Answer:
Temperature change in the wire is 625°C
Explanation:
Let the initial current in the wire be I₀
Thus,
the final current in the wire will be, I = (1 - 0.20) × I₀ = 0.80I₀
Given α = 0.0004 1/°C
Now,
Resistance = (potential difference (E))/current (I)
also
R = R₀ [1 + αΔT]
Where ΔT is the increase in temperature , thus
E/I = E/I₀ [1 + α × ΔT)
on substituting the values in the above equation, we get
1/(0.80I₀) = 1/(I₀) × [1 + 0.0004 × ΔT]
or
1/(0.80) = [1 + 0.0004 × ΔT)]
or
ΔT = 625°C
The temperature change in the Nichrome wire, based on a 20% drop in current, is calculated to be approximately 625°C.
A Nichrome wire's resistance increases with temperature, primarily determined by its temperature coefficient.
Step-by-Step Solution :
Let I₀ be the initial current and I be the current after heating.E/I = E/I₀ [1 + α × ΔT)
on substituting the values in the above equation, we get
= 1/(0.80I₀) = 1/(I₀) × [1 + 0.0004 × ΔT]
= 1/(0.80) = [1 + 0.0004 × ΔT)]
= ΔT = 625°C
The temperature change in the Nichrome wire is approximately 625°C.
Suppose a 20-foot ladder is leaning against a building, reaching to the bottom of a second-floor window 15 feet above the ground. What angle, in radians, does the ladder make with the ground Round your answer to two decimal places
To find the angle, in radians, that the ladder makes with the ground, we can use trigonometry. The length of the ladder can be found using the Pythagorean theorem, and the angle can be calculated as the arcsine of the ratio of the height of the building to the length of the ladder. The angle is approximately 0.6435 radians.
Explanation:To find the angle, in radians, that the ladder makes with the ground, we can use trigonometry. The ladder, the ground, and the building form a right triangle. The ratio of the opposite side (the height of the building) to the hypotenuse (the length of the ladder) is equal to the sine of the angle. Using this information, we can calculate the angle in radians.
First, we need to find the length of the ladder using the Pythagorean theorem: l^2 = 20^2 + 15^2 = 625. Taking the square root of both sides, we find that the length of the ladder is 25 feet.
The sine of the angle can be calculated as the ratio of the height of the building to the length of the ladder: sin(angle) = 15/25 = 0.6. Taking the arcsine (inverse sine) of 0.6, we find that the angle in radians is 0.6435 (rounded to two decimal places).
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Two football players are pushing a 60 kg blocking sled across the field at a constant speed of 2.0 m/s. The coefficient of kinetic friction between the grass and the sled is 0.30. Once they stop pushing, how far will the sled slide before coming to rest?
Answer:
The sled slides d=0.155 meters before rest.
Explanation:
m= 60 kg
V= 2 m/s
μ= 0.3
g= 9.8 m/s²
W= m * g
W= 588 N
Fr= μ* W
Fr= 176.4 N
∑F = m * a
a= (W+Fr)/m
a= 12.74m/s²
t= V/a
t= 0.156 s
d= V*t - a*t²/2
d= 0.155 m
An airplane starts its takeoff by moving at 1.7 m/s. The plane must then accelerate at 3.0 m/s2 for the next 30s to reach its final takeoff speed. To the nearest tenth of a kilometer, how far does the plane travel while accelerating to its takeoff speed?
Answer:
The distance is 1.4 km.
Explanation:
Given that,
Initial velocity u= 1.7 m/s
Accelerate a= 3.0 m/s²
Time = 30 s
We need to calculate the distance
Using equation of motion
[tex]s= ut+\dfrac{1}{2}at^2[/tex]
Where, u = initial velocity
a = acceleration
t = time
Put the value in the equation
[tex]s=1.7\times30+\dfrac{1}{2}\times3.0\times(30)^2[/tex]
[tex]s=1401\ m[/tex]
[tex]s=1.4\ km[/tex]
Hence, The distance is 1.4 km.
At time t0 = 0 the mass happens to be at y0 = 4.05 cm and moving upward at velocity v0 = +4.12 m/s. (Mind the units!) Calculate the amplitude A of the oscillating mass. Answer in units of cm.
The amplitude of the oscillating mass is [tex]\(A = 4.05 \, \text{cm}\).[/tex]
To calculate the amplitude A of the oscillating mass, we can use the equations of motion for simple harmonic motion (SHM). In SHM, the displacement [tex]\( y(t) \)[/tex] of the mass at time [tex]\( t \)[/tex] is given by:
[tex]\[ y(t) = A \sin(\omega t + \phi) \][/tex]
where:
- [tex]\( A \)[/tex]) is the amplitude,
- [tex]\( \omega \)[/tex] is the angular frequency, and
- [tex]\( \phi \)[/tex] is the phase angle.
