Answer:
The heat capacity of the calorimeter is 104.65 J/K
Explanation:
Heat lost by the hot water = Heat gained by cold water + Heat gained by the calorimeter
Heat lost by hot water = mCΔT
m = 75 g, C = 4.186 J/g.K, ΔT = (80 - 42.5) = 37.5 K
Heat lost by hot water = 75 × 4.186 × 37.5 = 11773.125 J
Heat gained by cold water = mCΔT
m = 100 g, C = 4.186 J/g.K, ΔT = (42.5 - 20) = 22.5 K
Heat gained by cold water = 100 × 4.186 × 22.5 = 9418.5 J
Heat gained by the calorimeter = Heat lost by hot water - Heat gained by cold water
Heat gained by the calorimeter = 11773.125 - 9418.5 = 2354.625 J
Heat gained by the calorimeter = Heat capacity of the calorimeter × ΔT
ΔT = (42.5 - 20) = 22.5 K
Heat capacity of the calorimeter = (Heat gained by the calorimeter)/(ΔT) = 2351.25/22.5 = 104.65 J/K
In some cases, neither of the two equations in the system will contain a variable with a coefficient of 1, so we must take a further step to isolate it. Let's say we now have3C+4D=52C+5D=2None of these terms has a coefficient of 1. Instead, we'll pick the variable with the smallest coefficient and isolate it. Move the term with the lowest coefficient so that it's alone on one side of its equation, then divide by the coefficient. Which of the following expressions would result from that process?a. C=53−43Db. C=1−52Dc. D=25−25Cd. D=54−34C
Answer:
According to the instructions given, only options a and b are correct.
That is,
C = (5/3) - (4D/3)
C = 1 – (5D/2)
D= -4/7
C= 17/7
Explanation:
3C + 4D = 5 and 2C + 5D = 2
So, following the instructions from the question,
1) we'll pick the variable with the smallest coefficient and isolate it.
In eqn 1, C has the smallest coefficient,
3C = 5 - 4D (isolated!)
In eqn 2, C still has the smallest coefficient,
2C = 2 - 5D
2) Move the term with the lowest coefficient so that it's alone on one side of its equation, then divide by the coefficient.
For eqn 1,
3C = 5 - 4D, divide through by the coefficient of C,
C = (5/3) - (4D/3)
This matches option a perfectly.
For eqn 2,
2C = 2 - 5D, divide through by the coefficient of C,
C = (2/2) - (5D/2) = 1 - (5D/2)
This matches option b perfectly!
Further solving the equations now,
Since C = C
(5/3) - (4D/3) = 1 - (5D/2)
(5D/2) - (4D/3) = 1 - (5/3)
(15D - 8D)/6 = -2/3
7D/6 = -2/3
D = -4/7
Substituting this into one of the eqns for C
C = 1 - (5D/2)
C = 1 - (5/2)(-4/7) = 1 - (-10/7) = 1 + (10/7) = 17/7.
QED!
The height, h , in meters of a dropped object after t seconds can be represented by h ( t ) = − 4.9 t 2 + 136 . What is the instantaneous velocity of the object one second after it is dropped?
Answer:
The velocity of the object 1 s after it is dropped is -9.8 m/s.
Explanation:
Hi there!
The instantaneous velocity is defined by the change in height over a very small time. Mathematically, it is expressed as the derivative of the function h(t):
instantaneous velocity = dh/dt
dh/dt = h´(t) = -2 · 4.9 · t
h´(t) = -9.8 · t
Now we have to eveluate the function h´(t) at t = 1 s:
h´(1) = -9.8 · (1) = -9.8
The velocity of the object 1 s after it is dropped is -9.8 m/s.
Final answer:
The instantaneous velocity of the object one second after it is dropped is 9.8 m/s, moving downwards.
Explanation:
The question asks for the instantaneous velocity of a dropped object after a specific time has elapsed, which is a physics concept related to mechanics and motion. Given the height equation h(t) = -4.9t2 + 136, the instantaneous velocity at time t can be found by taking the derivative of the height equation with respect to time, which gives us the velocity as a function of time v(t) = dh/dt. At t = 1 second, the derivative of the height equation is v(1) = -9.8(1) = -9.8 m/s. The negative sign indicates that the object is moving downwards. However, when we speak about the speed or magnitude of the velocity (instantaneous velocity), we typically refer to the positive value, which would be 9.8 m/s.
What is the current in amperes if 1400 Na+ ions flow across a cell membrane in 3.3 μs ? The charge on the sodium is the same as on an electron, but positive.
Answer:
Current, [tex]I=6.78\times 10^{-11}\ A[/tex]
Explanation:
In this case, we need to find the current in amperes if 1400 Na+ ions flow across a cell membrane in 3.3 μs.
