Question:
A spherical balloon with a 36 cm diameter is being deflated. Its volume V is a function of its radius r according to [tex]V(r) = \frac{4}{3}\pi r^3.[/tex]
As it's deflating, it is much easier to measure its radius than its volume. Suppose the radius of the balloon is [tex]r(t) = 18 - 18e^{-0.24t}[/tex] cm at t seconds.
Determine the value of V'(4) (accurate to 3 decimal places). Write a complete sentence including the units of both 4 and V'(4) in this context. Determine the value of r(4) (accurate to 3 decimal places). Write a complete sentence including the units of both 4 and r(4) in this context.Answer:
[tex]V'(4) = 201.143[/tex]
[tex]r(4) = 11.106[/tex]
Explanation:
Given
[tex]V(r) = \frac{4}{3}\pi r^3.[/tex]
[tex]r(t) = 18 - 18e^{-0.24}[/tex]
Solving (a): V'(4)
First, we determine V('r)
[tex]V(r) = \frac{4}{3}\pi r^3.[/tex]
Differentiate w.r.t r
[tex]V'(r) = 3 * \frac{4}{3}\pi r^{3-1}[/tex]
[tex]V'(r) = 3 * \frac{4}{3}\pi r^2[/tex]
[tex]V'(r) = 4\pi r^2[/tex]
Substitute 4 for r and take [tex]\pi = \frac{22}{7}[/tex]
[tex]V'(4) = 4 * \frac{22}{7} * 4^2[/tex]
[tex]V'(4) = 4 * \frac{22}{7} * 16[/tex]
[tex]V'(4) = \frac{4 * 22* 16}{7}[/tex]
[tex]V'(4) = \frac{1408}{7}[/tex]
[tex]V'(4) = 201.143[/tex]
This means that the volume of the balloon when the radius is deflated to 4 seconds is 201.143 cm^3
Solving (b): r(4)
Substitute 4 for t in [tex]r(t) = 18 - 18e^{-0.24t}[/tex]
[tex]r(4) = 18 - 18e^{-0.24*4}[/tex]
[tex]r(4) = 18 - 18e^{-0.96}[/tex]
[tex]r(4) = 18 - 18*0.383[/tex]
[tex]r(4) = 11.106[/tex]
This means that the radius of the balloon when at 4 seconds of deflation is 11.106 cm
Which heat related illness requires immediate medical attention
Answer:
Heat stroke
Explanation:
Heat Stroke is the most serious heat-related illness and requires immediate medical attention.
Answer:
Heat Stroke is the most serious heat-related illness and requires immediate medical attention. Symptoms include: confusion, fainting, seizures, very high body temperature and hot, dry skin or profuse sweating. CALL 911 if a coworker shows signs of heat stroke.
Explanation:
I HOPE THIS HELPS * pls mark me brainliest }
All motion will eventually stop due to the "loss" of energy to___.
a) friction and thermal energy
b) gravity
c) kinetic energy
d) potential energy
The greenhouse effect is
The kinetic energy of an object of mass 3.5 kg is 112 J. Its speed is?
64 m/s
8.0 m/s
5.67 m/s
6.8 m/s
Which property of a solid measures how resistant the material is to deformation?
A. Elasticity
B. Hardness
C. Plasticity
D. resilience
Answer: the answer is a
Explanation:
Write a paragraph describing Newton's 2nd Law in YOUR OWN WORDS.
Explanation:
if u apply more force to an object, it accelerates at a higher rate
Various radial points on a rotating Ferris wheel have: I. different linear velocities II. different angular velocities III. equal linear velocities IV. equal angular velocities
Answer:
I) True, II) False, III) False, IV) True
Explanation:
In this exercise, it is asked to answer different statements, for this we will use the relationship between angular and linear velocity
v = w r
let's review the claims
I) True. From the initial equation we see that the linear velocity depends on the radius
II) False. All points rotate with the same angular velocity
III) False. Linear velocity changes with radius
IV) True. The angular velocity of all points is the same
At various radial points on a rotating Ferris wheel have, different linear velocity (True), different angular velocity (false), equal linear velocity (false) and equal angular velocity (True).
