Answers
Answer:
Therefore, the velocity of the mass when the displacement is -1.5 cm is 0.121 m/s.
Explanation:
To calculate the velocity of the mass attached to a spring with the given parameters, we can use the principle of conservation of energy. At the maximum displacement (2 cm), all the potential energy stored in the spring is converted into kinetic energy of the mass. Therefore, we can write:
1/2 * m * v^2 = 1/2 * k * x^2
where m is the mass of the object, v is the velocity of the object, k is the spring constant, and x is the displacement of the mass from the equilibrium position.
Substituting the given values, we get:
1/2 * 8 kg * v^2 = 1/2 * 200 N/m * (0.02 m)^2
Solving for v, we get:
v = sqrt((0.02 m)^2 * 200 N/m / 8 kg) = 0.2 m/s
Therefore, the velocity of the mass when the displacement is 2 cm is 0.2 m/s.
Similarly, at a displacement of -1.5 cm, we can use the same equation to calculate the velocity:
1/2 * 8 kg * v^2 = 1/2 * 200 N/m * (-0.015 m)^2
Solving for v, we get:
v = sqrt((-0.015 m)^2 * 200 N/m / 8 kg) = 0.121 m/s (rounded to three decimal places)
Related Questions
1. A Ograph A Ograph B Ograph c Which graph represents what happens to the pressure in a tire as air is added to the tire, assuming the temperature is constant?
Answers
Answer:
Explanation:
It's graph A because the pressure in the tire is increasing as the amount of air going into it increases. B says the pressure drops exponentially as air goes in, and C says that the pressure stays the same as air goes in. Pressure in a tire increases proportionally to the amount of air in it.
A hunter who is standing 220.0-m away fires his rifle. How long (in seconds) will it take the sound to travel to your ear.
The air temperature is 43°F (6.0°C).
Answers
Answer:
t = 1.52 s
Explanation:
The speed of sound is constant and depends only on the properties of the medium in which the sound propagates, many of these properties change with temperature, in the case of propagation in air, the speed of sound
v =\(331 \ \sqrt{1+ \frac{T}{273} }\)
where the temperature is in degrees centigrade
v = 331 \(\sqrt{1+ \frac{6}{273} }\) = 331 1.0109
v = 334.6 m / s
let's use the uniform motion relationships
v = x / t
t = v / x
let's calculate
t = 334.6 / 220.0
t = 1.52 s
A mass m at the end of a spring vibrates with a frequency of 0.72 Hz . When an additional 700 g mass is added to m, the frequency is 0.64 Hz . Part A What is the value of m? Express your answer using two significant figures.
Answers
Answer:
The value of m is 2635.294 grams.
Explanation:
Let suppose that mass-spring system has a simple harmonic motion, to this respect the formula for frequency is:
\(f = \frac{\omega}{2\pi}\)
Where \(\omega\) is the angular frequency, measured in radians per second.
For a mass-spring system under simple harmonic motion, the angular frequency is:
\(\omega = \sqrt{\frac{k}{m} }\)
Where:
\(k\) - Spring constant, measured in newtons per meter.
\(m\) - Mass, measured in kilograms.
The following equation is obtained after replacing angular frequency in frequency formula:
\(f = \frac{1}{2\pi}\cdot \sqrt{\frac{k}{m} }\)
As this shows, frequency is inversely proportional to the square root of mass. Hence, the following relationship is deducted:
\(f_{1}\cdot \sqrt{m_{1}} = f_{2} \cdot \sqrt{m_{2}}\)
If \(m_{2} = m_{1} + 700\,g\), \(f_{1} = 0.72\,hz\) and \(f_{2} = 0.64\,hz\), the resulting expression is simplified and then initial mass is found after clearing it:
\(f_{1} \cdot \sqrt{m_{1}} = f_{2} \cdot \sqrt{m_{1}+700\,g}\)
\(f_{1}^{2} \cdot m_{1} = f_{2}^{2}\cdot (m_{1} + 700\,g)\)
\(\left(\frac{f_{1}}{f_{2}} \right)^{2}\cdot m_{1} = m_{1} + 700\,g\)
\(\left[\left(\frac{f_{1}}{f_{2}}\right)^{2} - 1\right]\cdot m_{1} = 700\,g\)
\(m_{1} = \frac{700\,g}{\left(\frac{f_{1}}{f_{2}} \right)^{2}-1}\)
\(m_{1} = \frac{700\,g}{\left(\frac{0.72\,hz}{0.64\,hz} \right)^{2}-1}\)
\(m_{1} = 2635.294\,g\)
The value of m is 2635.294 grams.