Charge, [tex]q=1400\times 1.6\times 10^{-19}=2.24\times 10^{-16}\ C[/tex]
Time taken, [tex]t=3.3\ \mu s=3.3\times 10^{-6}\ s[/tex]
Let I is the current. It is given by total charge per unit time. It is given by :
[tex]I=\dfrac{q}{t}[/tex]
[tex]I=\dfrac{2.24\times 10^{-16}}{3.3\times 10^{-6}}[/tex]
[tex]I=6.78\times 10^{-11}\ A[/tex]
So, the current of [tex]6.78\times 10^{-11}\ A[/tex] is flowing across a cell membrane. Hence, this is the required solution.
to what circuit element is an ideal inductor equivalent for circuits with constant currents and voltages?
Answer:
Short circuit
Explanation:
In an ideal inductor circuit with constant current and voltage, it implies that the voltage drop in the circuit is zero (0).
Also, In circuit analysis, a short circuit is defined as a connection between two nodes that forces them to be at the same voltage.
In an ideal short circuit, this means there is no resistance and thus no voltage drop across the connection. That is voltage drop is zero (0).
Therefore, the circuit element is short circuit.
For circuits with constant currents and voltages, an ideal inductor is equivalent to a short circuit or a piece of wire with no resistance, as it does not affect the circuit voltage or resistance.
An ideal inductor in a circuit with constant currents and voltages acts as if it is effectively a wire with no resistance, since an ideal inductor does not dissipate energy when the current is constant. However, if we consider the energy transfer in a circuit with an inductor and another circuit element, often referred to as a 'black box', which could be a resistor, we notice energy is exchanged only when there is a change in current. Using the lumped circuit approximation, the inductor's magnetic fields are assumed to be completely internal, meaning it only interacts with other components via the current flowing through the wires, not by overlapping magnetic fields in space.
Given the Kirchhoff's voltage law, which states that the sum of the voltage drops in a closed loop must be zero, an inductor with a constant current will have a voltage drop that is zero, making it equivalent to a short circuit in terms of its impact on the voltage in the circuit. Therefore, for circuits with constant currents and voltages, an ideal inductor is equivalent to a short circuit or a piece of wire with no resistance, as it does not contribute any voltage drop or generate heat like a resistor would.
int[] numList = {2,3,4,5,6,7,9,11,12,13,14,15,16}; int count=0; for(int spot=0; spot
Hi, there is not much information about what do you need to do, but base on the C++ code you need to complete it to count the number of items in the array, using the instructions already written.
Answer:
#include <iostream>
using namespace std;
int main()
{
int numList [] = {2,3,4,5,6,7,9,11,12,13,14,15,16};
int count=0;
for(int spot=0; spot < (sizeof(numList)/sizeof( numList[ 0 ])); ++spot)
{
cout << numList[spot];
cout << "\n";
++count;
}
cout << "The number of items in the array is: ";
cout << count;
return 0;
}
Explanation:
To complete the program we need to finish the for statement, we want to know the number of items, we can get it by using this expression: (sizeof(numList)/sizeof( numList[ 0 ])), sizeof() function returns the number of bytes occupied by an array, therefore, the division between the number of bytes occupied for all the array (sizeof(numList)) by the number of bytes occupied for one item of the array (sizeof( numList[ 0])) equal the length of the array. While iterating for the array we are increasing the variable count that at the end contains the result that we print using the expression cout << "The number of items in the array is: "
You spot a plane that is 1.37 km north, 2.71 km east, and at an altitude 4.65 km above your position. (a) How far from you is the plane? (b) At what angle from due north (in the horizontal plane) are you looking? °E of N (c) Determine the plane's position vector (from your location) in terms of the unit vectors, letting î be toward the east direction, ĵ be toward the north direction, and k be in vertically upward. ( km)î + ( km)ĵ + ( km) k (d) At what elevation angle (above the horizontal plane of Earth) is the airplane?
Answer:
Explanation:
a ) Position of the plane with respect to observer ( origin ) is
R = 2.71 i + 1.37 j + 4.65 k
magnitude of R = √ (2.71² + 1.37² + 4.65²)
√(7.344 + 1.8769 + 21.6225)
=√30.8434
= 5.55 km
b ) angle with north
cos Ф = 1.37 / 5.55
= .2468
Ф = 75°
c )
R = 2.71 i + 1.37 j + 4.65 k
=
In what ways do observed extrasolar planetary systems differ from our own solar system?
Answer:
Extrasolar solar system differ from our solar system in many ways such as of mass, size and shape of the planet, as well as temperature or amount of heat received in each planet.
Explanation:
An extrasolar planet is a planet outside the Solar System, while the Solar System orbit around the sun as a result of the gravitational pull of the sun.
Thus, we can say that the major difference between extrasolar planetary systems and solar system is that in solar system, planets orbit around the Sun, while in extrasolar planetary systems, planets orbit around other stars.
All of the planets in our solar system orbit around the Sun. Planets that orbit around other stars are called exoplanets or extrasolar.
Extrasolar solar system differ from our solar system in many ways such as of mass, size and shape of the planet. They also differ in terms of temperature, because the temperature in each planet in solar system depends on its distance from the sun while that of the extrasolar depends on the activities of the star.
What are (a) the lowest frequency, (b) the second lowest frequency, (c) the third lowest frequency of transverse vibrations on a wire that is 10.0m long, has a mass of 100g, and is stretched under tension of 250 N?