The angular velocity of a rotating Ferris is calculated as follows;
[tex]\omega = \frac{v}{r} = 2\pi N[/tex]
The linear velocity of a rotating Ferris is calculated as follows;
v = ωr
where;
v is the linear velocityr is the radius of the Ferrisω is the angular velocityThe linear velocity increases with increase in radius.
Thus, we can conclude that, at various radial points on a rotating Ferris wheel have;
different linear velocitiesconstant angular velocityLearn more about angular velocity here: https://brainly.com/question/540174
A car is traveling due north at 23.6 m>s. Find the velocity of the car after 7.10 s if its acceleration is (a) 1.30 m>s2 due north, or (b) 1.15 m>s2 due south.
Answer:
a) v = 32.8 m/s
b) v= 15.4 m/s
Explanation:
a)
Applying the definition of acceleration (assumed to be constant), we can write the following expression for the velocity v:[tex]v = v_{o} + a*t (1)[/tex]
where v₀ is the initial velocity and a is the acceleration, being t the
time elapsed.
In the case a) the acceleration and the velocity vectors have both the same direction (due north), so both have the same sign, which means that the car is speeding up.Replacing by the givens v₀ and t in (1), we get:[tex]v = 23.6 m/s + (1.30 m/s2 * 7.10 s) = 32. 8 m/s (2)[/tex]
b)
In this case, the acceleration vector and the velocity vector have opposite directions, so the car slows down, due to both vectors have opposite signs.Replacing by the givens in (1) and taking into account the signs, we get:[tex]v = 23.6 m/s + ((-1.15 m/s2) * 7.10 s)) = 15. 4 m/s (3)[/tex]
2 objects have a total momentum of 400kg m/s, they collide. Object A’s mass is5kg & object B’s mass is 11kg. After the collision Object B is moving at 15m/s.What is the velocity of Object A AFTER the collision?
Answer:
Explanation:
We shall apply law of conservation of momentum .
Momentum before collision = momentum after collision .
Momentum before collision = 400 kg m/s
Momentum after collision = 5 x v + 11 x 15
where v is velocity of A after the collision .
5 x v + 11 x 15 = 400
5 v = 400 - 165
5v = 235
v = 47 m /s .
You are assigned the design of a cylindrical, pressurized water tank for a future colony on Mars, where the acceleration due to gravity is 3.71 meters per second per second. The pressure at the surface of the water will be 150 KPa , and the depth of the water will be 14.4 m . The pressure of the air in the building outside the tank will be 88.0 KPa .
Find the net downward force on the tank's flat bottom, of area 2.15 m2 , exerted by the water and air inside the tank and the air outside the tank.
Answer: F = 6262.2 kN
Explanation: Pressure is defined as force per area. But pressure varies according to the depth of a fluid: in air, it decreases the higher the altitude, while in water, it increases the deeper you go.
So, at the bottom of the tank, besides the pressure of air inside the tank and air outside the tank, there is pressure of water due to its depth.
Pressure due to the depth is calculated as
[tex]P=h.\rho.g[/tex]
h is the depth in m
ρ is density of the fluid, in this case is water, so ρ = 997 kg/m³
g is acceleration due to gravity, which, in this case, is 3.71 m/s²
Then, pressure at the bottom of the tank due to variation in depth is
[tex]P=14.4(997)(3.71)[/tex]
P = 53263.73 Pa or 53.26 kPa
Assuming positive referential is downward, all pressures at the bottom point down, so total or resultant pressure is:
[tex]P_{r}=P_{1}+P_{2}+P_{3}[/tex]
[tex]P_{r}=150+88+53.26[/tex]
[tex]P_{r}=[/tex] 291.26 kPa
At last, pressure is force per area:
[tex]P=\frac{F}{A}[/tex]
[tex]F=P.A[/tex]
[tex]F_{r}=P_{r}.A[/tex]
[tex]F_{r}=291.26.10^{3}(2.15)[/tex]
[tex]F_{r}=[/tex] 626209 N or 626.2 kN
At the cylindrical tank's flat bottom, net force has magnitude 626.2 kN.