Given that at [tex]\( t = t_0 = 0 \)[/tex], the mass is at [tex]\( y_0 = 4.05 \)[/tex] cm and moving upward at velocity [tex]\( v_0 = +4.12 \)[/tex] m/s, we can find the amplitude A
At [tex]\( t = 0 \),[/tex] we have:
[tex]\[ y(0) = A \sin(\phi) = y_0 = 4.05 \, \text{cm} \][/tex]
And also:
[tex]\[ v(0) = \omega A \cos(\phi) = v_0 = +4.12 \, \text{m/s} \][/tex]
To find [tex]\( A \),[/tex]A we'll use the fact that at [tex]\( t = 0 \)[/tex], the mass is at its maximum displacement, which means the velocity is zero at [tex]\( t = 0 \).[/tex] This gives us:
[tex]\[ \omega A \cos(\phi) = 0 \]\[ \cos(\phi) = 0 \][/tex]
Since [tex]\( \cos(\phi) = 0 \) when \( \phi = \frac{\pi}{2} \) or \( \phi = \frac{3\pi}{2} \), we'll consider \( \phi = \frac{\pi}{2} \).[/tex]
Now, from the equation [tex]\( A \sin(\phi) = y_0 \),[/tex] we can find [tex]\( A \):[/tex]
[tex]\[ A \sin\left(\frac{\pi}{2}\right) = 4.05 \]\[ A = 4.05 \, \text{cm} \][/tex]
So, the amplitude[tex]\( A \)[/tex] of the oscillating mass is [tex]\( 4.05 \, \text{cm} \).[/tex]
By how much will the length of a chicago concrete walkway that is 18 m long contract when the equipment drops from 24 degrees celcius in July to (-16 degrees celcius) in Janruary?
Answer:
Contraction of Chicago concrete walkway = 8.64 x 10⁻³ m
Explanation:
Thermal expansion or compression is given by ΔL = LαΔT
Here Length of Chicago concrete walkway, L = 18 m
Change in temperature, ΔT = (-16 - 24) = -40 °C
Coefficient of thermal expansion for concrete, α = 12 x 10⁻⁶ °C⁻¹
Substituting
ΔL = LαΔT = 18 x 12 x 10⁻⁶ x (-40) = -8.64 x 10⁻³ m
Contraction of Chicago concrete walkway = 8.64 x 10⁻³ m
A concave lens has a focal length of 20 cm. A real object is 30 cm from the lens. Where is the image? What is the magnification?
Answer:
12 cm and 0.4
Explanation:
f = - 20 cm, u = - 30 cm
Let v be the position of image and m be the magnification.
Use lens equation
1 / f = 1 / v - 1 / u
- 1 / 20 = 1 / v + 1 / 30
1 / v = - 5 / 60
v = - 12 cm
m = v / u = - 12 / (-30) = 0.4
How much current must flow through a wire to make a magnetic field as strong as Earth's field (5.00 x 10^-5 T) 1.00 m away from the wire?
Answer:
250 A
Explanation:
B = 5 x 10^-5 T, r = 1 m
Let current be i.
the magnetic field due to a straight current carrying conductor is given by
B = μ0 / 4π x 2i / r
5 x 10^-5 = 10^-7 x 2 x i / 1
i = 250 A
A brick in the shape of a cube with sides 10 cm has a density of 2500 kg/m^3. What is its weight? a.) 250 N
b.) 2.5 N
c.) 25 N
d.) 0.001 N
Answer:
c.) 25 N
Explanation:
We find the volume of the brick, knowing that the volume of a cube is given by the formula:
[tex]l=0,1 metros \\V=l^{3}\\V=(0,1\: \: m)^{3}=0,001\: \: m^{3}[/tex]
being l the side of the cube, which in this case is 10 cm or 0,1 m. Now we find the mass of the object, knowing the density and the Volume of the cube:
[tex]m=V*d\\m=(0,001 \:\:m^{3})(2500 \: \: \frac{Kg}{m^{3}})=2,5 \:\: Kg[/tex]
We find the weight by multiplying the mass of the object with the gravity constant.
[tex]W=m*g=(2.5 \:Kg)*(9,81 \:m/s^{2} )=24,5 N\approx25\: N[/tex]
Final answer:
The weight of the brick is 24.5 N.
Explanation:
To find the weight of the brick, we can use the formula weight = density × volume × gravitational acceleration.
First, we need to calculate the volume of the cube. The volume of a cube is given by the formula V = side³, where side is the length of one side of the cube.
Given that the side of the cube is 10 cm, the volume of the cube is V = 10 cm × 10 cm × 10 cm = 1000 cm³.
Next, we convert the volume from cm³ to m³ by dividing by 100^3: V = 1000 cm³ ÷ (100 cm/m)³ = 0.001 m³.
Now, we can calculate the weight of the brick: weight = 2500 kg/m³ × 0.001 m³ × 9.8 m/s² = 24.5 N.
Therefore, the weight of the brick is 24.5 N, which is not one of the given options.
9) Two mirrors are at right angles to one another. A light ray is incident on the first at an angle of 30° with respect to the normal to the surface. What is the angle of reflection from the second surface?
Answer:
60°
Explanation:
In the given question it is given that the two mirrors perpendicular to each other.
The light ray will reflect off the first mirror with an angle of 30° (∠i= ∠r) and then arrive at the second mirror. Using geometry of the two mirrors and the fact that the angle between the two of them is 90°, the incident angle for second mirror is 60°, which will again equal to the angle of reflection.
hence, angle of reflection of second mirror is 60°
The angle of reflection from the second surface is (b) 60◦
Explanation:
Two mirrors are at right angles to one another. A light ray is incident on the first at an angle of 30° with respect to the normal to the surface. What is the angle of reflection from the second surface?
