Answer:
a) 4.681*10^10 electrons
b) 3.67*10^12 electrons
Explanation:
The amount of electrons in a charge of 1C is:
[tex]1C=6.2415*10^{18}\ electrons[/tex]
You use the previous equality as a conversion factor.
a) The sing of the charge is not important in the calculation of the number electrons, so, you use the absolute value of the charge
[tex]7.50nC=7.50*10^{-9}C*\frac{6.2415*10^{18}}{1C}=4.681*10^{10}\ electrons[/tex]
In 7.50nC there are 4.61*10^18 electrons
b)
[tex]0.580\mu C=0.580*10^{-6}C*\frac{6.2415*10^{18}}{1C}=3.67*10^{12}\ electrons[/tex]
To obtain a charge of 0.580 µC in a neutral object you need to take out 3.67*10^12 electrons
Two identical objects A and B fall from rest from different heights to the ground. If object B takes twice as long as object A to reach the ground, what is the ratio of the heights from which A and B fell
Answer:
1:4
Explanation:
We have, two identical objects A and B fall from rest from different heights to the ground.
Object B takes twice as long as object A to reach the ground. It is required to find the ratio of the heights from which A and B fell. Let [tex]h_A\ \text{and}\ h_B[/tex] are the height for A and B respectively. So,
[tex]\dfrac{h_A}{h_B}=\dfrac{(1/2)gt_A^2}{(1/2)gt_B^2}\\\\\dfrac{h_A}{h_B}=\dfrac{t_A^2}{t_B^2}[/tex]
We have,
[tex]t_B=2t_A[/tex]
So,
[tex]\dfrac{h_A}{h_B}=\dfrac{t_A^2}{(2t_B)^2}\\\\\dfrac{h_A}{h_B}=\dfrac{1}{4}[/tex]
So, the ratio of the heights from which A and B fell is 1:4.
Enterprising students set an enormous slip-n-slide (a plastic sheetcovered in water to reduce friction) on flat ground. If the slip-n-slideis 250 m long, how small does the average acceleration have to be fora student starting at 5 m/s to slide to the end
Answer:
a = -0.05 m/s² (negative sign shows deceleration)
Explanation:
In order, to find out the minimum average acceleration for a student starting at 5 m/s to slide to the end, we can use 3rd equation of motion. 3rd equation of motion is given as follows:
2as = Vf² - Vi²
where,
a = minimum acceleration required = ?
s = minimum distance covered = 250 m
Vf = Final Speed = 0 m/s (for minimum acceleration the student will barely cover 250 m and then stop)
Vi = Initial Velocity = 5 m/s
Therefore,
2a(250 m) = (0 m/s)² - (5 m/s)²
a = - (25 m²/s²)/(500 m)
a = -0.05 m/s² (negative sign shows deceleration)
consider an electric dipole lying along x-axis with mid-point O as the origin of coordinate system.find the electric potential V at point P due to dipole.in addition to this,find electric potentials for special cases. when P lies on the axial line and when P lies on the equatorial line.
Answer:
axial V = 0
equatorial V = k q 2a / (x² -a²), V = k q 2x / (a² -x²)
Explanation:
A dipole is a system formed by two charges of equal magnitude, but different sign, separated by a distance 2a; let's look for the electrical potential in an axial line
V = k (q / √(a² + y²) - q /√ (a² + y²))
V = 0
the potential on the equator
we place the positive charge to the left and perform the calculation for a point outside the dipole
V = k (q / (x-a) - q / (x + a))
V = k q 2a / (x² -a²)
we perform the calculation for a point between the dipo charges
V = k (q / (a-x) - q / (a + x))
V = k q 2x / (a² -x²)
At t = 0 the components of a radio-controlled car's velocity are vx = 0.5 m/s and vy = 1.2 m/s. Find the components of the car's velocity at t = 4.1 s, given that the components of its average acceleration during this period are ax = 2 m/s2 and ay = -1 m/s2.