Answer:f1 = 7.90Hz, f2= 15.811Hz, f3 = 23.71Hz.
Explanation: length of string = 10m, mass of string = 100g = 0.1kg, T= 250N
We need the velocity of sound wave in a string when plucked with a tension T, this is given below as
v = √T/u
Where u = mass /length = 0.1/ 10 = 0.01kg/m
Hence v = √250/0.01, v = √25,000 = 158.11
a) at the lowest frequency.
At the lowest frequency, the length of string is related to the wavelength with the formulae below
L = λ/2, λ= 2L.
λ = 2 * 10
λ = 20m.
But v = fλ where v = 158.11m/s and λ= 20m
f = v/ λ
f = 158.11/ 20
f = 7.90Hz.
b) at the first frequency.
The length of string and wavelength for this case is
L = λ.
Hence λ = 10m
v = 158.11m/s
v= fλ
f = v/λ
f = 158.11/10
f = 15.811Hz
c) at third frequency
The length of string is related to the wavelength of sound with the formulae below
L =3λ/2, hence λ = 2L /3
λ = 2 * 10 / 3
λ = 20/3
λ= 6.67m
v = fλ where v = 158.11m/s, λ= 6.67m
f = v/λ
f = 158.11/6.67
f = 23.71Hz.
In uniform circular motion, the acceleration is perpendicular to the velocity at every instant. Is this true when the motion is not uniform—that is, when the speed is not constant?
Answer:
No.
Explanation:
Through uniform We can presume you mean constant in both that is in magnitude as well as in direction ⠀
When you apply a steady, non-zero acceleration to a resting body, the velocity can be parallel to the acceleration and not always perpendicular at any time later.
We can do the same for an object with an initial velocity in a direction which is different than that of acceleration, and the direction of its velocity will asymptotically approach to that of acceleration over time.
In both cases the motion of a object undergoing a non-zero persistent acceleration can not be uniform That is the concept of acceleration: the velocity change over time.
A capacitor stores an energy of 8 Joules when there is a voltage of 51 volts across its terminals. A second identical capacitor of the same value is stores an energy of 2 Joules. What is the voltage across the terminals of the second capacitor?
Answer:
6.38 V
Explanation:
Note: Since the capacitors are identical, The same Charge flows through them.
For the first capacitor,
The Energy stored in a capacitor is given as
E = 1/2qv ............... Equation 1
Where E = Energy stored by the capacitor, q = charge in the capacitor v = Voltage.
make q the subject of the equation
q = 2E/v ................ Equation 2
Given: E = 8 J, v = 51 v.
Substitute into equation 2
q = 8/51
q = 0.3137 C.
For the second capacitor,
v = 2E/q ................... Equation 3
Given: q = 0.3137 C, E = 2 J.
Substitute into equation 3
v = 2/0.3137
v = 6.38 V
Hence the voltage across the second capacitor = 6.38 V
A 6.1-m-long solid circular metal rod (E = 150 GPa) must not stretch more than 10 mm when a load of 109 kN is applied to it. Determine the smallest diameter rod that should be used. State your answer in mm.
To solve this problem we will apply the concepts related to the deformation of a body and the normal effort, from which we will obtain the area. From this area applied to the geometric concept of a circular bar we will find the diameter.
The deformation equation in a rod tells us that
[tex]\delta = \frac{PL}{AE}[/tex]
Here,
P = Load
L = Length
A = Cross-sectional area
E = Elastic Modulus
Rearranging the Area,
[tex]A = \frac{PL}{\delta E}[/tex]
Replacing we have that the area is,
[tex]A = \frac{(109*10^{3})(6.1)}{(10*10^{-3})(150*10^9)}[/tex]
[tex]A = 0.000443266m^2[/tex]
[tex]A = 44.32*10^{-6}m^2[/tex]
Using the geometric expression for the Area we have,
[tex]A = \frac{\pi}{4} d^2[/tex]
[tex]d = \sqrt{\frac{4A}{\pi}}[/tex]
[tex]d = \sqrt{\frac{4(44.32)}{\pi}}[/tex]
[tex]d = 7.51mm[/tex]
Therefore the smalles diameter rod is 7.51mm
Can you find a vector quantity that has a magnitude of zero but components that are not zero? Explain. Can the magnitude of a vector be less than the magnitude of any of its components? Explain.
It is not possible to find a vector quantity of magnitude zero but components different from zero
The magnitude can never be less than the magnitude of any of its components
The volume of a fluid in a tank is 0.25 m3 . of the specific gravity of the fluid is 2.0. Determine the mass of the fluid. Given the density of water is 1000 kg/m3. Express the answer in Kg.
Answer:
Explanation:
Given
volume of Tank [tex]V=0.25\ m^3[/tex]
Specific gravity [tex]=2[/tex]
specific gravity is the defined as the ratio of density of fluid to the density of water
Density of water [tex]\rho _w=1000\ kg/m^3[/tex]
Density of Fluid [tex]\rho =2\times 1000=2000\ kg/m^3[/tex]
We know mass of a fluid is given by the product of density and volume
[tex]m=\rho \times V[/tex]
[tex]m=2000\times 0.25[/tex]
[tex]m=500\ kg[/tex]
A ball is released from rest at the top of an incline. It is measured to have an acceleration of 2.2. Assume g=9.81 m/s2. What is the angle of the incline in degrees?