the potential energy of a body if its mass is 30 kg and height 30 m and gravity 10m/sec2
Answers
Explanation:
potential energy= mgh
30 × 10 × 30 = 9000J or 9KJ
31) what is the energy required to change 20g of copper, whose specific heat is 0.39j/gc,
change from 20 to 40 degrees?
Answers
Explanation:
given :
m = 20 g
sh = 0.39 J/g°C
∆T = 40-20 = 20°C
Find the Energy!
solution :
E =m. sh. ∆T
= 20 × 0.39 × 20
= 156 J
So, energy required is
Energy = mass*sh*∆T
Energy = 20g*0.39j/g°c*20°
Energy = 156joule✅
~Physics#1
which image shows an example of kinetic energy
Answers
Answer:
Hello there seems to be no Images in this question but Kinetic energy is a push or a pull force which has to do with motion if you just need to know what t is. Next time be sure to add the pictures for it.
Explanation:
Thank you!
Hello the other person (#Sonichj123), was indeed correct there appears to be no picture in your question. Although there is no picture in your question, If you have another question I will be gladly to help you!
Explanation:
Thank you so much! (≥ФωФ≤)
A 0.0400 kg meter stick is placed on a thin rod at the 30.0 cm mark. What is the minimum mass required to be placed on the 0.00 cm mark on the stick to maintain equilibrium?
Answer in kg
Answers
The minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.
To maintain equilibrium, the torques acting on the meter stick must balance each other. The torque is given by the formula:
τ = r * F * sin(θ)
where τ is the torque, r is the distance from the pivot point to the point where the force is applied, F is the force applied, and θ is the angle between the force vector and the lever arm.
In this case, the meter stick is in equilibrium when the torques on both sides of the pivot point cancel each other out. The torque due to the weight of the meter stick itself is acting at the center of mass of the meter stick, which is at the 50.0 cm mark.
Let's denote the mass to be placed on the 0.00 cm mark as M. The torque due to the weight of M can be calculated as:
τ_M = r_M * F_M * sin(θ)
where r_M is the distance from the pivot point to the 0.00 cm mark (which is 30.0 cm), F_M is the weight of M, and θ is the angle between the weight vector and the lever arm.
Since the system is in equilibrium, the torques on both sides of the pivot point must be equal:
τ_M = τ_stick
r_M * F_M * sin(θ) = r_stick * F_stick * sin(θ)
Substituting the given values:
30.0 cm * F_M = 20.0 cm * (0.0400 kg * 9.8 m/s^2)
Solving for F_M:
F_M = (20.0 cm / 30.0 cm) * (0.0400 kg * 9.8 m/s^2)
F_M = 0.0264 kg * 9.8 m/s^2
F_M = 0.25872 N
Finally, we can convert the force into mass using the formula:
F = m * g
0.25872 N = M * 9.8 m/s^2
M = 0.0264 kg
Therefore, the minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.
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Which of the following are INCORRECT statements regarding how higher temperatures result in higher reaction rates? Select all that apply, this is a multiple response question. Othe average kinetic energy of reacting molecules is increased Oreacting molecules collide more frequently, and with higher kinetic energies Oreacting molecules have higher kinetic energies but lower collision frequencies Othe activation energy barrier for the reaction is lowered Oendothermic reactions become exothermic reactions at higher temperatures Oa greater fraction of colliding molecules has the minimum energy required to overcome the activation energy barrier
Answers
The incorrect statements regarding how higher temperatures result in higher
reaction rates are:
1) Reacting molecules have higher kinetic energies but lower collision frequencies.