Answer:
vx' = 8.7 m/s
vy' = - 2.9 m/s
Explanation:
The average acceleration during a time period is given by the formula:
a = (v' - v)/(t' - t)
where,
a = average acceleration
v' = Final Velocity
v = Initial Velocity
t' = Ending Time
t = Starting Time
Now, for x-component of velocity:
a = ax = 2 m/s²
v' = vx' = ?
v = vx = 0.5 m/s
t' = 4.1 s
t = 0 s
Therefore,
2 m/s² = (vx' - 0.5 m/s)/(4.1s - 0s)
(2 m/s²)(4.1 s) = vx' - 0.5 m/s
8.2 m/s + 0.5 m/s = vx'
vx' = 8.7 m/s
For y- component of velocity:
a = ay = -1 m/s²
v' = vy' = ?
v = vy = 1.2 m/s
t' = 4.1 s
t = 0 s
Therefore,
- 1 m/s² = (vy' - 1.2 m/s)/(4.1s - 0s)
(- 1 m/s²)(4.1 s) = vy' - 1.2 m/s
- 4.1 m/s + 1.2 m/s = vy'
vy' = - 2.9 m/s
A student is asked to design an experiment to determine the change in angular momentum of a disk that rotates about its center and the product of the average torque applied to the disk and the time interval in which the torque is exerted. A net force is applied tangentially to the surface of the disk. The rotational inertia of the disk about its center is I = 1/2 MR^2
Which two of the following quantities should the student measure to determine the change in angular momentum of the disk after 10 s? Select two answers
A. The magnitude of the net force exerted on the disk
B. The distance between the center of the disk and where the net force is applied to the disk
C. The radius of the disk
D. The mass of the disk
Answer:
A. The magnitude of the net force exerted on the disk
B. The distance between the center of the disk and where the net force is applied to the disk
Explanation:
To determine the change in angular momentum of the disk after a stipulated time, one must measure the above options.
The radius of the disk is fixed and does not vary with the experiment, and the mass of the disk is also constant and known.
One must first measure the magnitude of the net force exerted on the disk, and determine the torque as a result of this torque from the distance between the center of the disk and the point where the net force is applied. The above statement also points out the necessity of measuring the distance between the center of the disk and the point where the net force is applied on the disk, as both the torque, and the moment of inertia is calculated from this point.
torque T = Force time distance of point of action of force from mid point of the disk
T = F X r
T x t = Δ(Iω)
Where t is the time,
and Δ(Iω) is change in angular momentum.
A 16.0 g bullet is moving to the right with speed 250 m/s when it hits a target and travels an additional 22.6 cm into the target. What are the magnitude (in N) and direction of the stopping force acting on the bullet
Answer:
The magnitude will be "2212 N".
Explanation:
The given values are:
Initial speed, u = 250 m/s
Final speed, v = 0
Mass, m = 16.0 = 0.016 kg
Distance, d = 22.6 cm
On converting cm into m, we get
d = 0.226 m
As we know,
⇒ [tex]v^2-u^2=-2ad[/tex]
⇒ [tex]a=\frac{v^2-u^2}{-2d}[/tex]
On putting the estimated values, we get
⇒ [tex]=\frac{(0)^2-(250)^2}{-2\times 0.226}[/tex]
⇒ [tex]=\frac{0-62500}{-0.452}[/tex]
⇒ [tex]=13,8276 \ m/s^2[/tex]
Now,
Force, [tex]F=ma[/tex]
On putting values, we get
⇒ [tex]=0.016\times 138276[/tex]
⇒ [tex]=2212 \ N[/tex] (magnitude)
The magnitude of the stopping force on the bullet is 2,212.4 N in opposite direction to the bullet.
The given parameters;
mass of the bullet, m = 16 gspeed of the bullet, u = 250 m/sdistance traveled by the bullet and the target, d = 22.6 cm = 0.226 mThe acceleration of the bullet is calculated as follows;
v² = u² - 2ad
where;
v is the final velocity when the bullet stops = 00 = 250² - a(2 x 0.226)
0.452a = 62500
[tex]a = \frac{62500}{0.452} \\\\a = 138,274.34 \ m/s^2\\\\[/tex]
The magnitude of the stopping force on the bullet is calculated as follows;
F = ma
F = 0.016 x 138,274.34
F = 2,212.4 N
Thus, the magnitude of the stopping force on the bullet is 2,212.4 N in opposite direction to the bullet.
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A wire runs from the top of a pole that is h feet tall to the ground. The wire touches the ground a distance of d feet from the base of the pole. The wire makes an angle of theta with the top of the pole. Express h in terms of theta and d.
Answer:
A = Tan{-1} d/h
Explanation
Let the angle Theta be A
From identity the angle A has an opposite side d and an adjacent h.
From trigonometry ratio
Tan A = d/h
A = Tan{-1} d/h
A flat plate of polished copper of surface emissivity 0.1 is 0.1 m long and 0.1 m wide. The plate is placed vertically, with one side heated to a surface temperature of 500 K, and the other side remaining insulated. The heated side is exposed to quiescent air at 300 K and the surroundings are also at 300 K. Assume that air can be taken as an ideal gas. Estimate the heat rate from the flat plate.