Answer:
θ=12.7°
Explanation:
Lets take the mass of the ball = m
The acceleration due to gravity = g = 9.81 m/s²
The acceleration of the block = a
a= 2.2 m/s²
Lets take angle of incline surface = θ
When block slide down :
The gravitational force on the block = m g sinθ
By using Newton's second law
F= m a
F=Net force ,a acceleration ,m=mass
m g sinθ = ma
a= g sinθ
Now by putting the values in the above equation
2.2 = 9.81 sinθ
[tex]sin\theta =\dfrac{2.2}{9.81}\\sin\theta=0.22\\\theta = 12.7\ degrees[/tex]
θ=12.7°
Aristarchus measured the angle between the Sun and the Moon when exactly half of the Moon was illuminated. He found this angle to be A greater than 90 degrees. B exactly 90 degrees. C less than 90 degrees by an amount too small for him to measure. D less than 90 degrees by an amount that was easy for him to measure.
Answer:
when the Sun illuminates half of the Moon it must be at 90°
Explanation:
The Moon has a circular motion around the Earth and the relative position of the sun, the earth and the moon create the lunar phases.
For this case when the Sun illuminates half of the Moon it must be at 90°, this angle changes with the movement of the moon, it is zero degree for the new moon and 180° for the full moon
A rectangular dam is 101 ft long and 54 ft high. If the water is 35 ft deep, find the force of the water on the dam (the density of water is 62.4 lb/ft3).
Final answer:
The force of water on a rectangular dam is given by the formula F = pgh²L/2, where p is the density of water, h is the depth at the dam, and L is the length of the dam. Using the given values, we can calculate the force of the water on the dam to be approximately 1,130,946 lb.
Explanation:
The force of water on a rectangular dam is given by the formula F = pgh²L/2, where p is the density of water, h is the depth at the dam, and L is the length of the dam. We are given the values p = 62.4 lb/ft³, h = 35 ft, and L = 101 ft.
Substituting these values into the formula, we have F = (62.4 lb/ft³) * (35 ft)² * (101 ft) / 2.
Simplifying the expression, we get F = 1,130,946 lb. Therefore, the force of the water on the dam is approximately 1,130,946 lb.
A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. Ignore air resistance. (a) Where on the ground (relative to the position of the helicopter when she drops) should the stuntwoman have placed foam mats to break her fall? (b) Draw x-t, y-t, vx-t, and vy-t graphs of her motion.
The stuntwoman should place the foam mats approximately 37 meters south of the helicopter's position. Calculations are based on her dropping from a height of 30.0 m with an initial horizontal velocity of 15 m/s, taking into account gravitational acceleration and ignoring air resistance.
Explanation:To solve this problem, we need to calculate two things: how long the stuntwoman is in the air and how far she will travel horizontally during this time. Given the constant velocity components are 10.0 m/s upward and 15.0 m/s horizontal towards the south and ignoring air resistance, we'll tackle part (a) of the question first.
Part (a) - Determining the landing spot of the stuntwoman
Firstly, we acknowledge that the upward component of the helicopter's velocity will momentarily counteract gravity for the stuntwoman, but since air resistance is ignored, this effect is instantaneously null once she begins her descent. The primary considerations then are the height of 30.0 m and the horizontal component of 15.0 m/s.
To calculate the time (t) it takes for the stuntwoman to hit the ground, we use the equation for vertical motion under gravity:
h = 1/2gt^2
Where h is the height (30.0 m) and g is the acceleration due to gravity (~9.8 m/s^2). Solving for t, we get:
t = sqrt((2*h)/g) = sqrt((2*30)/9.8) ≈ 2.47 s
With the time in air known, we calculate the horizontal displacement (d) using:
d = v*t
Where v is the horizontal velocity (15.0 m/s). Thus, d ≈ 15.0 m/s * 2.47 s ≈ 37.05 m.
This means the stuntwoman should place the foam mats around 37 meters south of the helicopter's position at the moment she drops.
Part (b) - Drawing the graphs
For simplicity, the explanation of graph drawing is summarized: The x-t graph will show a linear increase in displacement over time, illustrating constant velocity in the horizontal direction. The y-t graph will depict a parabola, indicating acceleration (deceleration up then acceleration down) due to gravity in the vertical component. The vx-t graph will be a horizontal line showing constant horizontal velocity, and the vy-t graph will start at a positive value, decrease to zero at the peak of her motion, and then increase negatively as she accelerates downwards.
A screen is placed 1.20m behind a single slit. The central maximum in the resulting diffraction pattern on the screen is 1.40cm wide-that is, the two first-order diffraction minima are separated by 1.40cm
What is the distance between the two second-order minima?
