2 + 2ad[/tex]
Initial velocity is 0 m/s, so:
[tex]v_f^2 = 2ad\\\\a = \frac{v_f^2}{2d} = \frac{(3.704^2)}{2(2.10)} = 3.267 \frac{m}{s^2}[/tex]
Now, we can use a summation of forces for any block. We can do block 1:
[tex]\Sigma F = m_1g - T[/tex]
Using Newton's Second Law:
[tex]m_1a = m_1g - T\\\\T = m_1g - m_1a \\T = m_1 (g - a) = 4.10(9.8 - 3.267) = \boxed{26.828 N}[/tex]
1) How many joules of heat are required to raise the temperature of 550 g of water from
12.7 °C to 28.8°C ? Specific heat of liquid water is 4.184 J/g °C.
Answer:
Explanation:
You can use [tex]Q = mc\Delta T=(550)(4.184)(28.8-12.7)=37049.32[/tex] joule.
list three things that spectra can tell us about objects in space
Answer:
The temperature, the density, and the element of stars.
Explanation:
The spectral line also can tell us about any magnetic field of the star. The width of the line can tell us how fast the material is moving. We can learn about winds in stars from this.
A system of four capacitors is connected across a 90-V voltage source as shown in the figure.
(a) What is the potential difference across the plates of the 6.0-µF capacitor? (b) What is the charge on the 2.0-µF capacitor?
For a system of four capacitors is connected across a 90-V voltage source, the potential difference across the plates of the 6.0-µF and 2uF capacitors is mathematically given as
a) vd=30v
b) Q=119.7uc
What is the potential difference across the plates of the 6.0-µF and 2uF capacitors?Generally, the equation for the charge across 6uf is mathematically given as
Q=C6Vd
Where
1/c36=1/3+1/6
c36=2
Q3=2*90
Q3=180
Therefore
vd=180/6
vd=30v
In conclusion
1/c24=1/2+1/4
C24=1.33uf
Q2=1.33*90
Q=119.7uc
Read more about Charge
https://brainly.com/question/9156412
