While a Hobbit home may be a cooler design than a regular home, there are still functional considerations that should be taken into account when designing the front door. A larger handle, more leverage, and a lower handle would all make it easier to open the door and reduce the amount of force required to get it moving.
Bilbo may want to consider rethinking the design of the front door for a few reasons:
A larger handle is needed when pulling at the center of mass: The circular shape of the door means that the center of mass is not in the middle of the door. This makes it harder to pull the door open, especially if the handle is too small. A larger handle would provide more surface area to grip and make it easier to open the door.More leverage when pulling would be better: The circular shape of the door also means that there is less leverage when pulling the door open. A rectangular door with a longer handle would provide more leverage, making it easier to open the door.The handle should be lower for smaller hobbits to pull and creating less rotational inertia: The circular shape of the door creates more rotational inertia than a rectangular door would. This means that it takes more force to get the door moving, and once it is moving, it is harder to stop. A lower handle would make it easier for smaller hobbits to pull the door open and would also create less rotational inertia.To know more about leverage
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a green 10 kg ball is moving 25 m/s hits a non-moving red 15 kg ball. After they hit,the red ball is moving to the right at a 55 degree angle from the green ball's original direction. The green ball is now moving at a 35 degree angle to the left of its original direction. What is the red ball's final speed? what is the green ball's final speed?
The red ball's final speed is 3 m/s.
The green ball's final speed is sqrt((20.50 m/s)^2 + (14.29 m/s)^2) = 25 m/s.
Find the speed of the red and green ball.We can start by using conservation of momentum, which states that the total momentum of the system before the collision is equal to the total momentum of the system after the collision.
Let's first find the initial momentum of the system. The momentum of an object is given by its mass times its velocity.
Initial momentum = (mass of green ball) x (velocity of green ball) + (mass of red ball) x (velocity of red ball)
Initial momentum = (10 kg) x (25 m/s) + (15 kg) x (0 m/s) (since the red ball is not moving initially)
Initial momentum = 250 kg m/s
After the collision, the green ball is moving at a 35-degree angle to the left of its original direction. We can use trigonometry to find the x and y components of its velocity.
x component of velocity = (magnitude of velocity) x cos(angle)
x component of velocity = (25 m/s) x cos(35 degrees)
x component of velocity = 20.50 m/s
y component of velocity = (magnitude of velocity) x sin(angle)
y component of velocity = (25 m/s) x sin(35 degrees)
y component of velocity = 14.29 m/s
So the final velocity of the green ball can be represented as a vector (20.50 m/s, 14.29 m/s) at a 35-degree angle to the left of its original direction.
Now, let's find the final velocity of the red ball. We know that it is moving to the right at a 55-degree angle from the green ball's original direction. Again, we can use trigonometry to find the x and y components of its velocity.
x component of velocity = (magnitude of velocity) x cos(angle)
x component of velocity = (magnitude of velocity) x cos(55 degrees)
y component of velocity = (magnitude of velocity) x sin(angle)
y component of velocity = (magnitude of velocity) x sin(55 degrees)
We don't know the magnitude of the velocity, but we can use the conservation of momentum to find it. The final momentum of the system is also equal to 250 kg m/s (since there are no external forces acting on the system).
Final momentum = (mass of green ball) x (velocity of green ball) + (mass of red ball) x (velocity of red ball)
Final momentum = (10 kg) x (20.50 m/s) + (15 kg) x (magnitude of velocity)
Final momentum = 205 kg m/s + 15(magnitude of velocity)
250 kg m/s = 205 kg m/s + 15(magnitude of velocity)
45 kg m/s = 15(magnitude of velocity)
magnitude of velocity = 3 m/s
So the final velocity of the red ball can be represented as a vector (3 m/s, 2.69 m/s) at a 55-degree angle to the right of the green ball's original direction.
To summarize:
The red ball's final speed is 3 m/s.
The green ball's final speed is sqrt((20.50 m/s)^2 + (14.29 m/s)^2) = 25 m/s.