Answer:
2.8 cm
Explanation:
[tex]y_1[/tex] = Separation between two first order diffraction minima = 1.4 cm
D = Distance of screen = 1.2 m
m = Order
Fringe width is given by
[tex]\beta_1=\dfrac{y_1}{2}\\\Rightarrow \beta_1=\dfrac{1.4}{2}\\\Rightarrow \beta_1=0.7\ cm[/tex]
Fringe width is also given by
[tex]\beta_1=\dfrac{m_1\lambda D}{d}\\\Rightarrow d=\dfrac{m_1\lambda D}{\beta_1}[/tex]
For second order
[tex]\beta_2=\dfrac{m_2\lambda D}{d}\\\Rightarrow \beta_2=\dfrac{m_2\lambda D}{\dfrac{m_1\lambda D}{\beta_1}}\\\Rightarrow \beta_2=\dfrac{m_2}{m_1}\beta_1[/tex]
Distance between two second order minima is given by
[tex]y_2=2\beta_2[/tex]
[tex]\\\Rightarrow y_2=2\dfrac{m_2}{m_1}\beta_1\\\Rightarrow y_2=2\dfrac{2}{1}\times 0.7\\\Rightarrow y_2=2.8\ cm[/tex]
The distance between the two second order minima is 2.8 cm
The distance between the two second-order minima is 2.80 cm.
The central maximum's width given is 1.40 cm (this is the distance between the first-order minima, m = ±1). So, the distance from the center to the first-order minimum (m = ±1) is 0.70 cm.
Using the formula for the first-order minimum (m = 1):
a sin(θ₁) = λ
We know that the distance to the first minima (y₁) with the screen distance (L) is given by:
tan(θ₁) ≈ sin(θ₁) = y₁ / L
so, for the first-order minima:
y₁ = Lλ / a
We have y₁ = 0.70 cm, L = 1.20 m. Solving for aλ:
a = Lλ / 0.007
Next, for the second-order minima (m = 2), we use:
y₂ = 2Lλ / a
Thus, the distance between the second-order minima will be:
2y₂ = 2 × 2Lλ / a = 2 × 1.40 cm = 2.80 cm
So, the distance between the two second-order minima is 2.80 cm.
Assuming the same initial conditions as described in FNT 2.2.1-1, use the energy-interaction model in two different ways (parts (a) and (b) below) to determine the speed of the ball when it is 4 meters above the floor headed down:
a) Construct a particular model of the entire physical process, with the initial time when the ball leaves Christine’s hand, and the final time when the ball is 4 meters above the floor headed down.
b) Divide the overall process into two physical processes by constructing two energy-system diagrams and applying energy conservation for each, one diagram for the interval corresponding to the ball traveling from Christine’s hand to the maximum height, and then one diagram corresponding to the interval for the ball traveling from the maximum height to 4 meters above the floor headed down.
c) Did you get different answers (in parts (a) and (b)) for the speed of the ball when it is 4 meters above the floor headed down?
Answer:
(a). Vf = 7.14 m/s
(b). Vf = 7.14 m/s
(c). same answer
Explanation:
for question (a), we would be applying conservation of energy principle.
but the initial height is h = 1.5 m
and the initial upward velocity of the ball is Vi = 10 m/s
Therefore
(a). using conservation law
Ef = Ei
where Ef = 1/2mVf² + mghf ........................(1)
also Ei = 1/2mVi² + mghi ........................(2)
equating both we have
1/2mVf² + mghf = 1/2mVi² + mghi
eliminating same terms gives,
Vf = √(Vi² + 2g (hi -hf))
Vf = √(10² + -2*9.8*2.5) = 7.14 m/s
Vf = 7.14 m/s
(b). Same process as done in previous;
Ef = Ei
but here the Ef = mghf ...........(3)
and Ei = 1/2mVi² + mghi ...........(4)
solving for the final height (hf) we relate both equation 3 and 4 to give
mghf = 1/2mVi² + mghi ..............(5)
canceling out same terms
hf = hi + Vi²/2g
hf = 1.5 + 10²/2*9.8 = 6.60204m ............(6)
recalling conservation energy,
Ef = Ei
1/2mVf² + mghf = mghi
inputting values of hf and hi we have
Vf = √(2g(hi -hf)) = 7.14 m/s
Vf = 7.14 m/s
(c). From answer in option a and c, we can see there were no changes in the answers.
A ball player catches a ball 3.0 sec after throwing it vertically upward. With what speed did he throw it, and what height did it reach?
Answer:
14.715 m/s
11.03625 m
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 9.81 m/s² = a
Time taken to go up will be [tex]\dfrac{3}{2}=1.5\ s[/tex]. This is also equal to the time taken to go down.
