Answer:
m=Fcr/v^2
Explanation:
At a certain instant, coil A is in a 10-T external magnetic field and coil B is in a 1-T external magnetic field. Both coils have the same area and are oriented at right angles to the field. Which coil will have a greater emf induced in it
Answer:
Impossible to know without more information about the fields.
Explanation:
Changing the magnetic field induces the external magnetic field, but the information regarding magnetic field variation is not provided. We need to required more information for this
Therefore according to the above explanation the correct option is Impossible to know without more information about the fields.
Hence, the b option is correct
The orbit of a certain a satellite has a semimajor axis of 4.0 x 107 m and an eccentricity of 0.15. Its perigee (minimum distance) and apogee (maximum distance) are respectively
Answer:
100KM and 1kkm
Explanation:
A train at rest emits a sound at a frequency of 1057 Hz. An observer in a car travels away from the sound source at a speed of 20.6 m/s. What is the frequency heard by the observer
Answer:
993.52 Hz
Explanation:
The frequency of sound emitted by the stationery train is 1057 Hz.
The car travels away from the train at 20.6 m/s.
The frequency the observer hears is given by the formula:
[tex]f_o = \frac{v - v_o}{v}f[/tex]
where v = velocity of sound = 343 m/s
vo = velocity of observer
f = frequency from source
This phenomenon is known as Doppler's effect.
Therefore:
[tex]f_o = \frac{343 - 20.6}{343} * 1057\\ \\f_o = 322.4 / 343 * 1057\\\\f_o = 993.52 Hz[/tex]
The frequency heard by the observer is 993.52 Hz.
A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m2. Determine the magnitude of the electric field 3.0 mm from the axis.
Answer:
Explanation:
Gauss Theorem
E2πrL=o2πRL/εo
then
E=oR/(rεo)
E=(0.4*10^-9*2*10^-3) / (3*10^-3*8.85*10^-12)
= 30.13 N/C
A positive charge moves in the direction of an electric field. Which of the following statements are true?
a. The potential energy associated with the charge decreases.
b. The electric field does positive work on the charge.
c. The electric field does negative work on the charge.
d. The potential energy associated with the charge increases.
e. The electric field does not do any work on the charge.
f. The amount of work done on the charge cannot be determined without additional information.
Answer:
The potential enwrgy associated with charge decreases.
The ele ric field does negative work on the charge.
Explanation:
Answer:
The potential energy associated with the charge decreases
The electric field does positive work on the charge.
A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4Ï€r2) with respect to the radius r when r is each of the following. (Answers in unit ft2/ft)
(a) 1 ft
(b) 3 ft
(c) 6 ft
Answer:
A) 8π ft²/ft
B) 24π ft²/ft
C) 48π ft²/ft
Explanation:
Surface area of the spherical balloon is not clear here but it is supposed to be;
S = 4πr²
where:
r is the radius of the spherical balloon
So thus, the rate of change of the surface area of the spherical balloon by its radius will be:
dS/dr = 8πr
A) at r = 1ft;
dS/dr = 8 × π × 1
dS/dr = 8π ft²/ft
B) at r = 3 ft;
dS/dr = 8 × π × 3
dS/dr = 24π ft²/ft
C) at r = 6ft;
dS/dr = 8 × π × 6
dS/dr = 48π ft²/ft
A 6- F capacitor is charged to 90 V and is then connected across a 700- resistor. What is the initial charge on the capacitor
Answer:
540C.
Explanation:
A capacitor of capacitance C when charged to a voltage of V will have a charge Q given as follows;
Q = CV ----------(i)
From the question, the initial charge on the capacitor is the charge on it before it was connected to the resistor. In other words, the initial charge on the capacitor will have a maximum value which can be calculated using equation (i) above.
Where;
C = 6F
V = 90V
Substitute these values into equation (i) as follows;
Q = 6 x 90
Q = 540 C
Therefore, the initial charge on the capacitor is 540C.