2) The activation energy barrier for the reaction is lowered.
3) Endothermic reactions become exothermic reactions at higher temperatures.
Higher temperatures result in an increase in both kinetic energy and collision frequency of molecules.
The activation energy barrier for the reaction does not change with temperature,
But a greater fraction of colliding molecules has the minimum energy required to overcome the activation energy barrier at higher temperatures.
Endothermic reactions do not become exothermic reactions at higher temperatures. These reactions may occur at a faster rate, but the overall energy change of the reaction does not change.
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A ball is dropped from the height of 10m.at the same time, another ball is thrown vertically upward at an initial speed of 10m/s. How high above the ground will thr two balls collide?
Answers
Answer: H=5.1m
Explanation:
Given:
Ball 1 height= 10m
Ball 2 initial velocity=10m/s
use the kinematic equation:
S=(vi)t+12at2
I choose my sign convention to be up=positive, down=negative, so a=−9.81ms2 (a is taken as the value of gravity)
Ball 1 dropped from 10m :
−(10−H)=0+12(−9.81)t2
Note that (10-S) is negative because that displacement is *below* the starting point.
12(9.81)t2=10−H
——- equation (1)
Ball 2 thrown upward at 10 m/s :
H=(10)t+12(−9.81)t2
or
12(9.81)t2=10t−H
——- equation (2)
equation (1) minus equation (2):
0=(10−H)−(10t−H)
t=1 equation (1):
12(9.81)12=10−H
H=5.1m
Given Information:
Ball One:
\(\vec y_{0} = 10 \ m\) (Indicating the initial position)
We also know the ball was dropped from rest. So, \(\vec v_{0_{1} } = 0 \ m/s\).
Ball Two:
\(\vec v_{0} = 10 \ m/s\) (Indicating the initial velocity)
We also know the ball was throw from the ground. So, \(\vec y_{0_{1} } = 0 \ m\).
The Information we want to Find:
\(\vec y_{c} = ?? \ m\) (Indicating the position the two projectiles collide)
Using the Following Kinematic Equation to Solve:
\(\Delta \vec x = \vec v_{0}t + \frac{1}{2} \vec at\)
For ball one...
\(\Delta \vec y = \vec v_{0}t + \frac{1}{2} \vec a_{y} t\)
\(\Longrightarrow \vec y_{c}- \vec y_{0} = \vec v_{0_{1} }t + \frac{1}{2} \vec a_{y}t\)
\(\Longrightarrow \vec y_{c}- \vec y_{0} = (0)t + \frac{1}{2} \vec a_{y}t\)
\(\Longrightarrow \vec y_{c}- \vec y_{0} = \frac{1}{2} \vec a_{y}t\)
\(\Longrightarrow \vec y_{c} = \frac{1}{2} \vec a_{y}t +\vec y_{0}\) => Equation 1
For ball two...
\(\Delta \vec y = \vec v_{0}t + \frac{1}{2} \vec a_{y}t\)
\(\Longrightarrow \vec y_{c}- \vec y_{0_{1} } = \vec v_{0}t + \frac{1}{2} \vec a_{y}t\)
\(\Longrightarrow \vec y_{c} = \vec v_{0}t + \frac{1}{2} \vec a_{y}t +\vec y_{0_{1} }\)
\(\Longrightarrow \vec y_{c} = \vec v_{0}t + \frac{1}{2} \vec a_{y}t + 0\)
\(\Longrightarrow \vec y_{c} = \vec v_{0}t + \frac{1}{2} \vec a_{y}t\) => Equation 2
Set equations 1 and 2 equal to each other and solve for the time that they collide.