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A particle moves 5m in the positive x direction while being acted upon by a constant force vec F = (4 N) cap i + (2 N) cap j ? (4N) cap k. The work done on the particle by this force is: A. 20 J B. 10 J C. -20 J D. 30 J E. Is impossible to calculate without knowing other forces
The work done on the particle by the force F is 20 J. Answer A is correct.
The work done on the particle by the force F can be calculated using the formula:
[tex]W = F \int ds[/tex]
where F is the force vector and ds is the displacement vector. Since the force is constant, we can simplify this to:
[tex]W = F . \int ds[/tex]
where [tex]\int ds[/tex] is the displacement vector. In this case, the particle moves 5m in the positive x direction, so we have:
[tex]\int ds = 5 \hat{i}[/tex]
Substituting this into the equation for work, we get:
W = F · 5 [tex]\hat{i}[/tex]
where F is the force vector given as:
F = (4 N) [tex]\hat{i}[/tex] + (2 N) [tex]\hat{j}[/tex] − (4 N) [tex]\hat{k}[/tex]
Taking the dot product of F and 5[tex]\hat{i}[/tex], we get:
[tex]F . 5 \hat{i} = (4 N) (5) + (2 N) (0) - (4 N) (0)\\\\ = 20 J[/tex]
Choice A is correct.
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find the distance in nm between two slits that produces the first minimum for 420-nm violet light at an angle of 13.5°. 899.60 correct: your answer is correct. nm
The distance between the two slits that produces the first minimum for 420-nm violet light at an angle of 13.5° is approximately 899.60 nm.
To find the distance between two slits that produces the first minimum for 420-nm violet light at an angle of 13.5°, we can use the formula for the angular position of the minima in a double-slit interference pattern:
mλ = d * sinθ
Here, m is the order of the minimum (m = 1 for the first minimum), λ is the wavelength of light, d is the distance between the slits, and θ is the angle.
We are given λ = 420 nm and θ = 13.5°, and we need to find d.
1. Convert the angle to radians: θ = 13.5° * (π/180) = 0.2354 radians
2. Rearrange the formula to solve for d: d = mλ / sinθ
3. Plug in the given values and solve for d: d = (1 * 420 nm) / sin(0.2354 radians)
d ≈ 899.60 nm
Therefore, the distance between the two slits that produces the first minimum for 420-nm violet light at an angle of 13.5° is approximately 899.60 nm.
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a 5.8×10−2-t magnetic field passes through a circular ring of radius 5.3 cm at an angle of 16 ∘ with the normal.
Find the magnitude of the magnetic flux through the ring.
Express your answer using two significant figures.
The magnitude of the magnetic flux through the ring is approximately 4.9×10[tex]−4[/tex] Wb (we rounded the answer to two significant figures).
The magnetic flux through a circular loop is given by:
Φ = BAcosθ
Where Φ is the magnetic flux, B is the magnetic field, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop.
In this case, the magnetic field is 5.8×10[tex]-2[/tex] T, the radius of the loop is 5.3 cm (or 0.053 m), and the angle between the magnetic field and the normal is 16∘.
The area of a circle is given by:
A = πr^2
So the area of the loop is:
A = π(0.053 m)[tex]^2[/tex] ≈ 8.83×10₃
Substituting the values into the equation for magnetic flux, we get:
Φ =[tex](5.8×10−2 T)(8.83×10−3 m^2)cos(16∘) ≈ 4.9×10−4 Wb[/tex]
Therefore, the magnitude of the magnetic flux through the ring is approximately 4.9×1[tex]0−4 Wb[/tex] (we rounded the answer to two significant figures).
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calculate the final velocity right after a 115 kg rugby player who is initially running at 7.95 m/s collides head‑on with a padded goalpost and experiences a backward force of 17900 n for 5.50×10−2 s.
The final velocity right after a 115 kg rugby player collides head‑on with a padded goalpost is approximately 0.61 m/s backwards.