For each of the situations described below, the object considered is undergoing some changes. Among the possible changes you should consider are:
(Q) The object is absorbing or giving off heat.
(T) The object's temperature is changing.
(E) The object's thermal energy is changing.
(W) The object is doing mechanical work or having work done on it.
(C) The objects chemical energy is changing.
For each of the two situations, identify which of the five changes is taking place, indicating the applicable letters Q T U W C (or none) as appropriate while providing your reasoning.
a. An ice cube sits in the open air and is melting.
b. A cylinder with a piston on top contains a compressed gas and is sitting on a thermal reservoir (a large iron block that can provide or take thermal energy as the system needs). After everything has come to thermal equilibrium, the piston is moved upward somewhat (very slowly). The object to be considered is the gas in the cylinder.
Answer: a. (Q), (T), (E)
b. (Q), (T), (E), (W)
Explanation: Thermal Energy and Temperature are closely related: when the temperature rises causing atoms or molecules to move, thermal energy is produced. Thermal energy is the energy within the system.
Mechanical Work is the amount of energy transferred due to an applied force.
Chemical Energy is the energy contained in the bonds of chemical structures of the molecules released when a chemical reaction happens.
Given the explanations, let's analyse the situations:
a. For an ice cube to be melting, it has to be absorbing heat, which means its thermal energy is changing and, consequently, so does its temperature;
b. First, the gas inside the cylinder reaches a thermal equilibrium, which means its thermal energy and temperature changed. Since there were exchange of heat to reach the equilibrium, the gas absorbed or gave off heat. After the equilibrium, when the piston starts to be moved, the energy of the pressure is transferred to the gas, so mechanical work had been done.
A 2.00 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0300 m . The spring has force constant 815 N/m . The coefficient of kinetic friction between the floor and the block is μk=0.40. The block and spring are released from rest and the block slides along the floor.
Required:
What is the speed of the block when it has moved a distance of 0.0200 m from its initial position? (At this point the spring is compressed 0.0100 m.)
Answer:
v = 0.41 m/s
Explanation:
In this case, the change in the mechanical energy, is equal to the work done by the fricition force on the block.At any point, the total mechanical energy is the sum of the kinetic energy plus the elastic potential energy.So, we can write the following general equation, taking the initial and final values of the energies:[tex]\Delta K + \Delta U = W_{ffr} (1)[/tex]
Since the block and spring start at rest, the change in the kinetic energy is just the final kinetic energy value, Kf.⇒ Kf = 1/2*m*vf² (2)The change in the potential energy, can be written as follows:[tex]\Delta U = U_{f} - U_{o} = \frac{1}{2} * k * (x_{f} ^{2} - x_{0} ^{2} ) (3)[/tex]
where k = force constant = 815 N/m
xf = final displacement of the block = 0.01 m (taking as x=0 the position
for the spring at equilibrium)
x₀ = initial displacement of the block = 0.03 m
Regarding the work done by the force of friction, it can be written as follows:[tex]W_{ffr} = - \mu_{k}* F_{n} * \Delta x (4)[/tex]
where μk = coefficient of kinettic friction, Fn = normal force, and Δx =
horizontal displacement.