\(\left \{ {{\vec y_{c} = \frac{1}{2} \vec a_{y}t +\vec y_{0}} \atop { \vec y_{c} = \vec v_{0}t + \frac{1}{2} \vec a_{y}t } \right.\)
\(\Longrightarrow \frac{1}{2} \vec at +\vec y_{0}= \vec v_{0}t + \frac{1}{2} \vec at\)
\(\Longrightarrow \vec y_{0}= \vec v_{0}t\)
\(\Longrightarrow t=\frac{\vec y_{0}}{\vec v_{0}}\)
\(\Longrightarrow t=\frac{10}{10}\)
\(\Longrightarrow t=1 \ s\)
Thus, the balls collide at time, t=1 s. We can now use this time to plug into equation 1 or 2 to find the height at which they collide. I will use equation 1.
\(\Longrightarrow \vec y_{c} = \frac{1}{2} \vec a_{y}t +\vec y_{0}\)
\(\Longrightarrow \vec y_{c} = \frac{1}{2} (-9.8)(1) +10\)
\(\Longrightarrow \vec y_{c} = 5.1 \ m \ \therefore \ Sol.\)
*Note* \(\vec a_{y}\) is the acceleration of gravity (\(-9.8 \ m/s^2 \ or \ -32 \ ft/s^2\))
Final Answer: The balls collide at the height 5.1 m.
PLEASE ANSWER FASG I WILL MARK BRAINELIST PLEASEEEEE
The number of protons in the nucleus of an atom determines the species of the atom, i.e., the element to which the atom belongs. An atom has the same number of protons and neutrons. But the electron number cannot be used instead because (5 points)
a. electrons are not within the nucleus
b. electrons are negatively charged
c. electrons can be removed from or added to an atom
d. electrons are lighter than protons
Answers
The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)
Why the electron number cannot be used instead?The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.
This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.
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Someone who fears their actions or behaviors Will support negative ideas about a group to which they belong is experiencing.
A) cognitive dissonance
B) group polarization
C) misperception
D) stereotypes threat
Answers
817 cm3 at 80.8 kPa to 101.3 kPa: __________ cm3 (No temp. change)
Answers
The final volume of the gas, when the pressure changes from 80.8 kPa to 101.3 kPa at constant temperature, is approximately 652.9 cm³.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law can be represented by the equation: P₁V₁ = P₂V₂
Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
Given:
Initial volume, V₁ = 817 cm³
Initial pressure, P₁ = 80.8 kPa
Final pressure, P₂ = 101.3 kPa
We need to find the final volume, V₂.
Using Boyle's Law equation, we can rearrange it to solve for V₂:
V₂ = (P₁V₁) / P₂
Plugging in the given values:
V₂ = (80.8 kPa * 817 cm³) / 101.3 kPa
Simplifying the expression:
V₂ ≈ 652.9 cm³
Therefore, the final volume of the gas, when the pressure changes from 80.8 kPa to 101.3 kPa at constant temperature, is approximately 652.9 cm³.
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PLEASE HELP IT'S DUE IN LIKE 2 MINUTES
Answers
Answer:
1kg
Explanation:
this box is the smallest and weighs the least. Hope this helps :]
how are series and parallel circuits different in terms of current and voltage? how are they similar? why?
Answers
Answer:
LIKE Hmm
Explanation:
I CAN"T
Answer: I don't know exactly, but series circuits have an alternating current, while parallel has direct
Explanation:
How do I find the mass in kg
Answers
To find the mass in kilograms, you need to know the object's weight in newtons and the acceleration due to gravity. The formula for finding mass is mass = weight / acceleration due to gravity. So if you have an object with a weight of 100 N and the acceleration due to gravity is 9.8 m/s^2, the mass would be 10.204 kg.
The mass of the block is 0.025 kg or 25 g, when the spring has k = 28 N/m, and compresses 0.11 m before bringing the block to rest.