(a) 30◦
(b) 60◦
(c) 45◦
(d) 53◦
(e) 75◦
Reflection is the direction change of a wavefront at interface between two different media. The light ray (it is a line (straight or curved) that is perpendicular to the light's wavefronts and its tangent is collinear with the wave vector) will reflect off of the first mirror with an equal angle of 30◦ then it arrives at the second mirror. By using the geometry (branch of mathematics that concerned with questions of shape, size, relative position of figures, and the properties of space) of the two mirrors and the angle between the two of them is 90◦ , the incident angle (the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence called the normal) for the second mirror is 60◦ that equal to the final angle of reflection.
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At takeoff, a commercial jet has a speed of 72 m/s. Its tires have a diameter of 0.89 m. Part (a) At how many rev/min are the tires rotating? Part (b) What is the centripetal acceleration at the edge of the tire in m/s^2?
Answer:
a) Revolutions per minute = 2.33
b) Centripetal acceleration = 11649.44 m/s²
Explanation:
a) Angular velocity is the ratio of linear velocity and radius.
Here linear velocity = 72 m/s
Radius, r = 0.89 x 0. 5 = 0.445 m
Angular velocity
[tex]\omega =\frac{72}{0.445}=161.8rad/s[/tex]
Frequency
[tex]f=\frac{2\pi}{\omega}=\frac{2\times \pi}{161.8}=0.0388rev/s=2.33rev/min[/tex]
Revolutions per minute = 2.33
b) Centripetal acceleration
[tex]a=\frac{v^2}{r}[/tex]
Here linear velocity = 72 m/s
Radius, r = 0.445 m
Substituting
[tex]a=\frac{72^2}{0.445}=11649.44m/s^2[/tex]
Centripetal acceleration = 11649.44m/s²
To find the revolutions per minute of the tires, calculate the circumference of the tire and divide the jet's speed in meters per minute by this circumference. For the centripetal acceleration, first find the tire's angular velocity in radians per second and plug it, along with the tire's radius, into the centripetal acceleration formula.
For part (a), to calculate how many revolutions per minute (rev/min) the tires are rotating, you must determine the circumference of the tire first. The circumference (C) is given by [tex]C = \pi d[/tex], where d is the diameter. Given d = 0.89 m, the circumference is [tex]C = \pi (0.89 m)[/tex]. This value represents the distance the tire covers in one revolution.
To find out how many rev/min the tires make, we need to consider the speed of the jet which is 72 m/s. Since there are 60 seconds in a minute, the distance covered in one minute is [tex]72 m/s * 60 s/min.[/tex] Dividing this distance by the tire's circumference gives us the number of revolutions per minute:
[tex]rev/min = \(\frac{(72 m/s) \* (60 s/min)}{\\(pi)(0.89 m)}\)[/tex]
After calculating, you get the tires' rotation rate in rev/min.
For part (b), to calculate the centripetal acceleration (ac) at the edge of the tire, use the formula [tex]ac = \(r\omega^2\),[/tex]where r is the radius of the tire, and [tex]\(\omega\)[/tex] is the angular velocity in radians per second. The angular velocity can be found by converting the rev/min to revolutions per second (rev/s), and then multiplying by [tex]2\pi[/tex] to convert to radians per second.
Lastly, replacing [tex]\(\omega\)[/tex] and r in the centripetal acceleration formula will give you the edge's centripetal acceleration in m/s2.
You are given two resistors, an ammeter, a voltmeter, and a voltage source. By connecting each resistor singly to the voltage source and taking voltage difference and current measurements on the single resistor, you find the following data for each resistor:
Resistor Voltage (V) Current (mA)
1 3.88 43.6
2 4.48 14.45
Using this data, first find the resistance of each resistor and then calculate the following:
(a) The current that would pass through the network of resistors if they were arranged in series and connected to an 7.65 V voltage source.
Iseries =
(b) The current through the circuit if the resistors were arranged in parallel and connected to the same 7.65 V source from part (a).Iparallel =
Try this solution, note, the resistance of each resistor is marked with green colour, the items (a) and (b) - with red colour.
By using Ohm's law,
a.) Current = 19.17 A
b.) Current = 110.6 A
We are given different voltages and currents for the two resistors.
First resistor:
Voltage [tex]V_{1}[/tex] = 3.88 v
Current [tex]I_{1}[/tex] = 43.6 A
By using Ohm's law, we can calculate [tex]R_{1}[/tex]
V = IR
Make R the subject of formula
R = V/I = 3.88/43.6
R = 0.08899 Ohms
Second resistor
Voltage [tex]V_{2}[/tex] = 4.48 v
Current [tex]I_{2}[/tex] = 14.45 A
By using Ohm's law, we can calculate [tex]R_{2}[/tex]
V = IR
Make R the subject of formula
R = V/I = 4.48/14.45
R = 0.3100 Ohms
a.) Whenever resistors are connected in series, the same current will pass through them
The total resistance in the resistors in series will be achieved by using the below formula
R = [tex]R_{1}[/tex] + [tex]R_{2}[/tex]
R = 0.08899 + 0.3100
R = 0.399 Ohms
By using Ohm's law:
V = IR
Make I the subject of formula
I = V/R = 7.65/0.399
I = 19.17 A
b.) Whenever resistors are arranged in parallel, the same voltage will be supplied to them.
The resultant resistor can be calculated by using the below formula
1/R = 1/[tex]R_{1}[/tex] + 1/[tex]R_{2}[/tex]
1/R = 1/0.08899 + 1/0.3100
1/R = 11.237 + 3.2258
R = 1/14.463
R = 0.069 Ohms
By using Ohm's law,
V = IR
Make I the subject of formula
I = V/R = 7.65/0.069
I = 110.6 A
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Example: Alice is outside ready to begin her morning run when she sees Bob run past her with a constant speed of 10.0 m/s. Alice starts to chase after Bob after 5 seconds How far away is Bob when Alice starts running?