To calculate the final velocity of the rugby player after the collision, we need to use the impulse-momentum theorem. The equation for this is:
Impulse = Change in momentum
Impulse = Force × Time
Change in momentum = Mass × Change in velocity
Given values:
Initial velocity (v₁) = 7.95 m/s
Mass (m) = 115 kg
Force (F) = -17900 N (backward force)
Time (t) = 5.50 × 10⁻² s
First, we'll find the impulse:
Impulse = Force × Time
Impulse = -17900 N × 5.50 × 10⁻² s
Impulse ≈ -984.5 kg·m/s
Now, we'll find the change in momentum:
Change in momentum = Impulse
Change in momentum = -984.5 kg·m/s
Next, we'll calculate the change in velocity:
Change in velocity = Change in momentum / Mass
Change in velocity ≈ -984.5 kg·m/s / 115 kg
Change in velocity ≈ -8.56 m/s
Finally, we'll find the final velocity (v₂):
v₂ = Initial velocity + Change in velocity
v₂ = 7.95 m/s - 8.56 m/s
v₂ ≈ -0.61 m/s
So, the final velocity of the rugby player right after the collision is approximately -0.61 m/s (negative sign indicates the backward direction).
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Two different fluorescent probes are attached to separate sites on a protein: A ( λ ex =388 mm;λ em =475 mm) and B(λ er =483 nm;λ em =538 mm). The value of R0 is 64AThe following data are obtained. Fluorescence intensity of A in the absence of B: 160 units Fluorescence intensity of A in the presence of B:156 units At this efficiency, what is the distance between the probes? 117.86 A
64 A
0 A
34.75 A
˚
The distance between the probes is given as 117.86 A
How to solve for the distanceWe are given that the fluorescence intensity of probe A decreases from 160 units in the absence of probe B to 156 units in the presence of probe B. This decrease in intensity is due to the energy transfer from probe A to probe B. The efficiency of energy transfer can be calculated using the following equation:
E = 1 - (I_AB / I_A)
where I_AB is the fluorescence intensity of probe A in the presence of probe B and I_A is the fluorescence intensity of probe A in the absence of probe B.
Substituting the given values, we get:
E = 1 - (156 / 160) = 0.025
Now we can calculate the distance between the probes:
R = 64 A * [(1/0.025) - 1]^(1/6) = 117.86 A
Therefore, the distance between the probes is approximately 117.86 A.
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a beam of light of wavelength 630 nm is incident on a slit that is 0.400 mm wide. if the distance between the slit and the screen is 1.80 m, what is the width on the screen of the central bright fringe?
The width of the central bright fringe on the screen is approximately 5.67 mm.
To calculate the width on the screen of the central bright fringe, we need to use the equation:
w = (λL)/d
Substituting the given values, we get:
w = (630 nm x 1.80 m)/0.400 mm
w = 2.835 x 10^-3 m or 2.84 mm (rounded to two significant figures)
Width = 2 * (λL / a)
- Width is the width of the central bright fringe on the screen
- λ is the wavelength of light (630 nm or 630 x 10^-9 m)
- L is the distance between the slit and the screen (1.80 m)
- a is the width of the slit (0.400 mm or 0.400 x 10^-3 m)
Width = 2 * (630 x 10^-9 m * 1.80 m) / (0.400 x 10^-3 m)
Width ≈ 0.00567 m or 5.67 mm
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a 1.000 turn coil carries a 66.000 a current and has a magnetic moment of 5.100 x 10-2 am2. what is the radius of the coil?
The radius of a 1.000-turn coil that carries a 66.000 A current and has a magnetic moment of 5.100 x 10⁻² Am² is approximately 1.568 x 10⁻² meters.
To find the radius of the coil, we will use the formula for the magnetic moment, which is given by:
Magnetic moment (μ) = N * I * A
where N is the number of turns (1.000 turn), I is the current (66.000 A), and A is the area of the coil.
We know the magnetic moment (μ) = 5.100 x 10⁻² Am², so we can solve for the area (A):
A = μ / (N * I) = (5.100 x 10⁻²) / (1.000 * 66.000) = 7.727 x 10⁻⁴ m²
Since the coil is circular, we can use the formula for the area of a circle:
A = π * r²
where r is the radius of the coil.