Besides the gravitational force, a 2.80-kg object is subjected to one other constant force. The objectstarts from rest and in 1.20 s experiences a displacement of (4.20 i - 3.30 j) m, where the direction of jis the upward vertical direction. Determine the other force.
Answer:
the other force= (16.3i + 14.6j)N
EXPLANATION:
Given:
Mass=2.80-kg
t= 1.2s
Since the object started from rest, the origin is (0,0) which symbolize the the object's initial position.
We will need to calculate the magnitude of the displacement using the below formula;
d = (1/2)at2 + v0t + d0
But note that
d0 = 0,( initial position)
v0 = 0( initial position)
a is the net acceleration
d = √[4.202 + (-3.30)2] m = 5.34 m
Hence, the magnitude of the displacement is 5.34 m, then we can make 'a' the subject of formula in the above expression in order to calculate the value for acceleration, note that d0 = 0,( initial position) and v0 = 0( initial position)
d = (1/2)at2
a = 2d/t2 = 2(5.34)/(1.20)2 m/s2 = 7.42 m/s2
the net acceleration is 7.42 m/s2
Acceleration in terms of the vector can be calculated as
a=2(ri - r0)/t^2
Where t =1.2s which is the time
a= 2(4.2i - 3.30j)/ 1.2^2
a=( 5.83i - 4.58j)m/s
now the net force can now be calculated since we have known the value of acceleration, using the formula below;
F(x) = ma - mg
Where a = 5.83i - 4.58j)m/s and g= 9.8m/s
2.8(5.83i - 4.58j)m/s - (2.80 × 9.8)m/s^2
Therefore, the other force= (16.3i + 14.6j)N
A piece of purple plastic is charged with 9.31×106 extra electrons compared to its neutral state. What is its net electric charge (including its sign) in coulombs?
Answer:
Q = - 1.5 x 10⁻¹² Coulomb
Explanation:
While in the neutral state, the charge on the piece of purple plastic must be zero. So the net charge is due to the charge of the extra electrons. Therefore,
Q = ne
where,
Q = net charge on piece of purple plastic = ?
n = No. of extra electrons on piece of purple plastic = 9.31 x 10⁶ electrons
e = Charge on one electron = - 1.6 x 10⁻¹⁹ Coulomb
Therefore,
Q = (9.31 x 10⁶)(- 1.6 x 10⁻¹⁹ Coulomb)
Q = - 1.5 x 10⁻¹² Coulomb
A rubber ball is attached to a string and whirled around in a circle. If the string is 1.0 m long (measured from the center of the baseball to the far end of the string) and the ball’s speed is 10 m/s, what is the ball’s centripetal acceleration?
Centripetal acceleration = (speed squared) / (radius)
Centripetal acceleration = (10 m/s)² / (1.0 m)
Centripetal acceleration = (100 m²/s²) / (1.0 m)
Centripetal acceleration = 100 m/s²
What is the work-energy theorem equation?
Answer:
W = Fd = KE =1/2mv²
Explanation:
not sure if that's what your looking for but i'm pretty sure this is it.
A 1.30-kg particle moves in the xy plane with a velocity of v with arrow = (4.50 î − 3.30 ĵ) m/s. Determine the angular momentum of the particle about the origin when its position vector is r with arrow = (1.50 î + 2.20 ĵ) m.
Answer:
The angular momentum of the particle about the origin is [tex]\vec l = -19.305\,k\,\left[kg\cdot \frac{m}{s} \right][/tex].