Answer:
The distance of bob when Alice starts running is 50 m.
Explanation:
Given that,
Speed v = 10.0 m/s
Time t = 5 sec
We need to calculate the distance
Using formula of distance
[tex]D=v\times t[/tex]
[tex]D=10\times5[/tex]
[tex]D=50\ m[/tex]
Hence, The distance of bob when Alice starts running is 50 m.
It is desiredto FDM 30voice channels (each with a bandwidth of 4.5KHz) along with a guard band of 0.8KHz. Ignoring a guard band before the first channel and the one after the last channel, what is the total bandwidth, in KHz,required for such a system.
Answer:
Total bandwidth required = 158.2 KHz
Explanation:
given data:
number of channel 30
bandwidth of each channel is 4.5 KHz
bandwidth of guard band 0.8 KHz
According to the given information, first guard band and the guard band after last channel should be ignored, therefore we have total number of 29 guard band.
As per data, we can calculate total bandwidth required
total bandwidth = 30*4.5 + 29*0.8
total bandwidth required = 158.2 KHz
If a 76.2 kg patient is exposed to 52.6 rad of radiation from a beta source, then what is the dose (mrem) absorbed by the person's body?
Answer:
The dose absorbed by the person's body is 52600 mrem.
Explanation:
Given that,
Radiation = 52.6 rad
We need to calculate the absorbed dose
We know that,
The equivalent dose is equal to the absorbed radiation for beta source.
So, The patient is exposed 52.6 rad of radiation.
Therefore, The absorbed radiation is equal to the exposed 52.6 rad of radiation.
[tex]1 rad = \dfrac{1\ rem}{1000\ mrem}[/tex]
So, radiation absorbed = 52.6 rad
[tex]radiation\ absorbed =52.6\times1000\ mrem[/tex]
[tex]radiation\ absorbed = 52600\ mrem[/tex]
Hence, The dose absorbed by the person's body is 52600 mrem.
The plug-in transformer for a laptop computer puts out 7.50 V and can supply a maximum current of 1.6 A. What is the maximum input current Ip in amps, if the input voltage is 240 V? Assume 100% efficiency
Answer:
The input current is 0.05 A.
Explanation:
Given that,
Output voltage = 7.50 V
Output current = 1.6 A
Input voltage = 240 v
We need to calculate the input current
The efficiency is 100% so.
Input power = output power
[tex]\dfrac{V_{i}}{V_{o}}=\dfrac{I_{o}}{I_{i}}[/tex]
[tex]\dfrac{240}{7.50}=\dfrac{1.6}{I_{i}}[/tex]
[tex]I_{i}=\dfrac{1.6\times7.50}{240}[/tex]
[tex]I_{i}=0.05\ A[/tex]
Hence, The input current is 0.05 A.
The input current Ip for the plug-in transformer for a laptop computer in amps is 0.05 A.
What is the function of transformer?
The primary winding of the transformer converts the electric power into the magnetic power, and the secondary winding of the transformer converts it back into the required electric power.
The ratio of the input voltage to the output voltage is equal to the ratio of output current to the input current of the transformer (for 100 percent efficiency). Therefore
[tex]\dfrac{V_i}{V_o}=\dfrac{I_o}{I_i}[/tex]
The input and output voltage of the transformer is 240 V and 7.50 V respectively and the output current is 1.6 amp.
As, the efficiency of the transformer is 100 percent. Thus, put the values in the above formula as,
[tex]\dfrac{240}{7.50}=\dfrac{1.6}{I_i}\\I_i=0.05\rm A[/tex]
Thus, the input current Ip for the plug-in transformer for a laptop computer in amps is 0.05 A.
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Two long, straight wires are parallel and are separated by a distance of d = 0.210 m. The top wire in the sketch carries current I1 = 4.00 A , toward the right, and the bottom wire carries current I2 = 5.90 A , also to the right. At point P, midway between the two wires, what are the magnitude and direction of the net magnetic field produced by the two wires?
Answer:
[tex]1.88\cdot 10^{-5} T[/tex], inside the plane
Explanation:
We need to calculate the magnitude and direction of the magnetic field produced by each wire first, using the formula
[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]
where
[tex]\mu_0[/tex] is the vacuum permeability
I is the current
r is the distance from the wire
For the top wire,
I = 4.00 A
r = d/2 = 0.105 m (since we are evaluating the field half-way between the two wires)
so
[tex]B_1 = \frac{(4\pi\cdot 10^{-7})(4.00)}{2\pi(0.105)}=7.6\cdot 10^{-6}T[/tex]
And using the right-hand rule (thumb in the same direction as the current (to the right), other fingers wrapped around the thumb indicating the direction of the magnetic field lines), we find that the direction of the field lines at point P is inside the plane
For the bottom wire,
I = 5.90 A
r = 0.105 m
so
[tex]B_2 = \frac{(4\pi\cdot 10^{-7})(5.90)}{2\pi(0.105)}=1.12\cdot 10^{-5}T[/tex]
And using the right-hand rule (thumb in the same direction as the current (to the left), other fingers wrapped around the thumb indicating the direction of the magnetic field lines), we find that the direction of the field lines at point P is also inside the plane
So both field add together at point P, and the magnitude of the resultant field is:
[tex]B=B_1+B_2 = 7.6\cdot 10^{-6} T+1.12\cdot 10^{-5}T=1.88\cdot 10^{-5} T[/tex]
And the direction is inside the plane.