Now we can solve for the radius (r):
r² = A / π = (7.727 x 10⁻⁴) / π
r² ≈ 2.460 x 10⁻⁴
Taking the square root of both sides:
r ≈ √(2.460 x 10⁻⁴) ≈ 1.568 x 10⁻² m
So, the radius of the coil is approximately 1.568 x 10⁻² meters.
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Use the following steps to prove Kepler's Second Law. The notation is the same as in the proof of the First Law in Section 13.4. In particular, use polar coordinates so that r = (r cos theta)i + (r sin theta)j. (a) Show that h = r^2 d theta/dt k. (b) Deduce that r^2 = d theta/dt = h. (c) If A = A(t) is the area swept out by the radius vector r = r(t) in the time interval [t_0, t] as in the figure, show that dA/dt = 1/2 r^2 d theta/dt (d) Deduce that dA/dt = 1/2 h = constant This says that the rate at which A is swept out is constant and proves Kepler's Second Law. Let T be the period of a planet about the sun: that is, T is the time required for it to travel once around its elliptical orbit. Suppose that the lengths of the major and minor axes of the ellipse are 2a and 2b. (a) Use part (d) of Problem 1 to show that T = 2 pi ab/h. (b) Show that h^2/GM = ed = b^2/a. (c) Use parts (a) and (b) to show that T^2 = 4 pi^2/GM a^3. This proves Kepler's Third Law. [Notice that the proportionality constant 4 pi^2/(GM) is independent of the planet.]
We also know from Kepler's Second Law that the rate at which area is swept out by the radius vector is constant, which means dA/dt is constant. Therefore, we can deduce that 1/2 h is constant.
What is Velocity?
Velocity is a vector quantity that describes the rate of change of displacement of an object with respect to time. It is defined as the change in displacement per unit of time and includes both magnitude (speed) and direction. Velocity is typically denoted by the symbol "v" and is measured in units of distance per time, such as meters per second (m/s) or kilometers per hour (km/h).
d(theta)/dt = h/[tex]r^{2}[/tex]
Now, recall that the area A swept out by the radius vector r in a time interval dt is given by:
dA = (1/2)[tex]r^{2}[/tex] d(theta)
Taking the derivative of both sides with respect to time t, we get:
dA/dt = (1/2)[tex]r^{2}[/tex]d(theta)/dt
Substituting the expression for d(theta)/dt from above, we get:
dA/dt = (1/2)[tex]r^{2}[/tex] (h/[tex]r^{2}[/tex])
Simplifying, we get:
dA/dt = 1/2 h
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Air enters a nozzle steadily at 2.21 kg/m^3 and 40 m/s and leaves at 0.762 kg/m^3 and 180 m/s. If the inlet area of the nozzle is 90 cm,^2 , determine(a) the mass flow rate through the nozzle, and(b) the exit area of the nozzle
Air enters a nozzle steadily at 2.21 kg/m³ and 40 m/s and leaves at 0.762 kg/m³and 180 m/s. If the inlet area of the nozzle is 90 cm²,
(a) the mass flow rate through the nozzle is 0.7986 kg/s
(b) the exit area of the nozzle is 0.00582 m².
(a) To determine the mass flow rate through the nozzle,
we need to multiply the density of the air at the inlet (2.21 kg/m³) by the velocity of the air at the inlet (40 m/s) and the inlet area (90 cm²).
First, let's convert the inlet area from cm² to m²:
90 cm² = 90 * 0.0001 m²
= 0.009 m²
Now we can calculate the mass flow rate:
[tex]Mass flow rate = density * velocity * area[/tex]
Mass flow rate = 2.21 kg/m^3 × 40 m/s × 0.009 m^2
Mass flow rate = 0.7986 kg/s
So, the mass flow rate through the nozzle is 0.7986 kg/s.
(b) To find the exit area of the nozzle, we can use the mass flow rate and the exit conditions (density and velocity) provided.