When a block is dropped onto a spring with k=28 N/m, the block has a speed of 3.2 m/s just before it strikes the spring. If the spring compresses an amount of 0.11 m before bringing the block to rest, what is the mass of the block?The formula for the spring potential energy is given as follows; PE = (1/2) kx² where k is the spring constant and x is the amount of deformation of the spring. Substituting the values given;PE = (1/2) 28 (0.11)²PE = 0.16972 J. According to the law of conservation of energy, the potential energy stored in the spring at maximum compression is equal to the kinetic energy the block had before it struck the spring;KE = (1/2) mv²where m is the mass of the block and v is its velocity.Substituting the values;0.16972 = (1/2) m (3.2)²m = 0.025 kg or 25 gTherefore, the mass of the block is 0.025 kg or 25 g.For more questions on mass
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Select the statement(s) that accurately describe why people have to prepare for natural disasters.
Answers
1. People have to prepare for natural disasters in order to reduce the risk of injury, death, and property damage caused by the disaster.
What is natural disasters?Natural disasters are adverse events that occur naturally and are a result of the interaction between the physical environment and human activities. They can include floods, hurricanes, tornadoes, earthquakes, tsunamis, wildfires, landslides, volcanic eruptions, and extreme weather events. Natural disasters can have devastating impacts on communities, including loss of life, damage to property, displacement, and destruction of livelihoods. Governments, organizations, and individuals are increasingly working to reduce the impacts of natural disasters through improved risk management, infrastructure planning, and disaster response and recovery efforts.
2. People have to prepare for natural disasters in order to be able to respond quickly and efficiently in the event of an emergency.
3. People have to prepare for natural disasters in order to plan for the financial impacts of the disaster.
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9. If the mass of a 200 N object is cut in half, what would happen to its weight in Newtons?
Answers
Answer:
as we know that weight = mass ×gravity (earth's gravity 9.8m.s²)the weight will be also be cut in halfmass is directly proportional to the weightExplanation:
let's say our mass is 50 kgour gravity is 9.8m.s²therefore 50×9.8=490Nnow cut the mass in half therefore 25×9.8=245N(6) Consider water flowing through a nozzle as shown in the figure below. Determine the height h (cm) if the gauge pressure at A is 34.5 kPa. A 61 cm ma B -Water rhol 1000 kg/m³ Flow Open to atmosphere Mercury rho2- 13600 kg/m
Answers
The height h is 25.91 cm. Pressure can be exerted by liquids, gases, or solids and can be influenced by factors such as temperature, volume, and altitude.
What is Pressure?
Pressure is defined as the force per unit area applied in a direction perpendicular to the surface of an object. It is usually expressed in units such as pascals (Pa), pounds per square inch (psi), or atmospheres (atm).
To solve for the height h, we need to use Bernoulli's equation, which states that the sum of pressure, kinetic energy, and potential energy is constant along a streamline of fluid flow.
At point A, the gauge pressure is 34.5 kPa. Since the flow is open to the atmosphere, we can assume that the absolute pressure at point A is:
P_A = P_atm + P_gauge
= 101.3 kPa + 34.5 kPa
= 135.8 kPa
At point B, the fluid is at rest, so the velocity is zero. Therefore, the kinetic energy term in Bernoulli's equation is zero.
Using the density of water and the density of mercury, we can convert the heights of the water column and the mercury column into pressure terms.
Let h1 be the height of the water column, and h2 be the height of the mercury column. Then, the pressure difference between points A and B is:
ΔP = ρ_water * g * h1 - ρ_mercury * g * h2
where g is the acceleration due to gravity.
Setting the pressures at A and B equal to each other, we have:
P_A + ΔP = P_B
Solving for h1, we get:
h1 = (P_B - P_A + ρ_mercury * g * h2) / (ρ_water * g)
The pressure at point B is atmospheric pressure, which is 101.3 kPa.
Plugging in the given values, we get:
h1 = (101.3 kPa - 135.8 kPa + 13600 kg/m³ * 9.81 m/s² * h2) / (1000 kg/m³ * 9.81 m/s²)
h1 = (-34.5 kPa + 133137.6 Pa * h2) / 9810 Pa/m
Multiplying both sides by 100 cm/m to convert units, we get:
h1 = (-0.345 m + 13.31376 cm * h2)
Setting h1 = 0 (since we want the height at which the water column stops), we get:
0 = -0.345 m + 13.31376 cm * h2
Solving for h2, we get:
h2 = 0.345 m / (13.31376 cm)
= 25.91 cm
Therefore, the height h at which the water column stops is:
h = h1 + h2
= 0 + 25.91 cm
= 25.91 cm
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What are the similarities between theory and law ?