[tex]v=u+at\\\Rightarrow v=0+9.81\times 1.5\\\Rightarrow v=14.715\ m/s[/tex]
The speed of the ball when it reaches the player is 14.715 m/s
This is equal to the speed at which the player threw the ball
[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{14.715^2-0^2}{2\times 9.81}\\\Rightarrow s=11.03625\ m[/tex]
The ball reached a height of 11.03625 m
What are the units of the following properties? Enter your answer as a sequence of five letters separated by commas, e.g., A,F,G,E,D. Note that some properties listed may have the same units. 1) mass 2) heat 3) density 4) energy 5) molarity (A) g (B) J (C) mol (D) K (E) g/mol (F) mol/L (G) mol/K (H) g/mL (I) J/K (J) J/K*mol (K) J/K*g (L) kJ/L
Answer:
The sequence is A,B,H,B,F
Explanation:
The Standard International unit is Kilogram (kg) and the mass of a body can also be expressed in gram (g).Heat is a form of energy and the unit for energy is joule (J), thus the unit of heat is also joule (J).Density is mass per unit volume where the unit of mass is gram (g) and the unit of volume can be taken as milli-liter (mL). Thus g/mL is the unit of density.The unit of energy is joule (J).Molarity is number of solute in mol dissolved in 1 liter of solution. Thus mol/L is the the unit of molarity.A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at 43.0o above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of the cliff? (b) The ground at the top of the cliff is level, with a constant elevation of 25.0 m above the cannon. Under the conditions of part (a), how far does the shell land past the edge of the cliff?
Answer:
a) v₀ = 32.64 m / s , b) x = 59.68 m
Explanation:
a) This is a projectile launching exercise, we the distance and height of the cliff
x = v₀ₓ t
y = [tex]v_{oy}[/tex] t - ½ g t²
We look for the components of speed with trigonometry
sin 43 = v_{oy} / v₀
cos 43 = v₀ₓ / v₀
v_{oy} = v₀ sin 43
v₀ₓ = v₀ cos 43
Let's look for time in the first equation and substitute in the second
t = x / v₀ cos 43
y = v₀ sin 43 (x / v₀ cos 43) - ½ g (x / v₀ cos 43)²
y = x tan 43 - ½ g x² / v₀² cos² 43
1 / v₀² = (x tan 43 - y) 2 cos² 43 / g x²
v₀² = g x² / [(x tan 43 –y) 2 cos² 43]
Let's calculate
v₀² = 9.8 60 2 / [(60 tan 43 - 25) 2 cos 43]
v₀ = √ (35280 / 33.11)
v₀ = 32.64 m / s
.b) we use the vertical distance equation with the speed found
y = [tex]v_{oy}[/tex] t - ½ g t²
.y = v₀ sin43 t - ½ g t²
25 = 32.64 sin 43 t - ½ 9.8 t²
4.9 t² - 22.26 t + 25 = 0
t² - 4.54 t + 5.10 = 0
We solve the second degree equation
t = (4.54 ±√(4.54 2 - 4 5.1)) / 2
t = (4.54 ± 0.46) / 2
t₁ = 2.50 s
t₂ = 2.04 s
The shortest time is when the cliff passes and the longest when it reaches the floor, with this time we look for the horizontal distance traveled
x = v₀ₓ t
x = v₀ cos 43 t
x = 32.64 cos 43 2.50
x = 59.68 m
The minimum muzzle velocity of a cannon to clear a 25.0 m tall cliff from 60.0 m away involves using projectile motion equations to find the initial velocity components, while ensuring the shell reaches the required height and distance.
Explanation:To solve for the minimum muzzle velocity for a cannon to shoot a shell past a 25.0 m cliff from 60.0 m away, we can use projectile motion equations. First, we separate the initial velocity into its horizontal (vx) and vertical (vy) components:
vx = v0 × cos(θ)vy = v0 × sin(θ)The shell must reach a height of at least 25.0 m to clear the cliff. We use the equation of motion in the vertical direction, considering the initial vertical velocity (vy) and the displacement (s = 25 m), to find the time (t) it takes to reach the top of the cliff. Then, using the horizontal velocity (vx), we can calculate how far the shell would travel horizontally in that time, ensuring that it covers at least 60.0 m. With the horizontal distance (d) and time (t) determined, we can calculate the shell's trajectory past the cliff edge.
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A 500-Hz whistle is moved toward a listener at a speed of 10.0 m/s. At the same time, the listener moves at a speed of 20.0 m/s in a direction away from the whistle. What is the apparent frequency heard by the listener? (The speed of sound is 340 m/s.)
Answer:
f' = 485 Hz
Explanation:
given,
Frequency of whistle,f = 500 Hz
speed of source, v_s = 10 m/s
Speed of observer, v_o - 20 m/s
speed of sound,v = 340 m/s
Apparent frequency heard = ?
Using Doppler's effect formula to find apparent frequency
[tex]f' = (\dfrac{v-v_0}{v-v_s})f[/tex]
[tex]f' = (\dfrac{340-20}{340-10})\times 500[/tex]
[tex]f' = 0.9696\times 500[/tex]
f' = 485 Hz
Hence, the apparent frequency is equal to 485 Hz.
To determine the apparent frequency heard by the listener is equal to 545.45 Hz.