Explanation:
Vectorially speaking, the angular momentum is given by the following cross product:
[tex]\vec l = \vec r \times m\vec v[/tex]
This cross product can be solved with the help of determinants and its properties, that is:
[tex]\vec l = \left|\begin{array}{ccc}i&j&k\\r_{x}&r_{y}&0\\m\cdot v_{x}&m\cdot v_{y}&0\end{array}\right|[/tex]
[tex]\vec l = m\left|\begin{array}{ccc}i&j&k\\r_{x}&r_{y}&0\\v_{x}& v_{y}&0\end{array}\right|[/tex]
The 3 x 3 determinant is solved by the Sarrus Law:
[tex]\vec l = m \cdot (r_{x}\cdot v_{y} - r_{y}\cdot v_{x})k[/tex]
If [tex]m = 1.30\,kg[/tex], [tex]\vec r = 1.50\,i + 2.20\,j\,[m][/tex] and [tex]\vec v = 4.50\,i-3.30\,j\,\left[\frac{m}{s} \right][/tex], the angular momentum of the particle about the origin is:
[tex]\vec l = (1.30\,kg)\cdot \left[\left(1.50\,m\right)\cdot\left(-3.30\,\frac{m}{s} \right)-\left(2.20\,m\right)\cdot\left(4.50\,\frac{m}{s} \right)\right]k[/tex]
[tex]\vec l = -19.305\,k\,\left[kg\cdot \frac{m}{s} \right][/tex]
The angular momentum of the particle about the origin is [tex]\vec l = -19.305\,k\,\left[kg\cdot \frac{m}{s} \right][/tex].
A projectile is launched from ground level with an initial speed of 47 m/s at an angle of 0.6 radians above the horizontal. It strikes a target 1.7 seconds later. What is the vertical distance from where the projectile was launched to where it hit the target.
Answer:
30.67m
Explanation:
Using one of the equations of motion as follows, we can describe the path of the projectile in its horizontal or vertical displacement;
s = ut ± [tex]\frac{1}{2} at^2[/tex] ------------(i)
Where;
s = horizontal/vertical displacement
u = initial horizontal/vertical component of the velocity
a = acceleration of the projectile
t = time taken for the projectile to reach a certain horizontal or vertical position.
Since the question requires that we find the vertical distance from where the projectile was launched to where it hit the target, equation (i) can be made more specific as follows;
h = vt ± [tex]\frac{1}{2} at^2[/tex] ------------(ii)
Where;
h = vertical displacement
v = initial vertical component of the velocity = usinθ
a = acceleration due to gravity (since vertical motion is considered)
t = time taken for the projectile to hit the target
From the question;
u = 47m/s, θ = 0.6rads
=> usinθ = 47 sin 0.6
=> usinθ = 47 x 0.5646 = 26.54m/s
t = 1.7s
Take a = -g = -10.0m/s (since motion is upwards against gravity)
Substitute these values into equation (ii) as follows;
h = vt - [tex]\frac{1}{2} at^2[/tex]
h = 26.54(1.7) - [tex]\frac{1}{2} (10)(1.7)^2[/tex]
h = 45.118 - 14.45
h = 30.67m
Therefore, the vertical distance is 30.67m
A horizontal force of 14.0N is applied to a box of m=32.5kg with Vo=0. Ignoring friction, how far does the crate travel in 10.0s?
Un bloque de 10 kg se encuentra sobre un plano rugoso inclinado 37º respecto a la horizontal, sobre él actúa una fuerza constante, horizontal, de módulo 50 N. Si el bloque desciende sobre el plano 5 m, lentamente, determine la cantidad de trabajo que realiza la fuerza de rozamiento (considere g = 10 m/s2).
Answer:
El trabajo realizado por la fuerza de rozamiento sobre el bloque tras recorrer este último una distancia de 5 metros sobre el plano es de 500.566 joules.
Explanation:
El fenómeno alrededor del bloque puede ser modelado por el Principio de Conservación de la Energía y el Teorema del Trabajo y la Energía. Al descender lentamente, significa que la aceleración neta experimentada por el bloque es aproximadamente cero. El diagrama de cuerpo libre del bloque se presenta a continuación como archivo adjunto. Las ecuaciones de equilbrio del sistema son:
[tex]\Sigma F_{x'} = P\cdot \cos \theta + m\cdot g \cdot \sin \theta - f = 0[/tex]
[tex]\Sigma F_{y'} = N + P\cdot \sin \theta -m\cdot g\cdot \cos \theta = 0[/tex]
Donde:
[tex]P[/tex] - Fuerza externa aplicada a la caja, medida en newtons.