Since the surface is horizontal, and no acceleration is present in the vertical direction, the normal force must be equal and opposite to the force due to gravity, Fg:Fn = Fg= m*g (5)Replacing (5) in (4), and (3) and (4) in (1), and rearranging, we get:[tex]\frac{1}{2} * m* v^{2} = W_{ffr} - \Delta U = W_{ffr} - (U_{f} -U_{o}) (6)[/tex]
[tex]\frac{1}{2} * m* v^{2} = (- \mu_{k}* m*g* \Delta x) -\frac{1}{2} * k * (x_{f} ^{2} - x_{0} ^{2} ) (7)[/tex]
Replacing by the values of m, k, g, xf and x₀, in (7) and solving for v, we finally get:[tex]\frac{1}{2} * 2.00 kg* v^{2} = (-0.4*2.00 kg*9.8m/s2*0.02m) +( (\frac{1}{2} *815 N/m)* (0.03m)^{2} - (0.01m)^{2}) = -0.1568 J + 0.326 J (8)[/tex]
[tex]v =\sqrt{(0.326-0.1568} = 0.41 m/s (9)[/tex]Chirag, a champion weightlifter, raises 259 kg of weights a distance of 2.40 m. How much work is done by Brutus lifting the weights?
622 J
6090 J
2540 J
0 J
How much work is done by Chirag holding the weights above his head?
622 J
6090 J
2540 J
0 J
1.
6090 J
2.
622 J
I bet so~
6.
A runner completed the 100.-meter dash in
10.0 seconds. Her average speed was
A) 10.0 m/s
B) 1,000 m/s
C) 0.100 m/s
D) 100 m/s
Answer:
A) 10.0 m/s
Explanation:
the formula for average speed is v=d/t
the distance is 100 meters
The time is 10.0 seconds
so v=100m/10.0s
= 10.0m/s
so the runners average speed was 10.0m/s
The average speed of the runner is equal to 10.0 m/s. Therefore, option (A) is correct.
What is speed?The speed of a body can be described as the distance covered in a definite time interval. The average speed can be defined as a scalar parameter as it possesses magnitude with no direction.
The speed can be determined from the ratio of the distance traveled by the object to the time taken to travel that distance.
The speed of any object can be calculated from the formula equation mentioned below:
Speed = total distance /time taken
Given, the distance covered by the runner = 100 m
The time taken by the runner, t = 10.0 s
The average speed of the runner can be calculated from the formula as shown below:
Speed = 100/10 = 10 m/s
Therefore, the average speed of the runner is 10.0 m/s.
Learn more about the speed, here:
brainly.com/question/12322912
#SPJ2
The period of a pendulum is directly proportional to the mass of the bob.
true or false.
Answer:
false
Explanation:
i just took the test <3
The period of a pendulum is not directly proportional to the mass of the bob. The period of pendulum is independent of the mass of the bob. Thus, the given statement is false.
What is the period of pendulum?A simple pendulum is the one which consists of a small metal ball called as the bob or a mass which is suspended from a fixed point by a long piece of thread such that the bob is free to swing back and forth from its mean position under the influence of the gravity.
The time period of a simple pendulum is the time taken by it to complete one oscillation. The formula for the time period or period (T) of a simple pendulum is T = 2π (√L/g), where L is the length of the pendulum thread and g is the acceleration due to gravity.
Learn more about Pendulum here:
https://brainly.com/question/14759840
#SPJ6
1.
In the notation, 1s2, the number 1 represents the ________ __________ where electrons are located.
energy level
outer shell
2.
The four parts, or blocks, on the periodic table are _____, _____, d, and f.
s, p
a, b
3.
The 2 in 1s2 represents the number of __________ located in that energy level.
electrons
protons
Answer:
energy level
s,p
electrons
Explanation:
I already done this trust me
In the notation 1 s² number 1 represents energy levels where electrons are located.The 4 parts on periodic table are s,p,d and f blocks.The 2 in 1 s² represents number of electrons in energy level.
What is an energy level?Electrons present in an atom revolve in different orbits which are stationary states and are also called as energy levels. The energy levels are numbered as integers which are also called as principal quantum numbers.
Energy of the stationary state is given as E= -R
1/n² where R
is the Rydberg's constant. When an electron is excited, and it moves from lower to higher energy levels there is absorption of energy, while when it moves from higher energy level to lower energy level it radiates or gives out energy in the form of radiation.
They can also be defined as the distances between electron and nucleus of an atom . Electrons present in K energy level have least energy .Energy level diagrams are studied to understand nature of bonding , placement of electrons in orbits and and elemental behavior under certain conditions.