Answers
A law is created using a theory
Hope this helps you!!!
Urgent
The following picture is an example of which type of energy?
Electromagnetic Energy
Nuclear Energy
Electric Energy
Answers
Answer:
I think its n u c l e a r e n e r g y.
does the stirling engine follow the law of conservation energy
Answers
Answer:
Conservation of Energy: Like all things, Stirling Engines follow the conservation of energy principle (all the energy input is accounted for in the output in one form or another). ... The hot one supplies all of the energy QH, while the cold one removes energy QC (a necessary part of the cycle).
Explanation:
Answer: Yes
Explanation: All the energy input is accounted for in the output in one form or another
In the sport of billiards, event organizers often remove one of the rails on a pool table to allow players to measure the speed of their break shots (the opening shot of a game in which the player strikes a ball with his pool cue).
The top of a pool table is a height ℎ=2.75 ft from the floor. If a player's ball lands a distance =16.50 ft from the table edge, what is her break shot speed 0?
Answers
The break shot speed of the player is determined as 96.5 ft/s.
Time of motion of the playeruse the following kinematic equation to determine the time of motion of the player.
h = vt + ¹/₂gt²
h = 0 + ¹/₂gt²
h = ¹/₂gt²
t = √(2h/g)
t = √(2 x 2.75/32.17)
t = 0.171 s
break shot speedvx = x/t
vx = 16.5 ft / 0.171 s
vx = 96.5 ft/s
Thus, the break shot speed of the player is determined as 96.5 ft/s.
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A long piece of wire with a mass of 0.100 kg and a total length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hing along a horizontal side, carries a 3.80 A current, and is placed in a vertical magnetic field with a magnitude of 0.010 0 T.
a, Determine the angle that the plane of the coil makes with the vertical when the coil is in equilibrium. b Find the torque acting on the coil due to the magnetic force at equilibrium.
Answers
The torque is equal to zero since the coil is in equilibrium. As a result, will also equal zero, indicating that the coil's plane is parallel to the vertical direction at equilibrium.
Calculation-The current-carrying coil in a magnetic field is given by:
τ = μ * B * I * A * sin(θ)
where:
τ = torque (in Nm)
μ = magnetic moment of the coil (in Am^2)
B = magnetic field strength (in T)
I = current flowing through the coil (in A)
A = area of the coil (in m^2)
θ = angle between the plane of the coil and the magnetic field (in radians)
μ = N * A * I
N = number of turns of the coil
A = area of the coil (in m^2)
I = current flowing through the coil (in A)
the equations to calculate the angle θ:
m = 0.100 kg (mass of the wire)
L = 4.00 m (total length of the wire)
side length = 0.100 m
I = 3.80 A (current flowing through the coil)
B = 0.0100 T (magnetic field strength)
Calculations:
A = side length^2 * N = 0.100^2 * 1 = 0.0100 m^2
μ = N * A * I = 1 * 0.0100 * 3.80 = 0.0380 Am^2
Now we can rearrange the equation for torque to solve for θ:
θ = arcsin(τ / (μ * B * I * A))
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Match each letter to the description
A woman walks in a
straight line with the sun
to her right at six o'clock in
the morning. Toward
which pole does she walk?
A line of latitude.
A man walks in a straight
line with the sun to his
right at six o'clock in the
evening. Toward which
pole does he walk?
A line of longitude.
Answers
A woman walks in a straight line with the sun to her right at six o'clock in the morning.
The sun rises East of her, so the woman is walking toward the North pole.
A man walks in a straight line with the sun to his right at six o'clock in the evening.
The sun sets West of him, so the man is walking toward the South pole.
The woman and the man are both walking along lines of constant longitude.