[tex]m[/tex] - Masa del bloque, medida en kilogramos.
[tex]g[/tex] - Aceleración gravitacional, medidas en metros sobre segundo al cuadrado.
[tex]f[/tex] - Fuerza de rozamiento, medida en newtons.
[tex]N[/tex] - Fuerza normal del plano sobre la caja, medida en newtons.
[tex]\theta[/tex] - Ángulo de inclinación del plano, medido en grados sexagesimales.
Dado que todas las fuerzas son constantes, se puede emplear la definición de trabajo como el producto de la fuerza paralela a la dirección del movimiento y la magnitud de distancia recorrida en el movimiento, entonces la primera ecuación de equilibrio queda así al multiplicar cada lado por la distancia recorrida:
[tex]P\cdot \Delta s \cdot \cos \theta + m\cdot g \cdot \Delta s \cdot \sin \theta - W_{f} = 0[/tex]
Ahora, la cantidad de trabajo realizado por la fuerza de rozamiento es:
[tex]W_{f} = (P\cdot \cos \theta+m\cdot g\cdot \sin \theta)\cdot \Delta s[/tex]
Si [tex]P = 50\,N[/tex], [tex]m = 10\,kg[/tex], [tex]g = 10\,\frac{m}{s^{2}}[/tex], [tex]\theta = 37^{\circ}[/tex] and [tex]\Delta s = 5\,m[/tex], entonces el trabajo realizado por la fuerza de rozamiento es:
[tex]W_{f} = \left[(50\,N)\cdot \cos 37^{\circ}+(10\,kg)\cdot \left(10\,\frac{m}{s^{2}} \right)\cdot \sin 37^{\circ}\right]\cdot (5\,m)[/tex]
[tex]W_{f} = 500.566\,J[/tex]
El trabajo realizado por la fuerza de rozamiento sobre el bloque tras recorrer este último una distancia de 5 metros sobre el plano es de 500.566 joules.
An 100 V/m electric field is directed along the x axis. If the potential at the origin is 300 V, what is potential at the point ( -2m, 0) point
Answer:
200volts
Explanation:
Pls see attached file
Answer:
100 V
Explanation:
Electric field E = 100 V/m
Potential at the origin = 300 V
Potential at point (-2m, 0) i.e 2 m behind the origin = ?
From the equation ΔV = EΔd,
ΔV = [tex]V_{0} - V_{x}[/tex]
where [tex]V_{0}[/tex] is the potential at origin,
and [tex]V_{x}[/tex] is the potential at point (-2, 0)
E = electric field
Δd = 0 - (-2) = 2 m
[tex]V_{0} - V_{x}[/tex] = 300 - [tex]x[/tex]
equating, we have
300 - [tex]x[/tex] = 100 x 2
300 - [tex]x[/tex] = 200
[tex]x[/tex] = 100 V
The force per meter between the two wires of a jumper cable being used to start a stalled car is 0.335 N/m.
Required:
a. What is the current in the wires, given they are separated by 2.90 cm?
b. Is the force attractive or repulsive?
1. The force is repulsive because the currents are in opposite directions.
2. The force is repulsive because the currents are in the same direction.
3. The force is attractive because the currents are in the same direction.
4. The force is attractive because the currents are in opposite directions.
Answer:
a) I = 1.29 10⁻⁴ A , b) the current has the opposite direction in each cable, therefore the correct answer must be 1
Explanation:
a) Let's analyze this exercise, when a conductor carries a current the elctoenes generate a magnetic field around the cable and this field can interact with the electrons that carry a current in a nearby cable, the expression for force is
F₁ = I₁ L B₂
where F₁ is the force on a cable through the field created by elotorcable.