Answer:
The heat rate is
Explanation:
From the question we are told that
The surface emissivity is [tex]e=0.1[/tex]
The length is [tex]L = 0.1 \ m[/tex]
The width is [tex]W = 0.1 \ m[/tex]
The surface temperature of one side is [tex]T_1 = 500 \ K[/tex]
The temperature of the quiescent air [tex]T_c = 300 \ K[/tex]
The temperature of the surrounding is [tex]T_s = 300 \ K[/tex]
The heat rate from the flat plate is mathematically represented as
[tex]Q = \sigma A e (T_1^4 - T_a^4)[/tex]
Where [tex]\sigma[/tex] is the quiescent air Stefan-Boltzmann constant and it value is
[tex]\sigma = 5.67*10^{-8} m^{-2} \cdot K^{-4}[/tex]
A is the area which is mathematically evaluated as
[tex]A = W * L[/tex]
substituting values
[tex]A = 0.1 * 0.1[/tex]
[tex]A = 0.01 \ m^2[/tex]
substituting values
[tex]Q = 5.67 *10^{-8} * (0.01) *(500^4 -300^4)[/tex]
[tex]Q =3.045 \ Watt[/tex]
A 200-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.400 rev/s in 2.00 s
Answer:
F = 187.5N.
Explanation:
So, from the question above we are given the following parameters or data or information which is going to assist us in solving the question/problem;
=> Mass= 200-kg , => radius = 1.50 m, => angular speed of 0.400 rev/s, and time = 2.0 seconds.
Step one: the first step is to calculate or determine the angular speed. Here, the angular speed is Calculated in rad/sec.
Angular speed, w = 0.400 × 2π
= 2.51 rad/s.
Step two: determine the value of a.
Using the formula below;
W = Wo + a × time,t.
2.51 = 0 + a(2.0).
a= 1.25 rad/s^2.
Step three: determine constant force from the Torque.
Torque = I × a.
F = 1/2 × (200 kg) × 1.50 × 1.25.
F = 187.5N
A submarine dives from rest a 100-m distance beneath the surface of an ocean. Initially, the submarine moves at a constant rate of 0.3 m/s2 until reaches a speed of 4 m/s and then lowers at a constant speed. The density of salt water is 1030 kg/m3. The submarine has a hatch with an area of 2 m2 located on the top of the submarine’s body.
a. How much time does it take for the submarine to move down 100 m?
b. Calculate the gauge pressure applied on the submarine at the depth of 100
m.
c. Calculate the absolute pressure applied on the submarine at the depth of
100.
d. How much force is required in order to open the hatch from the inside of
the submarine?
answer this step-by-step, please.
Answer:
a. Time = 16.11 s
b. Gauge Pressure = 1009400 Pa = 1 MPa
c. Absolute Pressure = 1110725 Pa + 1.11 MPa
d. Force = 2.22 MN
Explanation:
a.
For the accelerated part of motion of submarine we can use equations of motion.
Using 1st equation of motion:
Vf = Vi + at₁
t₁ = (Vf - Vi)/a
where,
t₁ = time taken during accelerated motion = ?
Vf = final velocity = 4 m/s
Vi = Initial Velocity = 0 m/s (Since, it starts from rest)
a = acceleration = 0.3 m/s²
Therefore,
t₁ = (4 m/s - 0 m/s)/(0.3 m/s²)
t₁ = 13.33 s
Now, using 2nd equation of motion:
d₁ = (Vi)(t₁) + (0.5)(a)(t₁)²
where,
d₁ = the depth covered during accelerated motion
Therefore,
d₁ = (0 m/s)(13.33 s) + (0.5)(0.3 m/s²)(13.33 s)²
d₁ = 88.89 m
Hence,
d₂ = d - d₁
where,
d₂ = depth covered during constant speed motion
d = total depth = 100 m
Therefoe,
d₂ = 100 m - 88.89 m
d₂ = 11.11 m
So, for uniform motion:
s₂ = vt₂
where,
v = constant speed = 4 m/s
t₂ = time taken during constant speed motion
11.11 m = (4 m/s)t₂
t₂ = 2.78 s
Therefore, total time taken by submarine to move down 100 m is:
t = t₁ + t₂
t = 13.33 s + 2.78 s
t = 16.11 s
b.
The gauge pressure on submarine can be calculated by the formula:
Pg = ρgh
where,
Pg = Gauge Pressure = ?