In the Growing Plants activity within the lesson, you were asked to set up 3 pots:
Pot A: Bean seed, 2 lights on, 0 mL of water
Pot B: Bean seed, 2 lights on, 30 mL of water
Pot C: Bean seed, 2 lights on, 70mL of water
Which plant had the greatest height and mass at the end of 50 days?
A
B
C
Answers
The plant that had the greatest height and mass at the end of 50 days is Pot B
Which plant has the greatest height?We have to note that in the growth of the plants there are some parameters that we know to be very essential and those things that are very essential must be there if the plant is to grow and reproduce well.
The most essential things that the plant needs so as to function are;
a) Light
b) Water
c) Nutrients
If the water is too much, it can prevent the plant from getting to germinate and then grow up well in the soil.
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Suppose that a 117.5 kg football player running at 6.5 m/s catches a 0.43 kg ball moving at a speed of 26.5 m/s with his feet off the ground, while both of them are moving horizontally.
(a) Calculate the final speed of the player, in meters per second, if the ball and player are initially moving in the same direction.
(b) Calculate the change in kinetic energy of the system, in joules, after the player catches the ball.
(c) Calculate the final speed of the player, in meters per second, if the ball and player are initially moving in opposite directions.
(d) Calculate the change in kinetic energy of the system, in joules, in this case.
Answers
Answer:
a) 6.57 m/s
b) 53.75 J
c) 6.37 m/s
d) -98.297 J
Explanation:
mass of player = \(m_{p}\) = 117.5 kg
speed of player = \(v_{p}\) = 6.5 m/s
mass of ball = \(m_{b}\) = 0.43 kg
velocity of ball = \(v_{b}\) = 26.5 m/s
Recall that momentum of a body = mass x velocity = mv
initial momentum of the player = mv = 117.5 x 6.5 = 763.75 kg-m/s
initial momentum of the ball = mv = 0.43 x 26.5 = 11.395 kg-m/s
initial kinetic energy of the player = \(\frac{1}{2} mv^{2}\) = \(\frac{1}{2}\) x 117.5 x \(6.5^{2}\) = 2482.187 J
a) according to conservation of momentum, the initial momentum of the system before collision must equate the final momentum of the system.
for this first case that they travel in the same direction, their momenta carry the same sign
\(m_{p}\)\(v_{p}\) + \(m_{b}\)\(v_{b}\) = (\(m_{p}\) +\(m_{b}\))v
where v is the final velocity of the player.
inserting calculated momenta of ball and player from above, we have
763.75 + 11.395 = (117.5 + 0.43)v
775.145 = 117.93v
v = 775.145/117.93 = 6.57 m/s
b) the player's new kinetic energy = \(\frac{1}{2} mv^{2}\) = \(\frac{1}{2}\) x 117.5 x \(6.57^{2}\) = 2535.94 J
change in kinetic energy = 2535.94 - 2482.187 = 53.75 J gained
c) if they travel in opposite direction, equation becomes
\(m_{p}\)\(v_{p}\) - \(m_{b}\)\(v_{b}\) = (\(m_{p}\) +\(m_{b}\))v
763.75 - 11.395 = (117.5 + 0.43)v
752.355 = 117.93v
v = 752.355/117.93 = 6.37 m/s
d) the player's new kinetic energy = \(\frac{1}{2} mv^{2}\) = \(\frac{1}{2}\) x 117.5 x \(6.37^{2}\) = 2383.89 J
change in kinetic energy = 2383.89 - 2482.187 = -98.297 J
that is 98.297 J lost
Your friend is catching a falling basketball after it has passed through the basket. Her hands move straight down while catching the ball. It takes about 0.10 s
for the player to lower her hands to stop the ball. Assume the mass of the ball is 0.60 kg, and that the ball has fallen a vertical distance of 1.2 m before reaching the player's hand. Determine the average force that her hands exert on the ball while catching it.