The field sent by the other cable is
B₂ = μ₀ I² / 2πa
we substitute
F₁ = μ₀ I₁ I₂ / 2πa L
suppose the current in the two cables is the same
I₁ = I₂ = I
F₁ / L = μ₀ I₂ / 2πa
i = √ [(F₁ / L) 2πa / μ₀]
let's calculate
I = √ [0.335 2 π / 4π 10⁻⁷]
I = √ [0.335 / 2 10⁷]
I = 1.29 10⁻⁴ A
b) if the two cables have the current in the same direction the force is attractive and if it has the current in the opposite direction it is negative
the two possible answers are 1 and 2
In general, to start a car, one of the cables has a current from the battery at start-up and the other cable comes from the start to the battery, therefore the current has the opposite direction in each cable, therefore the correct answer must be 1
During a certain time interval, the angular position of a swinging door is described by θ = 4.91 + 9.7t + 2.06t2, where θ is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door at the following times.
(a) t = 0
θ = rad
ω = rad/s
α = rad/s2
(b) t = 2.94 s
θ = rad
ω = rad/s
α = rad/s2
Explanation:
a)
θ = 4.91 + 9.7t + 2.06t² when t = 0
θ = 4.91 rad
θ = 4.91 + 9.7t + 2.06t²
ω = dθ/dt = 9.7 + 2.06t, when t =0
ω = dθ/dt = 9.7 + 0
ω = 9.7 rad/s
α = d²θ/dt² = 2.06
α= 2.06 rad/s²
b) please use same method above for t = 2.94 s
At zero seconds, the angular position is 4.91 rad, the angular velocity is 9.7 radian/second and the angular acceleration is 2.06 rad/s².
What is Angular acceleration?When the angular velocity change in relation to time, then it results in angular acceleration. It comes with direction, so it is a vector quantity.
Given: Angular position equation (θ) = 4.91 + 9.7t + 2.06[tex]t^{2}[/tex]
If the angular velocity is ω, angular acceleration is α, and t is the time then
(A) At time t = 0 second
θ = 4.91 + 9.7 × 0 + 2.06 × [tex]0^{2}[/tex]
θ = 4.91 rad
Angular velocity (ω) = dθ/dt
ω = dθ/dt,
ω = 9.7 + 2.06t (at t = 0)
ω = 9.7 radian/second
Angular acceleration (α) = d²θ/dt²
α= 2.06 rad/s²
Similarly, at t= 2.94 sec
θ = 51.23 rad
ω = 15.76 rad/s
α = 2.06 rad/s²
To know more about Angular acceleration:
https://brainly.com/question/14769426
#SPJ2
A piston absorbs 42 J of heat from its surroundings while being compressed from 0.0007 m3 to 0.0002 m3 at a constant pressure of 1.0 × 105 Pa. What are the correct values for heat and work for the piston?
Answer:
D
Explanation:
W = P∆V
Use the above equation and substitute, thanks
A spinning top initially spins at 16rad/s but slows down to 12rad/s in 18s, due to friction. If the rotational inertia of the top is 0.0004kg.m2, by how much the angular momentum of the top changes?
Answer:
The change in angular momentum is [tex]\Delta L = 0.0016 \ kgm^2/s[/tex]
Explanation:
From the question we are told that
The initial angular velocity of the spinning top is [tex]w_1 = 16 \ rad/s[/tex]
The angular velocity after it slow down is [tex]w_2 = 12 \ rad/s[/tex]
The time for it to slow down is [tex]t = 18 \ s[/tex]
The rotational inertia due to friction is [tex]I = 0.0004 \ kg \cdot m^2[/tex]
Generally the change in the angular momentum is mathematically represented as
[tex]\Delta L = I *(w_1 -w_2)[/tex]
substituting values
[tex]\Delta L = 0.0004 *(16 -12)[/tex]
[tex]\Delta L = 0.0016 \ kgm^2/s[/tex]
Transverse waves are sent along a 4.50 m long string with a speed of 85.00 m/s. The string is under a tension of 20.00 N. What is the mass of the string (in kg)?