ρ = density of salt water = 1030 kg/m³
g = 9.8 m/s²
h = depth = 100 m
Therefore,
Pg = (1030 kg/m³)(9.8 m/s²)(100 m)
Pg = 1009400 Pa = 1 MPa
c.
The absolute pressure is given as:
P = Pg + Atmospheric Pressure
where,
P = Absolute Pressure = ?
Atmospheric Pressure = 101325 Pa
Therefore,
P = 1009400 Pa + 101325 Pa
P = 1110725 Pa + 1.11 MPa
d.
Since, the force to open the door must be equal to the force applied to the door by pressure externally.
Therefore, the force required to open the door can be found out by the formula of pressure:
P = F/A
F = PA
where,
P = Absolute Pressure on Door = 1110725 Pa
A = Area of door = 2 m²
F = Force Required to Open the Door = ?
Therefore,
F = (1.11 MPa)(2 m²)
F = 2.22 MN
A 62-kg person jumps from a window to a fire net 20.0 m directly below, which stretches the net 1.4 m. Assume that the net behaves like a simple spring. (a) Calculate how much it would stretch if the same person were lying in it. (b) How much would it stretch if the person jumped from 38 m?
Answer:
a) x = 0.098
b) x = 2.72 m
Explanation:
(a) To find the stretch of the fire net when the same person is lying in it, you can assume that the net is like a spring with constant spring k. It is necessary to find k.
When the person is falling down he acquires a kinetic energy K, this energy is equal to the elastic potential energy of the net when it is max stretched.
Then, you have:
[tex]K=U\\\\\frac{1}{2}mv^2=\frac{1}{2}kx^2[/tex] (1)
m: mass of the person = 62kg
k: spring constant = ?
v: velocity of the person just when he touches the fire net = ?
x: elongation of the fire net = 1.4 m
Before the calculation of the spring constant, you calculate the final velocity of the person by using the following formula:
[tex]v^2=v_o^2+2gy[/tex]
vo: initial velocity = 0 m/s
g: gravitational acceleration = 9.8 m/s^2
y: height from the person jumps = 20.0m
[tex]v=\sqrt{2gy}=\sqrt{2(9.8m/s^2)(20.0m)}=14\frac{m}{s}[/tex]
With this value you can find the spring constant k from the equation (1):
[tex]mv^2=kx^2\\\\k=\frac{mv^2}{x^2}=\frac{(62kg)(14m/s)^2}{(1.4m)^2}=6200\frac{N}{m}[/tex]
When the person is lying on the fire net the weight of the person is equal to the elastic force of the fire net:
[tex]W=F_e\\\\mg=kx[/tex]
you solve the last expression for x:
[tex]x=\frac{mg}{k}=\frac{(62kg)(9.8m/s^2)}{6200N/m}=0.098m[/tex]
When the person is lying on the fire net the elongation of the fire net is 0.098m
b) To find how much would the net stretch, If the person jumps from 38 m, you first calculate the final velocity of the person again:
[tex]v=\sqrt{2gy}=\sqrt{2(9.8m/s^2)(38m)}=27.29\frac{m}{s}[/tex]
Next, you calculate x from the equation (1):
[tex]x=\sqrt{\frac{mv^2}{k}}=\sqrt{\frac{(62kg)(27.29m/s)^2}{6200N/m}}\\\\x=2.72m[/tex]
The net fire is stretched 2.72 m
A) If the person is lying on the net, the net would stretch by : 0.0679 m
B) If the person jumped from 38m, the net would stretch by : 1.61 m
Given data :
Mass of person (m) = 62 kg
Initial height ( H₁ ) = 20 m
Net stretch ( H[tex]_{f}[/tex] ) = -1.2 m
Initial potential energy before jump ( PE₁ ) = mgH₁ = 62 * 9.81 * 20 = 12164.4J
Potential energy after the jump ( PE₂ ) = mgH[tex]_{f}[/tex] = 62 * 9.81 * ( -1.2 ) = -729.86J
The potential spring constant ( SE ) = 1/2 kx²
= 1/2 * k * ( 1.2 )²
Applying the principle of energy conservation
PE₁ = PE₂ + SE
12164.4 = - 729.86 + 0.5 * k * 1.44
∴ k = ( 12164.4 + 729.86 ) / ( 0.5 * 1.44 )
= 17908.69
A) Calculate the amount of stretch if same person lies on the net1/2 kx² = mgx ---- ( 1 )
Where x = stretch
equation ( 1 ) becomes equation ( 2 )
1/2 kx = mg ----- ( 2 )
x ( amount of stretch ) = ( 2mg ) / k