Given the following data:
Observer velocity = 20.0 m/sFrequency of sound = 500 HzSource velocity = 10.0 m/sSpeed of sound = 340 m/sTo determine the apparent frequency heard by the listener, we would apply Doppler's effect of sound waves:
Mathematically, Doppler's effect of sound waves is given by the formula:
[tex]F_o = \frac{V \;+ \;V_o}{V\; - \;V_s} F[/tex]
Where:
V is the speed of a sound wave.F is the actual frequency of sound.[tex]V_o[/tex] is the observer velocity.[tex]V_s[/tex] is the source velocity.[tex]F_o[/tex] is the apparent frequency.Substituting the given parameters into the formula, we have;
[tex]F_o = \frac{340 \;+ \;20}{340\; - \;10} \times 500\\\\F_o =\frac{360}{330} \times 500\\\\F_o =1.0909 \times 500[/tex]
Apparent frequency = 545.45 Hz.
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A charge of 32.0 nC is placed in a uniform electric field that is directed vertically upward and has a magnitude of 4.30x 104 V/m
Part A What work is done by the electric force when the charge moves a distance of 0.480 m to the right?
Part B What work is done by the electric force when the charge moves a distance of 0.660 m upward?
Part C What work is done by the electric force when the charge moves a distance of 2.50 m at an angle of 45.0° downward from the horizontal?
A) The work done by the electric field is zero
B) The work done by the electric field is [tex]9.1\cdot 10^{-4} J[/tex]
C) The work done by the electric field is [tex]-2.4\cdot 10^{-3} J[/tex]
Explanation:
A)
The electric field applies a force on the charged particle: the direction of the force is the same as that of the electric field (for a positive charge).
The work done by a force is given by the equation
[tex]W=Fd cos \theta[/tex]
where
F is the magnitude of the force
d is the displacement of the particle
[tex]\theta[/tex] is the angle between the direction of the force and the direction of the displacement
In this problem, we have:
The force is directed vertically upward (because the field is directed vertically upward)The charge moves to the right, so its displacement is to the rightThis means that force and displacement are perpendicular to each other, so
[tex]\theta=90^{\circ}[/tex]
and [tex]cos 90^{\circ}=0[/tex]: therefore, the work done on the charge by the electric field is zero.
B)
In this case, the charge move upward (same direction as the electric field), so
[tex]\theta=0^{\circ}[/tex]
and
[tex]cos 0^{\circ}=1[/tex]
Therefore, the work done by the electric force is
[tex]W=Fd[/tex]
and we have:
[tex]F=qE[/tex] is the magnitude of the electric force. Since
[tex]E=4.30\cdot 10^4 V/m[/tex] is the magnitude of the electric field
[tex]q=32.0 nC = 32.0\cdot 10^{-9}C[/tex] is the charge
The electric force is
[tex]F=(32.0\cdot 10^{-9})(4.30\cdot 10^4)=1.38\cdot 10^{-3} N[/tex]
The displacement of the particle is
d = 0.660 m
Therefore, the work done is
[tex]W=Fd=(1.38\cdot 10^{-3})(0.660)=9.1\cdot 10^{-4} J[/tex]
C)
In this case, the angle between the direction of the field (upward) and the displacement (45.0° downward from the horizontal) is
[tex]\theta=90^{\circ}+45^{\circ}=135^{\circ}[/tex]
Moreover, we have:
[tex]F=1.38\cdot 10^{-3} N[/tex] (electric force calculated in part b)
While the displacement of the charge is
d = 2.50 m
Therefore, we can now calculate the work done by the electric force:
[tex]W=Fdcos \theta = (1.38\cdot 10^{-3})(2.50)(cos 135.0^{\circ})=-2.4\cdot 10^{-3} J[/tex]
And the work is negative because the electric force is opposite direction to the displacement of the charge.
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A jet fighter pilot wishes to accelerate from rest at a constant acceleration of 5 g to reach Mach 3 (three times the speed of sound) as quickly as possible. Experimental tests reveal that he will black out if this acceleration lasts for more than 5.0 s. Use 331 m/s for the speed of sound. (a) Will the period of acceleration last long enough to cause him to black out? (b) What is the greatest speed he can reach with an acceleration of 5g before he blacks out?
Final answer:
The jet fighter pilot will black out during the acceleration period as it lasts longer than 5.0 s. The greatest speed the pilot can reach with an acceleration of 5g before blacking out is 245 m/s.
Explanation:
To determine whether the jet fighter pilot will black out, we need to calculate the time of acceleration. The speed of sound is v = 331 m/s. The speed the pilot wants to reach is 3 times the speed of sound, so the desired speed is 3 * 331 m/s = 993 m/s. We can use the equation:
v = u + at
Where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration (5 g = 5 * 9.8 m/s^2 = 49 m/s^2), and t is the time.
Substituting the values, we get:
993 m/s = 0 m/s + 49 m/s² x t
Rearranging this equation to solve for t, we get:
t = 993 m/s / 49 m/s^2 = 20.265 s
Since the acceleration lasts for longer than 5.0 seconds, the pilot will black out during the acceleration period.
To calculate the greatest speed the pilot can reach before blacking out, we can use the same equation, but rearrange it to solve for v:
v = u + at
Substituting the values, we get:
v = 0 m/s + 49 m/s^2 x 5.0 s = 245 m/s
Therefore, the greatest speed the pilot can reach with an acceleration of 5 g before blacking out is 245 m/s.