First, we can rearrange the mass flow rate equation to solve for the exit area:
[tex]Exit area = mass flow rate / (exit density * exit velocity)[/tex]
Now, plug in the given values:
Exit area = 0.7986 kg/s / (0.762 kg/m^3 × 180 m/s)
Exit area = 0.7986 kg/s / 137.16 kg/(m^2 s)
Exit area ≈ 0.00582 m^2
The exit area of the nozzle is approximately 0.00582 m^2.
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An AC voltage of the form Δv = (85.0 V)sin(260t) is applied to aseries RLC circuit. If R = 52.0 Ω, C = 28.0 μF, and L = 0.250 H,find the following.(a) impedance of the circuit Incorrect: ____ Ω(b) rms current in the circuit: _______A(c) average power delivered to the circuit: _____ W
a). Impedance of the circuit Incorrect: Z = 85.9 ohms
(b) Rms current in the circuit: 0.69 A
c) Average power delivered to the circuit: 35.88 W
What does an AC current frequency not include?Due to the fact that DC current is a sort of continuous current, its frequency is 0 hertz. Therefore, AC current is not limited to zero Hz as its rest frequency.
Given : 85 sin(260t)
C = 28mF = 28x 10⁻³ F
Inductance = L = 0.250 H
a) Inductive reactance = X(L) = ω L = (350)(0.2) = 70 ohms
Capacitive reactance = X(C) = 1 / ωC = 0.114 ohms
Reactance = Z = [tex]\sqrt{R^{2} + (X_{L} - X_{C} ) }[/tex]
= [tex]\sqrt{52^{2} +(70 -0.114)^{2} }[/tex]
=85.9
B ) current = I = 85 / 85.9 = 0.98 A
Irms = 0.98 / [tex]\sqrt{2}[/tex] = 0.69 A
c) P = R = (0.69)(52) = 35.88 W
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to 56.4°c contains pure carbon resistors. what is the percent difference in resistance over this range? the temperature coefficient of resistivity for carbon is −0.500 ✕ 10-3/°c.
tThe percent difference in resistance over this temperature range is 2.82% when coefficient of resistivity for carbon is -0.500 × 10⁻³/°C.
To determine the percent difference in resistance over this range, we need to use the given temperature coefficient of resistivity for carbon, which is -0.500 × 10⁻³/°C. First, we need to find the change in resistance:
ΔR = R × α × ΔT
Where ΔR is the change in resistance, R is the initial resistance, α is the temperature coefficient of resistivity, and ΔT is the change in temperature.
In this case, ΔT = 56.4°C, and α = -0.500 × 10⁻³/°C. We can't find the exact change in resistance without the initial resistance value, but we can still find the percent difference in resistance:
Percent difference = (ΔR / R) × 100
Plugging in the given values:
Percent difference = (R × (-0.500 × 10⁻³/°C) × 56.4°C) / R × 100
The R values cancel out, leaving:
Percent difference = (-0.500 × 10⁻³/°C × 56.4°C) × 100 = -2.82%
The negative sign indicates a decrease in resistance, so the percent difference in resistance over this temperature range is 2.82%.
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what current flows when a 45 v potential difference is imposed across a 1.8 kω resistor?
When a 45 V potential difference is applied across a 1.8 kΩ resistor, a current flows through the resistor, following Ohm's law (I = V/R). Therefore, the current can be calculated by dividing the voltage by the resistance: I = 45 V / 1.8 kΩ = 0.025 A. This means that a current of 0.025 A, or 25 milliamperes (mA), flows through the resistor.
The flow of current through the resistor can cause various effects, depending on the circuit design and the properties of the resistor itself. For example, the resistor may generate heat as a result of the current flow, which can be a concern in some applications.
Additionally, the resistor can serve to limit the amount of current that flows through the circuit, which can help protect other components from damage due to overloading or short circuits.
Overall, understanding how current flows through resistors and other components is essential for designing and troubleshooting electrical circuits. By applying the principles of Ohm's law and other fundamental concepts, engineers, and technicians can ensure that circuits operate safely and effectively.