Answer:
m = 0.0125 kg
Explanation:
Let us apply the formula for the speed of a wave on a string that is under tension:
[tex]v = \sqrt{\frac{F}{\mu} }[/tex]
where F = tension force
μ = mass per unit length
Mass per unit length is given as:
μ = m / l
where m = mass of the string
l = length of the string
This implies that:
[tex]v = \sqrt{\frac{F}{m/l} }\\ \\v = \sqrt{\frac{F * l}{m} }[/tex]
Let us make mass, m, the subject of the formula:
[tex]v^2 = \frac{F * l}{m}\\\\m = \frac{F * l}{v^2}[/tex]
From the question:
F = 20 N
l = 4.50 m
v = 85 m/s
Therefore:
[tex]m = \frac{20 * 4.5}{85^2}\\\\m = \frac{90}{7225}\\ \\m = 0.0125 kg[/tex]
Good day can I get some help please?
Answer:
432 J
Explanation:
When moving linearly:
Kinetic Energy = (1/2)mV^2
So here you have:
KE=(1/2)(6)(12^2)=(1/2)(6)(144)=432
The unit for energy is Joules (J), so your answer would be 432 J.
A square conducting plate 52.0 cm on a side and with no net charge is placed in a region, where there is a uniform electric field of 82.0 kN/C directed to the right and perpendicular to the plate.
Find
(a) the charge density of each face of the plate and
(b) the total charge on each face.
Explanation:
Given: uniform electric field E= 82.0 kN/C.
a) charge density σ =ε_0 E.
therefore, [tex]\sigma =82\times10^3\times3.85\times10^{-12}\\=0.0000003157= 315.7 nC/m^2[/tex]
b)Total charge on each face = σA
q=σA
[tex]=315.7\times10^{-9}\times52\times10^{-4}\\=1.614\times10^{-9}= 1.614 \text{ nC}\\\text{Similarly on the other face } = -1.614 \text{ nC}[/tex]
Two parallel plates, each of area 7.37 cm2, are separated by 6.00 mm. The space between the plates is filled with air. A voltage of 7.55 V is applied between the plates. Calculate the magnitude of the electric field between the plates. Tries 0/20 Calculate the amount of the electric charge stored on each plate. Tries 0/20 Now distilled water is placed between the plates and the capacitor is charged up again to the same voltage as before. Calculate the magnitude of charge stored on each plate in this case. (Use κ = 80.0 for the dielectric constant of water.)
Answer:
- E = 1.25*10^3 N/C
- Q = 1.08*10^-12 C
- Q = 8.69*10^-11 C
Explanation:
- In order to calculate the magnitude of the electric field between the plates, you use the following formula:
[tex]E=\frac{V}{d}[/tex] (1)
V: potential difference between the plates = 7.55V
d: distance between the plates = 6.00mm = 6.00*10^-3m
You replace the values of the parameters n the equation (1):
[tex]E=\frac{7.55V}{6.00*10^{-3}m}=1.25*10^3\frac{N}{C}[/tex]
The magnitude of the electric field between the plates is 1.25*10^3N/C
- The charge on each plate is given by the following formula:
[tex]Q=CV[/tex] (2)
C: capacitance of the capacitor
The capacitance of a parallel plate capacitor is:
[tex]C=\epsilon_o \frac{A}{d}[/tex] (3)
You replace the previous formula into the equation (2) and solve for Q:
[tex]Q=(\epsilon_o k\frac{A}{d})(V)=(8.85*10^{-12}C^2/Nm^2)\frac{7.37*10^{-4}m^2}{6.00*10^{-3}m}\\\\Q=1.08*10^{-12}C[/tex]
The charge on each plate is 1.08*10^-12C = 1.08pC
- If water is placed in between the plates, the dielectric permittivity is changes by a factor of k = 80.0.