The magnitude and direction of the net magnetic field generated by the two wires will be [tex]1.55\times 10^{-8}[/tex].
What is magnetic field strength?
The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength .it is denoted by B.
[tex]B = \frac{u_00I}{2\pi r}[/tex]
(I) is the current
r is the distance from the probe
B is the induced magnetic field
r denotes the distance between the wire and the object.
[tex]u_0[/tex] is the permeability to vacuum
For magnetic field in the top wire
Given
0.105 m = r = d/2
[tex]B_1= \frac{4\pi\times10^{-7}\times4.00}{2\pi \times 0.105}[/tex]
[tex]\rm{B_1=7.6\times 10^{-6}}[/tex] T
As the current to the left other fingers wrapped around the thumb showing the direction of the magnetic field lines.
Given data for bottom wire
I= 5.90 A
r = 0.105 m r = 0.105 m r = 0.105 m
[tex]B_2= \frac{4\pi\times10^{-7}\times5.90}{2\pi \times 0.105}[/tex]
[tex]\rm{B_2=1.12 \times 10^-5[/tex] T
As the current to the left other fingers wrapped around the thumb showing the direction of the magnetic field lines. The field lines direction at point P is also inside the plane.
The megnitude of the resultant magnetic field be the sum of both the field
[tex]\rm{B=B_1+B_2}[/tex]
[tex]\rm{B=7.6\times 10^{-6}+ 1.12\times 10^{-5}}[/tex]
[tex]B = 1.88\times 10^{-5}[/tex] T
Hence The megnitude of the resultant magnetic field be the sum of both the fields [tex]1.88\times 10^{-5}[/tex]T.
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The electic field inside a spherical volume of radius a is given by: vector E = p_0 r^2 / 4 epsilon r cap Find an expression for the charge density inside the spherical volume that gives rise to this electric field.
Answer:
[tex]\rho = \rho_0 r[/tex]
Explanation:
As we know by Gauss law
[tex]\int E. dA = \frac{q}{\epsilon}[/tex]
here we know that
[tex]E = \frac{\rho_0 r^2}{4\epsilon}[/tex]
so here we have
[tex](\frac{\rho_0 r^2}{4\epsilon})(4\pi r^2) = \frac{(\int\rho dV)}{\epsilon}[/tex]
now we have
[tex]\frac{\pi \rho_0 r^4}{\epsilon} = \frac{(\int\rho dV)}{\epsilon}[/tex]
[tex]\pi \rho_0 r^4 = (\int\rho dV)[/tex]
now differentiate both sides by volume
[tex]\frac{d(\pi \rho_0 r^4)}{dV} = \rho [/tex]
[tex]\frac{\pi \rho_0 4r^3 dr}{4\pi r^2 dr} = \rho[/tex]
[tex]\rho = \rho_0 r[/tex]
An electron moving with a velocity v⃗ = 5.0 × 107 m/s i^ enters a region of space where perpendicular electric and a magnetic fields are present. The electric field is E⃗ = 104 V/m j^. What magnetic field will allow the electron to go through the region without being deflected?
To allow the electron to pass through the region without being deflected, the magnetic field should be equal and opposite to the electric field with a magnitude of 5.0 x 10^3 T in the -i^ direction.
Explanation:The force experienced by an electron moving in a magnetic field is given by the formula F = qvB sin(θ), where q is the charge of the electron, v is its velocity, B is the magnetic field, and θ is the angle between the direction of velocity and the magnetic field. To allow the electron to pass through the region without being deflected, the magnetic force should be equal and opposite to the electric force. Since the electric field is in the j^ direction, the magnetic field should be in the -i^ direction with a magnitude of 5.0 x 10^3 T.
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To prevent the electron from being deflected, the magnetic field should be [tex]2.0 \times 10{^-4} T[/tex]. This is calculated by balancing the electric and magnetic forces acting on the electron.
To determine the magnetic field that allows an electron to pass through a region with perpendicular electric and magnetic fields without being deflected, we use the concept of force balance. When the forces from the electric field and the magnetic field are equal and opposite, the electron will move in a straight line without deflection. Given the electron's velocity[tex]v = 5.0 \times 10^7 m/s \hat i[/tex] and the electric field [tex]E = 10^4 V/m \hat j[/tex], we can use the formula:
[tex]qE = qvB[/tex]
Here, q is the charge of the electron, E is the magnitude of the electric field, v is the electron's velocity, and B is the magnetic field strength. Solving for B, we get:
[tex]B = E/v[/tex]
Plug in the given values:
[tex]B = 10^4 V/m / 5.0 \times 10^7 m/s[/tex]
This simplifies to:
[tex]B = 2.0 \times 10^{-4} T[/tex]
Therefore, the magnetic field required is [tex]2.0 \times 10^{-4} T[/tex].
Phosphorous reacts with chlorine gas to produce phosphorous pentachloride. Calculate the mass of product produced when 25.0 g of phosphorous reacts with 25.0 grams of chlorine. Calculate the mass of product produced if the reaction occurred with a 70.5 percent yield.
Answer : The mass of product produced if the reaction occurred with a 70.5 percent yield will be, 20.67 grams.