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A 0.75-kg mass oscillates according to the equation x(t)=0.21 cos(145t), where the position x(t) is mcasured in meters 25% What is the period, in seconds, of this mass?
The period of a mass oscillating according to the equation x(t)=0.21 cos(145t) is equal to the inverse of the frequency, which is equal to 145. This means that the mass completes one cycle of oscillation every 0.0069 seconds.
Therefore, the period of a mass with a mass of 0.75 kg oscillating according to this equation is equal to 1/145 seconds, or about 0.0069 seconds. This means that the mass oscillates at a frequency of 145 Hz, or cycles per second.
This means that the mass completes a full cycle of oscillation every 0.0069 seconds. Therefore, it takes the mass 0.0069 seconds to move from its maximum position to its minimum position and back again. This is the period of oscillation for the mass.
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Please I need help finding this answer in this textbook!!!
ASAP
In Racial Formations, race is defined as a socio historical concept, what does that mean
to the authors? Do you agree with this definition why or why not? Explain how race is
socially constructed or strictly biological. Support your response with two paragraphs.
Yes I agree and the socio historical concept implies that race is created and maintained through systems of power and inequality.
What is race?According to Michael Omi and Howard Winant, in Racial Formations, race is a socio-historical concept that is constructed through the intersection of cultural, political, and economic forces.
In this book, they argue that race is not an immutable, biologically determined characteristic of individuals or groups but rather a social construct that is created and maintained through systems of power and inequality. The authors illustrate how race is constructed through examples from different historical periods and social contexts.
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a balloon containing methane gas has a volume of 2.40 l at 57.0 °c . what volume will the balloon occupy at 114 °c ?
If the pressure stays constant at atmospheric pressure, the balloon containing methane gas will have a volume of 4.80 L at 114 °C. However, if the pressure changes, the final volume will be different.
To solve this problem, we need to use the combined gas law equation, which relates the pressure, volume, and temperature of a gas,
(P1 * V1) / T1 = (P2 * V2) / T2
where P1 and P2 are the initial and final pressures (which we can assume to be constant), V1 is the initial volume, V2 is the final volume (what we're trying to find), T1 is the initial temperature, and T2 is the final temperature.
We're given that the initial volume (V1) is 2.40 L, the initial temperature (T1) is 57.0 °C, and the final temperature (T2) is 114 °C. We're trying to find the final volume (V2). We're not given the pressure, but we can assume it's constant (since the balloon isn't being compressed or expanding).
Plugging in the values we have, we get,
(P1 * 2.40) / 57.0 = (P2 * V2) / 114
We can simplify this equation by multiplying both sides by 114,
(P1 * 2.40 * 114) / 57.0 = P2 * V2
Now we can solve for V2 by dividing both sides by P2,
V2 = (P1 * 2.40 * 114) / (57.0 * P2)
Since we don't know the pressure, we can't solve for the exact final volume. However, we can make some assumptions. For example, if we assume that the pressure stays constant at atmospheric pressure (which is around 1 atm), we can plug that value in for P1 and P2:
V2 = (1 * 2.40 * 114) / (57.0 * 1) = 4.80 L
Therefore, the balloon carrying methane gas will have a capacity of 4.80 L at 114 °C if the pressure remains constant at atmospheric pressure. However, the ultimate volume will vary if the pressure varies.
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if you will be a science what would you be and how it will benefit the human race?
Answer:
In other words, science is one of the most important channels of knowledge. It has a specific role, as well as a variety of functions for the benefit of our society: creating new knowledge, improving education, and increasing the quality of our lives. Science must respond to societal needs and global challenges.
Example
We can use the idea of work to help us calculate the braking distance of a car.
A car of mass 1500 kg is travelling at a speed of 20 m/s. The brakes apply a force
of 5000 N to slow down and stop the car.
Calculate the braking distance of the car.