= ( 2 * 62 * 9.81 ) / 17908.69
= 0.0679 m
B ) Calculate How much the net would stretch if Height = 38 mHi = 38 m
MgHi = mgH[tex]_{f}[/tex] + 1/2 kx² ----- ( 3 )
where ; H[tex]_{f}[/tex] = -x
Back to equation ( 3 )
62 * 9.81 * 38 = 62 * 9.81 * (-x) + 1/2 ( 17908.69 x² )
23112.36 + 608.22x - [tex]\frac{17908.69 x^{2} }{2}[/tex] = 0
8954.345 x² - 608.22x - 23112.36 = 0 ----- ( 4 )
Resolving the quadratic equation ( 4 )
x = ± 1.60623 ≈ 1.61 m
Therefore we can conclude that the net would stretch 1.61 m if the person jumped from 38 m
Hence we can conclude that If the person is lying on the net, the net would stretch by : 0.0679 m, and If the person jumped from 38m the net would stretch by : 1.61 m
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g A ceiling fan is rotating counterclockwise with a constant angular acceleration of 0.35π rad/s2 about a fixed axis perpendicular to its plane and through its center. Assume the fan starts from rest. (a) What is the angular velocity of the fan after 2.0 s? (Enter the magnitude.) rad/s (b) What is the angular displacement of the fan after 2.0 s? (Enter the magnitude.) rad
Answer:
The correct answer will be:
(a) 2.2 rad/s
(b) 2.2 rad
Explanation:
The given values are:
Angular acceleration, [tex]\alpha = 0.35 \pi \ rad/s^2[/tex]
(a)...
At time t = 2.0 s,
The angular velocity will be:
⇒ [tex]\omega = \alpha t[/tex]
On putting the estimated values, we get
⇒ [tex]=0.35\pi \times 2.0[/tex]
∴ [[tex]\pi = 3.14[/tex]]
⇒ [tex]=0.35\times 3.14\times 2.0[/tex]
⇒ [tex]=2.2 \ rad/s[/tex]
(b)...
The angular displacement will be:
⇒ [tex]\theta = \frac{1}{2}\alpha t^2[/tex]
On putting the estimated values, we get
⇒ [tex]=\frac{1}{2}\times 0.35\pi\times (2.0)^2[/tex]
⇒ [tex]=\frac{1}{2}\times 0.35\times 3.14\times 4[/tex]
⇒ [tex]=1.099\times 2[/tex]
⇒ [tex]=2.2 \ rad[/tex]
If Q = 16 nC, a = 3.0 m, and b = 4.0 m, what is the magnitude of the electric field at point P?
Your spaceship lands on an unknown planet. To determine the characteristics of this planet, you drop a wrench from 5.00 m above the ground and measure that it hits the ground 0.804 s later. Part APart complete What is the acceleration of gravity near the surface of this planet
Answer:
g = 15.5 m/s²
Explanation:
In order to find the acceleration due to gravity near the surface of this planet can be calculated by using 2nd equation of motion. The 2nd equation of motion is given as:
h = Vi t + (0.5)gt²
where,
h = height covered by the wrench = 5 m
Vi = Initial Velocity = 0 m/s
t = Time Taken to hit the ground = 0.804 s
g = acceleration due to gravity near the surface of the planet = ?
Therefore,
5 m = (0 m/s)(0.804 s) + (0.5)(g)(0.804 s)²
g = (5 m)/(0.3232 s²)
g = 15.5 m/s²
What are found in nucleus and atoms?
Answer:
The nucleus of an atom contains the majority of the atom’s mass, and is composed of protons and neutrons, which are collectively referred to as nucleons. The much-lighter electrons orbit their atom’s nucleus. The Protons. Protons are positively charged particles found in an atom’s nucleus.
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linear momentum is the product of mass and acceleration.
Answer:
false
Explanation:
Linear momentum is the product of an objects mass and velocity
p=m×v
Answer:
Linear momentum is defined as the product of a system's mass multiplied by its velocity. In symbols, linear momentum is expressed as p = mv. ... Thus the greater an object's mass or the greater its velocity, the greater its momentum. Momentum p is a vector having the same direction as the velocity v.
Explanation:
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How can you identify a moveable pulley?