Explanation : Given,
Mass of P = 25 g
Mass of [tex]Cl_2[/tex] = 25 g
Molar mass of P = 30.97 g/mole
Molar mass of [tex]Cl_2[/tex] = 71 g/mole
Molar mass of [tex]PCl_5[/tex] = 208.24 g/mole
First we have to calculate the moles of [tex]P[/tex] and [tex]Cl_2[/tex].
[tex]\text{Moles of }P=\frac{\text{Mass of }P}{\text{Molar mass of }P}=\frac{25g}{30.97g/mole}=0.807moles[/tex]
[tex]\text{Moles of }Cl_2=\frac{\text{Mass of }Cl_2}{\text{Molar mass of }Cl_2}=\frac{25g}{71g/mole}=0.352moles[/tex]
Now we have to calculate the limiting and excess reagent.
The balanced chemical reaction is,
[tex]2P+5Cl_2\rightarrow 2PCl_5[/tex]
From the balanced reaction we conclude that
As, 5 moles of [tex]Cl_2[/tex] react with 2 moles of [tex]P[/tex]
So, 0.352 moles of [tex]Cl_2[/tex] react with [tex]\frac{2}{5}\times 0.352=0.1408[/tex] moles of [tex]P[/tex]
That means, in the given balanced reaction, [tex]Cl_2[/tex] is a limiting reagent and it limits the formation of products and [tex]P[/tex] is an excess reagent because the given moles are more than the required moles.
Now we have to calculate the moles of [tex]PCl_5[/tex].
As, 5 moles of [tex]Cl_2[/tex] react with 2 moles of [tex]PCl_5[/tex]
So, 0.352 moles of [tex]Cl_2[/tex] react with [tex]\frac{2}{5}\times 0.352=0.1408[/tex] moles of [tex]PCl_5[/tex]
Now we have to calculate the mass of [tex]PCl_5[/tex].
[tex]\text{Mass of }PCl_5=\text{Moles of }PCl_5\times \text{Molar mass of }PCl_5[/tex]
[tex]\text{Mass of }PCl_5=(0.1408mole)\times (208.24g/mole)=29.32g[/tex]
Now we have to calculate the mass of product produced (actual yield).
[tex]\%\text{ yield of }PCl_5=\frac{\text{Actual yield of }PCl_5}{\text{Theoretical yield of }PCl_5}\times 100[/tex]
[tex]70.5=\frac{\text{Actual yield of }PCl_5}{29.32g}\times 100[/tex]
[tex]\text{Actual yield of }PCl_5=20.67g[/tex]
Therefore, the mass of product produced if the reaction occurred with a 70.5 percent yield will be, 20.67 grams.
What is the unit of k (spring constant) in SI system?
Answer:
SI unit of k (spring constant) = N/m
Explanation:
We have expression for force in a spring extended by x m given by
F = kx
Where k is the spring constant value.
Taking units on both sides
Unit of F = Unit of k x Unit of x
N = Unit of k x m
Unit of k = N/m
SI unit of k (spring constant) = N/m
Answer:
N/m
Explanation:
The unit of k (spring constant) in SI system is N/m.
SI unit of k (spring constant) = N/m
Your swimming pool is square and 5.8 m on a side. It is 4.2 m deep in the morning If the temperature changes by 24 degrees C during the afternoon, how much the depth of the water increase?
Answer:
The increases depth of the water is 0.021 m.
Explanation:
Given that,
One side of square = 5.8 m
Depth = 4.2 m
Temperature = 24°C
Coefficient of volume expansion for water[tex]\beta = 210\times10^{-6}\ /^{\circ}C[/tex]
We need to calculate the volume of the pool
[tex]V= 5.8\times5.8\times4.2[/tex]
[tex]V=141.288\ m^3[/tex]
Using formula of coefficient of volume expansion
[tex]\Delta V=\Beta V_{0}\times\Delta T[/tex]
If the temperature changes by 24 degrees C during the afternoon,
[tex]5.8\times5.8\times h=210\times10^{-6}\times141.288\times24[/tex]
[tex]h=\dfrac{210\times10^{-6}\times141.288\times24}{5.8\times5.8}[/tex]
[tex]h=0.021\ m[/tex]
Hence. The increases depth of the water is 0.021 m.
What is the kinetic energy of the rocket with mass 15,000 kg and speed of 5200 m/s? A. 2.01 x 10^11 J B. 2.02x 10^11 J C. 2.03 x 10^11 J D. 2.04 x 10^11 J
C. [tex]E_{k}=2.03x10^{11}J[/tex]
The kinetic energy of a body is the ability to perform work due to its movement given by the equation [tex]E_{k}=\frac{1}{2}mv^{2}[/tex].
To calculate the kinetic energy of a rocket with mass 15000kg and speed of 5200m/s:
[tex]E_{k}=\frac{1}{2}(15000kg)(5200m/s)^{2}=202800000000J=2.03x10^{11}J[/tex]
An electron with kinetic energy 2.9 keV moving along the positive direction of an x axis enters a region in which a uniform electric field of magnitude 7.5 kV/m is in the negative direction of the y axis. A uniform magnetic field is to be set up to keep the electron moving along the xaxis, and the direction of the field is to be chosen to minimize the required magnitude of the field. What is the magnitude of the magnetic field in mT?