Learn more about energy level,here:
https://brainly.com/question/12806827
#SPJ2
what does correlation mean
a mutual relationship or connection between two or more things.
a car accelerate at 9 m/s squared. Assuming the car starts from rest how far will it travel in 10 seconds
Answer:
450m
Explanation:
[tex]s = ut + \frac{1}{2} a {t}^{2} \\ s = 0 + t + \frac{1}{2} a {t}^{2} \\ \frac{1}{2 } \times 9 \times {10}^{2} = 450m[/tex]
A 2.34-kg gun has a recoil velocity of 5.2 m/sec. At what velocity does it fire its 95-gram bullets?
Explanation:
We need to use the conservation of energy to help us solve this one.
The energy imparted onto the bullet projectile is equal to the energy imparted into the recoiling gun. We can ignore potential energy and only consider the kinetic energy of the two masses (bullet and gun).
Remember that kinetic energy is expressed as [tex]K_E = \frac{1}{2}mv^2[/tex]
Conservation of energy means that both the gun and the bullet have the same amount of energy.
[tex]\frac{1}{2}m_gv_g^2 = \frac{1}{2}m_b v_b^2[/tex]
We'll want to put the mass terms into the same units. So the gun has a mass of 2340 grams.
Define specific charge of an electron. Write its value.
Answer:
The specific charge is defined as a charge by mass ratio i.e e/m. The charge on an electron (e) = 1.602 X 10-19C. The mass of the electron (m) = 9.1×10−31Kg.
Which is an example of current electricity?
The winter solstice, the shortest day of the year in the Northern hemisphere, occurs when the Earth is in which position?
Answer:
A
Explanation:
Two resistors, A and B, are connected in parallel across of a 6V battery. The current through B is found to be 2.0 A. When the two resistors are connected in series to the 6V battery, a voltmeter connected across the resistor A measures a voltage of 4V. Find the resistances of A and B.
Answer:
Resistance of A is [tex]6\ \Omega[/tex] and B is [tex]3\ \Omega[/tex]
Explanation:
The voltage across both the resistances will be the same as they are connected in parallel.
V = Voltage = 6 V
[tex]I_B=2\ \text{A}[/tex]
Resistance is given by
[tex]R_B=\dfrac{V}{I_B}\\\Rightarrow R_B=\dfrac{6}{2}\\\Rightarrow R_B=3\ \Omega[/tex]
[tex]V_B=V_b-V_A\\\Rightarrow V_B=6-4\\\Rightarrow V_B=2\ \text{V}[/tex]
Series connection
[tex]V_A=4\ \text{V}[/tex]
The current is constant in series connection
[tex]I=\dfrac{V_B}{R_B}\\\Rightarrow I=\dfrac{2}{3}\ \text{A}[/tex]
[tex]R_A=\dfrac{V_A}{I}\\\Rightarrow R_A=\dfrac{4}{\dfrac{2}{3}}\\\Rightarrow R_A=6\ \Omega[/tex]
The resistance of A is [tex]6\ \Omega[/tex] and B is [tex]3\ \Omega[/tex].
What are similarities between homogeneous mixture and
heterogeneous mixture
Answer:
they both are the mixture of substance
Answer:
a homogeneous mixture is a uniform mixture whose components appear to be in a single state while a heterogeneous mixture is non uniform mixture whose components remain separate
Explanation:
example of homogeneous_ water and ethanol
heterogeneous_ water and chalk
50 j of work was performed in 20 seconds. How much power was used to preform this task
Answer:
Power = 2.5 [W]
Explanation:
To be able to solve this problem we must remember that power is defined as the relationship of the work done in a given time interval.