A muon is produced by a collision between a cosmic ray and an oxygen nucleus in the upper atmosphere at an altitude of 50 . It travels vertically downward to the surface of the Earth where it arrives with a total energy of 178 . The rest energy of a muon is 105.7 . What is the kinetic energy of a muon at the surface
Answer:
72.3 MeV
Explanation:
E = Total energy of muon = 178 MeV
[tex]E_0[/tex] = Rest energy of a muon = 105.7 MeV
Kinetic energy of the muon at the surface of the Earth is given by the difference of the total energy and the rest energy of the muon
[tex]K=E-E_0\\\Rightarrow K=178-105.7\\\Rightarrow K=72.3\ MeV[/tex]
The kinetic energy of a muon at the surface is 72.3 MeV
Two identical stones, A and B, are thrown from a cliff from the same height and with the same initial speed. Stone A is thrown vertically upward, and stone B is thrown vertically downward. Which of the following statements best explains which stone has a larger speed just before it hits the ground, assuming no effects of air friction?
a. Both stones have the same speed; they have the same change in Ugand the same Ki
b. A, because it travels a longer path.
c. A, because it takes a longer time interval.
d. A, because it travels a longer path and takes a longer time interval.
e. B, because no work is done against gravity.
Answer:
Option A
Explanation:
This can be explained based on the conservation of energy.
The total mechanical energy of the system remain constant in the absence of any external force. Also, the total mechanical energy of the system is the sum of the potential energy and the kinetic energy associated with the system.
In case of two stones thrown from a cliff one vertically downwards the other vertically upwards, the overall gravitational potential energy remain same for the two stones as the displacement of the stones is same.
Therefore the kinetic energy and hence the speed of the two stones should also be same in order for the mechanical energy to remain conserved.
Answer:
b. A, because it travels a longer path.
Explanation:
If the stone A is thrown is thrown vertically upwards and another stone is dropped down directly from the same height above the ground then the stone A will hit the ground with a higher speed because it falls down from a greater height above the earth surface.This can be justified by the equation of motion given below:
[tex]v^2=u^2+2\times a\times s[/tex]
where:
[tex]v=[/tex] final velocity
[tex]u=[/tex] initial velocity
[tex]a=[/tex] acceleration = g (here)
[tex]s=[/tex] displacement of the body
Now we know that at the maximum height the speed of the object will be zero for a moment. So for both the stones A and B the initial velocity is zero, stone B is also dropped from a height with initial velocity zero.Acceleration due to gravity is same for the stones so the only deciding factor that remains is s, displacement of the stones. Since stone A is thrown upwards it will attain a greater height before falling down.Why are jovian planets so much larger than terrestrial planets?
Explanation:
The temperature in the inner solar system was too high for light gases to condense, while in the outer solar system, the temperature was much lower, which allowed the Jovian planets to form, which grew enough to accumulate and retain the hydrogen gas that remained in the solar nebula, which led to its high levels of hydrogen and large size.
A steel piano wire is 0.7 m long and has a mass of 5 g. It is stretched with a tension of 500 N. What is the speed of transverse waves on the wire? To reduce the wave speed by a factor of 2 without changing the tension, what mass of copper wire would have to be wrapped around the wire?
The speed of transverse waves on the steel piano wire can be calculated using the formula √(Tension / (Mass per unit length)). To reduce the wave speed by a factor of 2 without changing the tension, we can solve for the new wave speed, and then calculate the difference in mass per unit length with the copper wire.
Explanation:The speed of transverse waves on a steel piano wire can be calculated using the formula:
Speed = √(Tension / (Mass per unit length))
Where the tension in the wire is 500 N and the mass per unit length is calculated by dividing the mass of the wire by its length. Therefore, the mass per unit length is 5 g / 0.7 m = 7.14 g/m.
To reduce the wave speed by a factor of 2 without changing the tension, we can use the equation:
New wave speed = √(New tension / (Mass per unit length))
We can solve this equation for the new tension by rearranging it as:
New tension = (New wave speed)^2 * (Mass per unit length)
Since we want to reduce the wave speed by a factor of 2, the new wave speed is half the original speed. Substituting these values into the equation, we have:
(0.5 * Old wave speed)^2 * (Mass per unit length) = 500 N
Solving for the new mass per unit length gives:
New mass per unit length = 500 N / (0.5 * Old wave speed)^2
The difference between the new mass per unit length and the mass per unit length of copper wire is the mass of copper wire that needs to be wrapped around the steel wire. However, we would need additional information to calculate this difference.
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(2 points) A ring weighing 9.45 g is placed in a graduated cylinder containing 25.3 mL of water. After the ring is added to the cylinder the water rises to 27.4 mL. What metal is the ring made out of? Assume the ring is a single metal.
Answer:
Titanium.
Explanation:
Density of a metal is defined as the mass of the metal and its volume.
Volume of the metal = total volume- volume of initial water
= 27.4 - 25.3
= 2.1 ml
Mathematically,
Density = mass/volume
= 0.00945 kg/0.0000021 m3
= 4500 kg/m3.
The metal is Titanium.