The electric force on the electron is opposite in direction to the electric field E. E points in the -y direction, so the electric force will point in the +y direction. The magnitude of the electric force is given by:
F = Eq
F = electric force, E = electric field strength, q = electron charge
We need to set up a magnetic field such that the magnetic force on the electron balances out the electric force. Since the electric force points in the +y direction, we need the magnetic force to point in the -y direction. Using the reversed right hand rule, the magnetic field must point in the -z direction for this to happen. Since the direction is perpendicular to the +x direction of the electron's velocity, the magnetic force is given by:
F = qvB
F = magnetic force, q = charge, v = velocity, B = magnetic field strength
The electric force must equal the magnetic force.
Eq = qvB
Do some algebra to isolate B:
E = vB
B = E/v
Let's solve for the electron's velocity. Its kinetic energy is given by:
KE = 0.5mv²
KE = kinetic energy, m = mass, v = velocity
Given values:
KE = 2.9keV = 4.6×10⁻¹⁶J
m = 9.1×10⁻³¹kg
Plug in and solve for v:
4.6×10⁻¹⁶ = 0.5(9.1×10⁻³¹)v²
v = 3.2×10⁷m/s
B = E/v
Given values:
E = 7500V/m
v = 3.2×10⁷m/s
Plug in and solve for B:
B = 7500/3.2×10⁷
B = 0.00023T
B = 0.23mT
To minimize the required magnitude of the magnetic field and keep the electron moving along the x-axis, the direction of the magnetic field should be chosen to cancel out the force due to the electric field. The magnitude of the magnetic field needed is 2.59 mT.
Explanation:To keep the electron moving along the x-axis and minimize the required magnitude of the magnetic field, the force on the electron due to the magnetic field should cancel out the force on the electron due to the electric field.
The force on the electron due to the electric field is given by:The frequency factor and activation energy for a chemical reaction are A = 4.23 x 10–12 cm3/(molecule·s) and Ea = 12.9 kJ/mol at 384.7 K, respectively. Determine the rate constant for this reaction at 384.7 K.
Final answer:
The rate constant for this reaction at 384.7 K is 7.945 x 10^-4 cm^3/(molecule·s).
Explanation:
The rate constant, denoted by k, can be determined using the Arrhenius equation: k = Ae^-Ea/RT, where A is the frequency factor, Ea is the activation energy, R is the ideal gas constant, and T is the temperature in Kelvin. To find the rate constant at 384.7 K, we first need to convert Ea from kJ/mol to J/mol by multiplying it by 1000, giving us 12,900 J/mol. Plugging in the values A = 4.23 x 10^-12 cm^3/(molecule·s), Ea = 12,900 J/mol, and R = 8.314 J/mol/K, into the Arrhenius equation, we can calculate k as follows:
k = (4.23 x 10^-12 cm^3/(molecule·s)) * e^(-12,900 J/mol / (8.314 J/mol/K * 384.7 K))
k = 7.945 x 10^-4 cm^3/(molecule·s)
A solenoid has a radius Rs = 14.0 cm, length L = 3.50 m, and Ns = 6500 turns. The current in the solenoid decreases at the rate of 79.0 A/s. A circular coil with a single turn and radius rc = 20.0 cm encircles the solenoid with its plane perpendicular to the axis of the solenoid. Determine the magnitude of the average induced electric field in the coil.
Final answer:
The magnitude of the average induced electric field in the coil, encircling a solenoid with given dimensions and a decreasing current of 79.0 A/s, is approximately [tex]\(1.80 \times 10^{-4}\)[/tex]volts per meter.
Explanation:
The induced electric field in the coil is determined by Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a closed loop is equal to the negative rate of change of magnetic flux through the loop. In this scenario, the solenoid serves as the primary coil, and the circular coil is the secondary coil.
The magnetic flux through a single turn of the circular coil is given by[tex]\(\Phi = B \cdot A\)[/tex], where is the magnetic field strength and is the area of the coil. The magnetic field inside a solenoid is given by[tex]\(B = \mu_0 \cdot N_s \cdot I\)[/tex].
Substituting these expressions into the formula for magnetic flux, we get [tex]\(\Phi = \mu_0 \cdot N_s \cdot I \cdot A\).[/tex] The induced emf is then given by Faraday's law: [tex]\(\mathcal{E} = -\frac{d\Phi}{dt}\)[/tex]. Taking the derivative with respect to time and using the given values, we find[tex]\(\mathcal{E} = -\mu_0 \cdot N_s \cdot A \cdot \frac{dI}{dt}\).[/tex]
Finally, the induced electric field in the coil is given by [tex]\(E = \frac{\mathcal{E}}{A}\)[/tex]. Substituting the values into this formula provides the magnitude of the average induced electric field in the coil, approximately[tex]\(1.80 \times 10^{-4}\)[/tex]volts per meter. This calculation yields a quantitative measure of the induced electric field strength in response to the changing current in the solenoid.
Two 10-cm-diameter charged rings face each other, 23.0 cm apart. Both rings are charged to + 10.0 nC . What is the electric field strength at the center of the left ring?
The question asks for the electric field strength at the center of a charged ring, which involves using physics concepts related to electric fields and charge distributions. An accurate calculation would require application of formulas for fields due to point charges distributed in a ring, or thorough integration techniques taught at high school level physics.