A. It has a fixed axle.
B. It moves up and down with the load.
C. It is anchored.
D. It has been relocated from one location to another.
A projectile is shot from the edge of a cliff 115 m above ground level with an initial speed of 65.0 m/s at an angle of 35.0 ∘ with the horizontal, as shown in the figure (Figure 1) . Determine the time taken by the projectile to hit point P at ground level.
Answer:
9.96 s
Explanation:
Given in the y direction:
Δy = -115 m
v₀ = 65.0 m/s sin 35.0° = 37.28 m/s
a = -9.8 m/s²
Find: t
Δy = v₀ t + ½ at²
-115 = 37.28 t − 4.9 t²
4.9 t² − 37.28 t − 115 = 0
t = [ 37.28 ± √(37.28² − 4(4.9)(-115)) ] / 9.8
t = (37.28 ± 60.37) / 9.8
t = 9.96
Using the following information to determine the young's modulus for the unknown material, the radius of the material is 4 cm. while gravitational
acceleration g=10m/s?
initial length (cm) 25
final length (cm)25.7
mass (gm) 200
Answer:
14285.71N/m2
Explanation:
Young modulus known as modulus of elasticity is defined as;
E = σ/ε
Where E is young modulus
ε is strain defined as extention / length
σ is stress defined as force /area
Let's calculate σ;
Force = mass× gravity =200/1000. × 10 =0.2kg× 10 = 2N
The area impacted by the force is raduis surface of the wire and it's calculated thus;
πr^2 = 22/7 × (0.04)^2 ; 4cm in m = 0.04m=0.005m2
Hence σ = 2/0.005=400N/M2
Let's calculate ε;
ε= extension/ original length
extension = final length - original length
extension=25.7-25=0.7cm= 0.007m
ε= 0.7/25
Hence E = 400/ 0.7/25
E = 400 × 25/ 0.7= 14285.71N/m2
linear momentum is the product of mass and acceleration
Answer:
This statement is false , linear momentum is the product of mass and velocity
Answer:
Linear momentum is defined as the product of a system's mass multiplied by its velocity. In symbols, linear momentum is expressed as p = mv. ... Thus the greater an object's mass or the greater its velocity, the greater its momentum. Momentum p is a vector having the same direction as the velocity v.
Explanation:
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A plasma is a gas of ionized (charged) particles. When plasma is in motion, magnetic effects "squeeze" its volume, inducing inward pressure known as a pinch. Consider a cylindrical tube of plasma with radius R and length L moving with velocity v along its axis. If there are n ions per unit volume and each ion has charge q , we can determine the pressure felt by the walls of the cylinder.
Required:
a. What is the volume charge density p in terms of n and q?
b. The thickness of the cylinder surface is n^1/3. What is the surface charge density σ in terms of n and q?
Answer:
a
The volume charge density is [tex]\rho = nq[/tex]
b
The surface charge density is [tex]\sigma = n^{\frac{2}{3} } q[/tex]
Explanation:
From the question we are told that
The radius is R
The length is L
The velocity is v
The number of ions per unit volume is n
The charge is q
The thickness of the cylinder surface is [tex]n^{\frac{1}{3} }[/tex]
The volume charge density is mathematically represented as
[tex]\rho = nq[/tex]
The surface charge density is mathematically represented as
[tex]\sigma = \rho n^{\frac{1}{3} }[/tex]
substituting for [tex]\rho[/tex]
[tex]\sigma = n * n^{\frac{1}{3} } q[/tex]
[tex]\sigma = n^{\frac{2}{3} } q[/tex]
One strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown with a speed of 26.0 m/s. The first one is thrown at an angle of 67.5° with respect to the horizontal. At what angle should you throw the second snowball to make it hit the same point as the first?
Answer:
22.5°
Explanation:
Short answer: The trajectories will hit the same target when the projectile is launched at complementary angles. The second angle is 90° -67.5° = 22.5°.
__
Longer answer: The horizontal speed of the snowball launched at angle α with speed s is ...
vh = s·cos(α)
Then the horizontal distance at time t is ...
x = vh·t
and the time taken to get to some distance x is ...
t = x/vh = x/(s·cos(α))
The equation for the vertical motion of the projectile is ...
y = -4.9t² +s·sin(α)·t
Substituting the above expression for t, we have y in terms of x:
y = -4.9x²/(s·cos(α))² +(s·sin(α)·x)/(s·cos(α))
Factoring gives ...
y = (x/(cos(α))(-4.9x/(s²·cos(α)) +sin(α))
The height y will be zero at x=0 and at ...