The capacitance of a parallel plate capacitor with a substance with a constant dielectric k, is given by:
[tex]C=\epsilon_o k\frac{A}{d}[/tex] (4)
You replace the previous formula in the equation (2) and replace the values of all parameters:
[tex]Q=(\epsilon_o k\frac{A}{d})(V)=(8.85*10^{-12}C^2/Nm^2)(80.0)\frac{7.37*10^{-4}m^2}{6.00*10^{-3}m}\\\\Q=8.69*10^{-11}C[/tex]
The charges on each plate is 8.69*10^-11 C
During the time a compact disc (CD) accelerates from rest to a constant rotational speed of 477 rev/min, it rotates through an angular displacement of 1.5758 rev. What is the angular acceleration of the CD
Answer:
126.01 rad/s^2
Explanation:
since it starts from rest, initial angular speed ω' = 0 rad/s
angular speed N = 477 rev/min
angular speed in rad/s ω = [tex]\frac{2\pi N}{60}[/tex] = [tex]\frac{2*3.142* 477}{60}[/tex] = 49.95 rad/s
angular displacement ∅ = 1.5758 rev
angular displacement in rad/s = [tex]2\pi N[/tex] = 2 x 3.142 x 1.5758 = 9.9 rad
angular acceleration [tex]\alpha[/tex] = ?
using the equation of angular motion
ω^2 = ω'^2 + 2[tex]\alpha[/tex]∅
imputing values, we have
[tex]49.95^{2} = 0^{2} + (2 *\alpha*9.9 )[/tex]
2495 = 19.8[tex]\alpha[/tex]
[tex]\alpha[/tex] = 2495/19.8 = 126.01 rad/s^2
A skydiver of mass 80.0 kg jumps from a slow-moving aircraft and reaches a terminal speed of 50.0 m/s. (a) What is her acceleration when her speed is 30.0 m/s
Answer:
6.22²
Explanation:
Given that
Mass of the skydiver, m = 80 kg
Terminal speed of the skydiver, v(f) = 50 m/s
Speed of the skydiver, v(i) = 30 m/s
Acceleration of the skydiver, a = ?
To solve this, we use the formula
W - k v² = ma, where
W = weight of the skydiver
k = constant
v = speed of the skydiver
m = mass of the skydiver
So, if we substitute the values into it we have
W = mg = 80 * 9.8 = 784 N
784 - k 50² = 80 *0
784 - 2500k = 0
784 = 2500k
k = 0.3136
Now, we use this value of k to find the needed acceleration using the same formula at a speed of 30 m/s
784 - 0.3136 * 30² = 80 * a
784 - 0.3136 * 900 = 80a
784 - 282.24 = 80a
497.76 = 80a
a = 497.76 / 80
a = 6.22 m/s²
Thus, we can conclude that the acceleration when the speed of the skydiver is 30 m/s, is 6.22 m/s²
Suppose that the moment of inertia of a skater with arms out and one leg extended is 3.1 kg⋅m2 and for arms and legs in is 0.90 kg⋅m2 . If she starts out spinning at 4.0 rev/s , what is her angular speed (in rev/s) when her arms and one leg open outward?
Answer:
The angular speed (in rev/s) when her arms and one leg open outward is 1.161 rev/s
Explanation:
Given;
moment of inertia of a skater with arms out, [tex]I_{arms \ out}[/tex] = 3.1 kg.m²
moment of inertia of a skater with arms in, [tex]I_{arms \ in}[/tex] = 0.9 kg.m²
inward angular speed, [tex]\omega _{in}[/tex] = 4 rev/s
The angular momentum of the skater when her arms are out and one leg extended is equal to her angular momentum when her arms and legs are in.
[tex]L_{out} = L_{in}[/tex]
[tex]I_{out} \omega_{out} = I_{in} \omega_{in}\\\\\omega_{out} = \frac{ I_{in} \omega_{in} }{I_{out} } \\\\\omega_{out} = \frac{0.9*4}{3.1} \\\\\omega_{out} = 1.161 \ rev/s[/tex]
Therefore, the angular speed (in rev/s) when her arms and one leg open outward is 1.161 rev/s
how many electrons does a neutral atom of sudium-25 have
Answer:
Option A. 11
Explanation:
The atomic number of an element does not change.