The subject of the question is Physics, and it pertains to the concept of electric fields created by charged objects. We are considering two identical rings, each with a positive charge of +10.0 nC, facing each other with a separation of 23.0 cm. What is required is to calculate the electric field strength at the center of the left ring. By the symmetry of the setup and since the charges are identical and positive, the electric field at the center of the left ring due only to it would be zero because there is no charge displacement leaving the right ring's field to consider. The electric field strength at a point due to a charged ring on the ring's axis can be calculated using the formula for electric fields due to point charges, since a charged ring can be thought of as a distribution of point charges.
However, without precise formulae for the field due to a ring or detailed integration methods, we cannot calculate the precise value for this field. A good physics course at the high school level will offer the tools necessary to derive such formulae and solve this problem accurately.
A 21.6−g sample of an alloy at 93.00°C is placed into 50.0 g of water at 22.00°C in an insulated coffee-cup calorimeter with a heat capacity of 9.20 J/K. If the final temperature of the system is 31.10°C, what is the specific heat capacity of the alloy?
The specific heat capacity of the alloy can be calculated using the formula q = m * c * ΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. We can use the principle of conservation of heat to calculate the specific heat capacity of the alloy.
Explanation:The specific heat capacity of the alloy can be calculated using the formula: q = m * c * ΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. In this case, the heat transferred to the water can be calculated by q_water = m_water * c_water * ΔT_water. Using the principle of conservation of heat, q_water = -q_alloy. We can rearrange the equation to solve for c_alloy: c_alloy = -q_water / (m_alloy * ΔT_alloy)
Plugging in the values, we have: c_alloy = -q_water / (m_alloy * (ΔT_final - ΔT_initial)). This gives us the specific heat capacity of the alloy.
In this case, the final temperature of the system is 31.10°C, which means that ΔT_alloy = 31.10°C - 93.00°C = -61.90°C. Plugging in the values, we get: c_alloy = -(-50.0 g * 4.184 J/g °C * (31.10°C - 22.00°C)) / (21.6 g * -61.90°C). After calculating, you will find the specific heat capacity of the alloy.
Learn more about specific heat capacitycapacitycapacitycapacity#SPJ12The specific heat capacity of the alloy can be calculated using the formula: q = m × c × ΔT.
Explanation:
The specific heat capacity of the alloy can be calculated using the formula:
q = m × c × ΔT
where q is the heat transferred, m is the mass of the alloy, c is the specific heat capacity of the alloy, and ΔT is the change in temperature. In this case, the heat transferred to the alloy is equal to the heat transferred from the water:
m1 × c1 × ΔT1 = m2 × c2 × ΔT2
Substituting the given values, we can solve for c2 to find the specific heat capacity of the alloy:
c2 = (m1 × c1 × ΔT1) / (m2 × ΔT2)
Learn more about specific heat capacity here:https://brainly.com/question/28302909
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A photon has a momentum of 5.55 x 10-27 kg-m/s. (a) What is the photon's wavelength? nm (b) To what part of the electromagnetic spectrum does this wavelength correspond? the tolerance is +/-2%
Explanation:
It is given that,
Momentum of the photon, [tex]p=5.55\times 10^{-27}\ kg-m/s[/tex]
(a) We need to find the wavelength of this photon. It can be calculated using the concept of De-broglie wavelength.
[tex]\lambda=\dfrac{h}{p}[/tex]
h is the Planck's constant
[tex]\lambda=\dfrac{6.67\times 10^{-34}\ Js}{5.55\times 10^{-27}\ kg-m/s}[/tex]
[tex]\lambda=1.2\times 10^{-7}\ m[/tex]
or
[tex]\lambda=120\ nm[/tex]
(b) The wavelength lies in the group of ultraviolet rays. The wavelength of UV rays lies in between 400 nm to 10 nm.
Choose the statement(s) that is/are true about an electric field. (i) The electric potential decreases in the direction of an electric field. (ii) A positive charge experiences a force in the direction of an electric field. (iii) An electron placed in an electric field will move opposite to the direction of the field.
Answer:
A positive charge experiences a force in the direction of an electric field.
Explanation:
Electric field is defined as the electric force acting per unit positive charge. Mathematically, it is given by :
[tex]E=\dfrac{F}{q}[/tex]
We know that like charges repel each other while unlike charges attract each other. The direction of electric field is in the direction of electric force. For a positive charge the field lines are outwards and for a negative charge the electric field lines are inwards.
So, the correct option is (b) "A positive charge experiences a force in the direction of an electric field".
A 2 meter long bar has a longitudinal/axial wave speed of 5,000 m/s. If the bar is fixed at each end, what is the second natural frequency an for this system in rad/s? a. 12,450 b. 14,850 e 15,710 d. 16,800 e. 18,780 f. None of the above
Answer:
The second natural frequency an for this system is 15710 rad/s.
(e) is correct option.
Explanation:
Given that,
Length = 2 m
Wave speed = 5000 m/s
We need to calculate the second natural frequency
Using formula of Time period
[tex]T = \dfrac{L}{v}[/tex]
[tex]T=\dfrac{2}{5000}\ s[/tex]
We know that,
The frequency is the reciprocal of time period.
[tex]f=\dfrac{1}{T}[/tex]
[tex]f=\dfrac{5000}{2}[/tex]
[tex]f=2500\ Hz[/tex]
We know that,
[tex]1\ rad/s =\dfrac{1}{2\pi}\ Hz[/tex]
So, The frequency is in rad/s
[tex]f= 15710\ rad/s[/tex]
Hence, The second natural frequency an for this system is 15710 rad/s.