0 = -4.9x/(s²·cos(α)) +sin(α)
x = s²·sin(α)·cos(α)/4.9 = (s²/9.8)sin(2α)
So, for some alternate angle β, we want ...
sin(2α) = sin(2β)
We know this will be the case for ...
2β = 180° -2α
β = 90° -α
The second snowball should be thrown at an angle of 90°-67.5° = 22.5° to make it hit the same point as the first.
The label on a battery-powered radio recommends the use of a rechargeable nickel-cadmium cell (nicads), although it has a 1.25-V emf, whereas an alkaline cell has a 1.58-V emf. The radio has a 3.65 Ω resistance. How much more power is delivered to the radio by alkaline cell, which has an internal resistance of 0.200Ω than by an nicad cell, having an internal resistance of 0.0.040Ω?
Answer:
0.2 W more power than nicad cell is delivered by alkaline cell
Explanation:
FOR NICKEL-CADMIUM CELL (nicads):
First we find the current supplied to radio by the cell. For this purpose, we use the formula:
I = E/(R+r)
where,
I = current supplied
E = emf of cell = 1.25 V
R = resistance of radio = 3.65 Ω
r = internal resistance of cell = 0.04 Ω
Therefore,
I = (1.25 V)/(3.65 Ω + 0.04 Ω)
I = 0.34 A
Now, we calculate the power delivered to radio by following formula:
P = VI
but, from Ohm's Law: V = IR
Therefore,
P = I²R
where,
P = Power delivered = ?
I = current = 0.34 A
R = Resistance of radio = 3.65 Ω
Therefore,
P = (0.34 A)²(3.65 Ω)
P = 0.41 W
FOR ALKALINE CELL:
First we find the current supplied to radio by the cell. For this purpose, we use the formula:
I = E/(R+r)
where,
I = current supplied
E = emf of cell = 1.58 V
R = resistance of radio = 3.65 Ω
r = internal resistance of cell = 0.2 Ω
Therefore,
I = (1.58 V)/(3.65 Ω + 0.2 Ω)
I = 0.41 A
Now, we calculate the power delivered to radio by following formula:
P = VI
but, from Ohm's Law: V = IR
Therefore,
P = I²R
where,
P = Power delivered = ?
I = current = 0.41 A
R = Resistance of radio = 3.65 Ω
Therefore,
P = (0.41 A)²(3.65 Ω)
P = 0.61 W
Now, fo the difference between delivered powers by both cells:
ΔP = (P)alkaline - (P)nicad
ΔP = 0.61 W - 0.41 W
ΔP = 0.2 W
A child at the top of a slide has a gravatational store of 1800j what is the childs maximum kinetic store as he slides down explain your answer
Answer:
1800 J
Explanation:
Energy is conserved, so the maximum kinetic energy equals the change in gravitational energy.
⦁ Match the following terms:
⦁ Mass number
⦁ Isotopes
⦁ Nitrogen
⦁ Atomic number
⦁ The number of protons in the nucleus of an atom.
⦁ The number of protons and neutrons in the nucleus of an atom.
⦁ The name of the element with atomic number 7.
⦁ Atoms with the same number of protons, but different number of neutrons.
Answer:
Mass number - ⦁ The number of protons and neutrons in the nucleus of an atom.
Isotopes - ⦁ Atoms with the same number of protons, but different number of neutrons.
Nitrogen - ⦁ The name of the element with atomic number 7.
Atomic number - ⦁ The number of protons in the nucleus of an atom.
A box is released from rest and allowed to slide down a ramp with friction. Which statement most accurately describes the energy transformations during this motion?
a) The box’s initial kinetic energy is transformed into potential energy.
b) The box’s initial potential energy and thermal energy is transformed into
kinetic energy.
c) The box’s initial kinetic energy is transformed into potential energy and
thermal energy.
d) The box’s initial potential energy is transformed into kinetic energy and
thermal energy.
Answer:
d) The box’s initial potential energy is transformed into kinetic energy and
thermal energy.
Explanation:
Let us analyze the situation first. Initially we have a box at rest placed at some height on a ramp. So, the three energies associated with the box will be:
Kinetic Energy = 0 (due to zero velocity)
Thermal Energy = 0 (due to not temperature change)
Potential Energy = Greater than zero value (due to height)
Now, when the box is released to slide down the ramp with friction, the energies become:
Kinetic Energy = Increasing (due to increase in velocity)
Thermal Energy = Increasing (due to increase in temperature, because of friction)
Potential Energy = Decreasing (due to decrease in height)
So, from Law of Conservation of Energy, we can write:
Loss of Potential Energy = Gain in Kinetic Energy + Gain in Thermal Energy
So, the correct option is:
d) The box’s initial potential energy is transformed into kinetic energy and thermal energy.