Recall:
Atomic number = proton number
If the atom is neutral, then,
Proton number = electron number
Since the element is sodium, then, the atomic number of sodium–25 is 11.
Also, we were told to obtain the electrons of a neutral atom of sodium–25
Therefore,
Atomic number = proton number = 11
Since the atom is neutral,
Proton number = electron number = 11
Answer:
A. 11
Explanation:
A neutral atom of sodium-25 has the same number of protons and electrons. Since it has 11 protons, it also must have 11 electrons!
Two bullets are fired simultaneously parallel to a horizontal plane. The bullets have different masses and different initial velocities. Which one will strike the plane first?
a) The fastest one.b) The lightest one.c) The heaviest one.d) The slowest one.e) They strike the plane at the same time.
Answer:
Therefore, the answer is E. They strike the plane at the same time.
Explanation:
Here, it is seen that the time depends only on acceleration due to gravity (which is a constant) and vertical displacement, and not on velocity of the bullets or mass of the bullets.
Hence, the bullets that are fired simultaneously parallel to the horizontal plane will strike the plane at the same time.
using equation of motion for displacement
s= ut + ¹/₂gt²
here, g is the acceleration due to gravity along y- direction
U along y is 0
s = (0)t + ¹/₂gt²
s=¹/₂gt²
make t the subject of formula = [tex]\sqrt{\frac{2s}{g} }[/tex]
An internal explosion breaks an object, initially at rest, into two pieces, one of which has 1.8 times the mass of the other.
Requried:
a. If 7230 J were released in the explosion, how much kinetic energy did the heavier piece acquire?
b. How much kinetic energy did the lighter piece acquire?
Answer:
a) The heavier piece has a translational kinetic energy of 4647.857 joules, b) The lighter piece has a translational kinetic energy of 2582.143 joules.
Explanation:
a) The object breaking can be described by means of the Principle of Energy Conservation, knowing that heavier piece has 1.8 times the mass of the lighter ([tex]m_{h} = 1.8\cdot m_{l}[/tex]), both are modelled as particle due to the absence of rotation and that energy liberated by explosion is transform into kinetic energy, the equation that describes the phenomenon is:
[tex]E_{ex} = K_{h} + K_{l}[/tex]
Where:
[tex]E_{ex}[/tex] - Energy liberated by the explosion, measured in joules.
[tex]K_{h}[/tex], [tex]K_{l}[/tex] - Translational kinetic energies of the heavier and lighter piece, respectively.
This expression is expanded by using the definition of translational kinetic energy and supposing the both parts are liberated at the same initial speed ([tex]v_{o}[/tex]). Then:
[tex]E_{ex} = \frac{1}{2}\cdot (m_{h} + m_{l})\cdot v_{o}^{2}[/tex]
As can be seen, the energy liberated by expression is directly proportional to the mass of the system. Hence, the kinetic energy can be estimated by simple rule of three:
[tex]K_{h} = \frac{m_{h}}{m_{h}+m_{l}}\times E_{ex}[/tex]
If [tex]m_{h} = 1.8\cdot m_{l}[/tex] and [tex]E_{ex} = 7230\,J[/tex], then:
[tex]K_{h} =\frac{1.8\cdot m_{l}}{2.8\cdot m_{l}}\times E_{ex}[/tex]
[tex]K_{h} = \frac{9}{14}\cdot (7230\,J)[/tex]
[tex]K_{h} = 4647.857\,J[/tex]
The heavier piece has a translational kinetic energy of 4647.857 joules.
b) The translational kinetic energy of the lighter piece is calculated by using the equation derived from the Principle of Energy Conservation:
[tex]K_{l} = E_{ex} - K_{h}[/tex]
Given that [tex]E_{ex} = 7230\,J[/tex] and [tex]K_{h} = 4647.857\,J[/tex], the translational kinetic energy of the lighter piece is:
[tex]K_{l} = 7230\,J - 4647.857\,J[/tex]
[tex]K_{l} = 2582.143\,J[/tex]
The lighter piece has a translational kinetic energy of 2582.143 joules.