Answers
The average force exerted by the player's hands on the ball while catching it is approximately 20.6 N. To determine the average force exerted by the player's hands on the ball while catching it, we can use the equation:
F = m ×(Δv / Δt)
where F is the force exerted, m is the mass of the ball, Δv is the change in velocity, and Δt is the time taken to make that change.
Since the player's hands are moving downward to catch the ball, the change in velocity is equal to the final velocity of the ball, which is zero, minus its initial velocity. The initial velocity of the ball can be determined using the equation:
v² = u² + 2gh
where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height through which the ball has fallen (1.2 m).
Solving for u, we get:
u = sqrt(v² - 2gh) = sqrt(2 × 9.8 × 1.2) ≈ 3.43 m/s
Using this value of u, we can now calculate the change in velocity:
Δv = 0 - u = -3.43 m/s
We are given that the time taken to stop the ball is Δt = 0.10 s, and the mass of the ball is m = 0.60 kg. Substituting these values into the equation for force, we get:
F = m × (Δv / Δt) = 0.60 × (-3.43 / 0.10) ≈ -20.6 N
The negative sign indicates that the force is directed upwards, opposite to the direction of the player's hands. This is because the player's hands have to decelerate the ball as it falls towards them. So the average force exerted by the player's hands on the ball while catching it is approximately 20.6 N.
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Microevolution three mechanisms that cause allelic frequencies to change in a population: gene flow, genetic drift, natural selection bottleneck effect founder effect population gene pool stabilizing, directional and disruptive selection hardy-weinberg equilibrium five conditions that must be met in order for population to be in hardy-weinberg equilibrium adptive evolution relative fitness sexual selection sexual dimorphism intrasexual selection intersexual selection neutral variation balancing selection heterozygote advantage hardy-weinberg problems
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Microevolution refers to the evolution occurring at species-level involves three mechanisms that cause allelic frequencies to change in a population: gene flow, genetic drift, and natural selection.
Changes in the environment can affect population gene pools on both a small- and large-scale. Microevolution is the process of population-level changes in allele frequency. Some alterations take place at the species level or lower. There are hence variations in allele frequencies between or within groups.
Natural selection is one of the mechanisms of microevolution. It serves as an editor for allele frequency in populations to determine whether individuals with particular features have a higher or lower chance of surviving and procreating. Populations' gene pools can occasionally shift as a result of individuals leaving or entering the community. This transfer of alleles between populations is referred to as gene flow. Genes can "flow" from one area to another just like water does in a river.
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A person standing at the edge of a seaside cliff kicks a rock horizontally of the cliff from a
height of 52 m and it lands a distance of 35 m from the base of the cliff. What is the speed at
which the rock was initially kicked?
Answers
The time will be the same for both horizontal and vertical component. The initial speed is 10.7 m/s
What is Speed ?Speed is a distance travel per time taken. It is a scalar quantity and it is measured in m/s
Given that a person standing at the edge of a seaside cliff kicks a rock horizontally of the cliff from a height of 52 m and it lands a distance of 35 m from the base of the cliff.
The rock will move vertically downward with initial velocity = 0. The time taken will be constant. That is, same horizontally.
Let us first calculate the time by using the formula
h = ut + 1/2gt²
Where
h = 52 mu = 0Range R = 35 mg = 9.8 m/s²Substitute all the necessary parameters into the formula
52 = 0 + 1/2 × 9.8 × t²
52 = 4.9t²
t² = 52/4.9
t² = 10.6
t = √10.6
t = 3.26 s
The speed at which the rock was initially kicked can be found by
R = Ut
35 = U × 3.26
U = 35/3.26
U = 10.7 m/s
Therefore, rock was initially kicked at a speed of 10.7 m/s
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Help me the question should be in the document.
Answers
The total system momentum would remain the same before and after the collision. Option D
What is the law of conservation of momentum?The law of conservation of momentum, which states that when no external forces are exerted on a system of objects, the system's overall momentum will remain constant, is a fundamental principle of physics.
The momenta of all the objects added together in the system prior to an event or interaction are equal to the momenta of the objects added together after the event or interaction.
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