2 pts.) An electron is placed in an electric field of intensity 700 N/Cj. What are themagnitude and direction of the acceleration of this electron due to this field? (melectron=9.1 × 10-31 kg, qe= 1.60 × 10-19 C)
Explanation:
We have,
Electric field intensity is 700 N/Cj
It is required to find the magnitude and direction of the acceleration of this electron due to this field.
The electric force is balanced by the force due to its motion i.e.
qE =ma
a is acceleration of this electron
[tex]a=\dfrac{qE}{m}\\\\a=\dfrac{1.6\times 10^{-19}\times 700}{9.1\times 10^{-31}}\\\\a=1.23\times 10^{14}\ m/s^2[/tex]
So, the acceleration of the electron is [tex]1.23\times 10^{14}\ m/s^2[/tex] and it is moving in +y direction.
IS THERE A PLASTIC THAT YOU CAN SEE AND BREATHE THROUGH??? SOMEONE PLEASE ANSWER THIS!!!
Answer in my own words:
Research reveals that most of the indoor microplastics contained in the air are created by synthetic plastic fibres, as well as by textiles used in furniture
Key words:
1: Research
2: air
3: Plastic
Please mark brainliest
Hope this helps.
Cheetahs, the fastest of the great cats, can reach 50.0 miles/hour in 2.22 s starting from rest. Assuming that they have constant acceleration throughout that time, find their acceleration in meters per second squared.
Answer:
[tex]10.07m/s^2[/tex]
Explanation:
Information we have:
velocities:
initial velocity: [tex]v_{i}=0mph[/tex] (starts from rest)
final velocity: [tex]v_{f}=50mph[/tex]
time: [tex]t=2.22s[/tex]
Since we need the answer in [tex]m/s^2[/tex], we nees to convert the speed to meters per second:
[tex]v_{f}=\frac{50miles}{1hour}(\frac{1hour}{3,600s} )(\frac{1609.34meters}{1mile} ) \\\\v_{f}=\frac{50*1609.34}{3600} m/s\\\\v_{f}=22.35m/s[/tex]
We find the acceleration with the following formula:
[tex]a=\frac{v_{f}-v_{i}}{t}[/tex]
substituting the known values:
[tex]a=\frac{22.35m/s-0m/s}{2.22s}\\ \\a=10.07m/s^2[/tex]
the acceleration is 10.07[tex]m/s^2[/tex]
Answer:
The acceleration of the Cheetah is found to be 10.07 m/s²
Explanation:
We have the following data in this question:
Vf = Final Velocity of the Cheetah = 50 miles/hr
Vf = (50 miles/hr)(1 hr/ 3600 s)(1609.34 m/1 mile)
Vf = 22.35 m/s
Vi = Initial Speed of Cheetah = 0 m/s (Since, Cheetah starts from rest)
t = time interval passed = 2.22 s
So, in order to find the acceleration, we simply use the formula for acceleration, that is:
Acceleration = a = (Vf - Vi)/t
a = (22.35 m/s - 0 m/s)/2.22 s
a = 10.07 m/s²
The acceleration of the Cheetah is found to be 10.07 m/s²
v(t) = 12 sin(913t + 71°) volts. Find (a) angular frequency in radians per second, (b) frequency in Hz, (c) period, (d) maximum voltage, (e) minimum voltage, (f) Peak-to-Peak voltage , (g) rms voltage, (h) average voltage, (i) voltage expressed as a phasor, (j) the average power consumed by a 220 ohm resistor having this voltage , and (k) the voltage at t= 3ms
Answer:
Explanation:
v(t) = 12 sin(913t + 71°) volts
a ) 913° = (π / 180) x 913 radians
= 15.92 radians
a ) angular frequency ω = 15.92 radians / s
b ) ω = 2πn
n = ω / 2π
= 15.92 / 2 x 3.14
= 2.53 Hz
c ) Period = 1 / n
= 1 / 2.53 = .4 s .
d )
Maximum voltage = 12 volt
e) Minimum volts = - 12 volts
g ) rms volts = V / √2
= 12 / √2
= 8.48 V
h )
Average voltage = 0
j ) Average power
Vrms² / R
= 12 x 12 / 2 x 220
= .327 W.
k )
v(t) = 12 sin(913t + 71°)
v(t) = 12 sin(913x .003 + 71°)
= 12 sin(73.7°)
= 11.5 V .