[tex]P=W/t[/tex]
where:
P = power [W] (units of watts)
W = work = 50 [J]
t = time = 20 [s]
Now replacing:
[tex]P=50/20\\P=2.5[W][/tex]
Answer:
2.5
Explanation:
what is physical quantity
Answer:
physical quantity is a property of a material or system that can be qualified by measurement
[tex] \huge\mathfrak{ANSWER}[/tex]
the quantities by meals of which we describe the law of physics are known as physical quantities.
in order to measure a physical quantity we as you my certain magnitude of this quantity a standard and call its unit of that quantity to express the measurement of any physical quantity two thing must be mentioned.
the unit in which the quantity is measured.the numerical value which do not the magnitude of that quantity in term of the choosen unit.For Example -:
when we say that the length of a road is 20 m its mean that the unit of length is matter and the length of rod 20 time magnitude of metre.in other number the numerical value of physical quantities inversely proportional to its unit if N1 and N2 be the numerical value of a physical quantity into different unit u1 and u2 then[tex] \bold{ n_1 (u_1) = n_2(u_2)}[/tex]
a projectile is shot horizontally from the edge of a cliff, 230m above the ground. the projectile lands 300m from base of the cliff
Answer:
The time taken by the projectile to hit the ground is 6.85 sec.
Explanation:
Given that,
Vertical height of cliff = 230 m
Distance = 300 m
Suppose, determine the time taken by the projectile to hit the ground.
We need to calculate the time
Using second equation of motion
[tex]s=ut+\dfrac{1}{2}gt^2[/tex]
Where, s = vertical height of cliff
u = initial vertical velocity
g = acceleration due to gravity
Put the value in the equation
[tex]230=0+\dfrac{1}{2}\times9.8\times t^2[/tex]
[tex]t=\sqrt{\dfrac{230\times2}{9.8}}[/tex]
[tex]t=6.85 sec[/tex]
Hence, The time taken by the projectile to hit the ground is 6.85 sec.
can i eat air? im hungry
Answer:
Yes
Explanation:
What happens to the molecules of a substance when it changes phase?
When it comes to phase shifts or phase change the greater the intermolecular interactions are the closer the molecules are to one another.
What is phase change?A phase change occurs when matter transitions from one state to another (solid, liquid, gas, plasma). When enough energy is provided to the system (or when a significant quantity is removed), as well as when the pressure on the system is adjusted, these changes occur.Any two phases of matter can undergo phase transitions.All phase shifts are accompanied by an energy shift.Isothermal phase shifts occur in all cases.Temperature changes can cause substances to change phase often. Most substances are solid at low temperatures; as the temperature rises, they become liquid; and at even higher temperatures, they become gaseous.To Know more about Phase change here
https://brainly.com/question/14327191
#SPJ2
The asteroid Icarus orbits the sun like other planets. Its period is about 410 days. What is its mean distance from the sun
Answer:
Mean distance = 1.61 x 10^8 km
Explanation:
Given the following data;
Orbital period for Icarus, T2 = 410 days
To find the mean distance of Icarus, we would use Kepler's third law of motion.
According to Kepler's third law of planetary motion, the square of any planetary body's orbital period (P) is directly proportional to the cube of its orbit's semi-major axis.
Mathematically, it is given by the formula;
[tex] (\frac {T_{1}}{T_{2}})^2 = (\frac {r_{1}}{r_{2}})^3 [/tex]
Where;
T1 & T2 is the orbital period of a planetary object.
r1 & r2 is the mean distance of a planetary object.
Also, we know that the orbital period for earth, T1 = 365 days
Mean distance of earth = 1.49x10^8 km
Substituting into the equation, we have;
[tex] (\frac {365}{410})^2 = (\frac {1.49x10^{8}}{r_{2}})^3 [/tex]
[tex] (\frac {365}{410}})^2 = (\frac {1.49x10^{8}}{r_{2}})^3 [/tex]
[tex] (0.8902)^2 = (\frac {1.49x10^{8}}{r_{2}})^3 [/tex]
[tex] (0.7925) = (\frac {1.49x10^{8}}{r_{2}})^3 [/tex]
Cross-multiplying, we have;
[tex] (r_{2})^3 = \frac {1.49x10^{8}}{0.7925} [/tex]
Taking the cube root of both sides;
[tex] r_{2} = 1.61 * 10^8 km[/tex]