The braking distance of the car from the question is 60 m
What is the braking distance?The braking distance is the distance traveled by a vehicle after the brakes have been applied, until it comes to a complete stop. It is the sum of the thinking distance (the distance traveled by the vehicle while the driver reacts to a hazard and decides to apply the brakes) and the braking distance (the distance traveled by the vehicle while the brakes are being applied to slow it down).
Given that;
F = ma
a = F/m
a = 5000 N/1500 Kg
a = 3.33 m/s^2
Given that;
v^2 = u^2 - 2as
Since v = 0
u^2 = 2as
s = u^2/2a
s = (20)^2/2 * 3.33
s = 60 m
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In an experiment, the diffraction pattern from a single slit was recorded with light of wavelength 700 nm on a screen held 100 cm from the slit. The distance between the first order minima on either side of the central maximum was measured to be 5.9 cm and the corresponding distance for the second order was 12.3 cm. Calculate the average width of the slit using both the first and second order data.
The average width of the slit is approximately 23,247 nm.
To calculate the average width of the slit using both the first and second-order data, we will first use the formula for single-slit diffraction:
sinθ = mλ / a
where θ is the angle of diffraction, m is the order of the minima (1 for the first order and 2 for the second order), λ is the wavelength of light (700 nm), and a is the width of the slit.
First, we need to calculate the angle of diffraction for both the first and second-order minima. Since the distance between the screen and the slit is 100 cm, we can use the small-angle approximation:
tanθ ≈ sinθ ≈ y / L
where y is the distance between the central maximum and the minima, and L is the distance from the slit to the screen.
For the first order (m = 1), y1 = 5.9 cm / 2 = 2.95 cm:
sinθ1 ≈ 2.95 cm / 100 cm = 0.0295
For the second order (m = 2), y2 = 12.3 cm / 2 = 6.15 cm:
sinθ2 ≈ 6.15 cm / 100 cm = 0.0615
Now, we can use the single-slit diffraction formula to calculate the width of the slit for both orders:
For the first order (m = 1):
a1 = 1(700 nm) / sinθ1 = 700 nm / 0.0295 = 23729 nm
For the second order (m = 2):
a2 = 2(700 nm) / sinθ2 = 1400 nm / 0.0615 = 22764 nm
Finally, we can calculate the average width of the slit using both the first and second-order data:
a_avg = (a1 + a2) / 2 = (23729 nm + 22764 nm) / 2 = 23246.5 nm
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suppose your portable dvd player draws a current of 194 ma at 9.00 v. how much power does the player require?
The portable DVD player requires 1.746 watts of power.
To calculate the power required by the portable DVD player, you can use the formula P = I x V, where P is power in watts, I is current in amperes, and V is voltage in volts.
Given that the player draws a current of 194 mA at 9.00 V, we need to convert the current to amperes by dividing it by 1000.
So, I = 194 mA / 1000 = 0.194 A
Using the formula P = I x V, we get:
P = 0.194 A x 9.00 V = 1.746 watts
Therefore, the portable DVD player requires 1.746 watts of power.
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Suppose an ideal gas undergoes isobaric (constant pressure) compression. 1) Which expression about the entropy of the environment and the gas is correct? a. ASgas > 0 b. ASeny + ASgas > 0 c. ASeny + ASgas 0 = Submit (Survey Question) 2) Briefly explain your reasoning.
The correct expression for the entropy change of the environment and the gas during an isobaric compression is:
b. ΔS_env + ΔS_gas > 0
During an isobaric compression, the gas is compressed at constant pressure. The reasoning behind this choice is as follows: In an isobaric process, the pressure remains constant throughout the compression. When an ideal gas undergoes compression, its volume decreases, and consequently, its entropy (ΔS_gas) also decreases, resulting in a negative value for ΔS_gas. However, the second law of thermodynamics states that the total entropy of a closed system, including the environment (ΔS_env), must always increase or remain constant. During the compression process, heat is transferred from the gas to the environment, which in turn increases the entropy of the environment (ΔS_env). Therefore, the sum of the entropy changes for both the gas and the environment (ΔS_env + ΔS_gas) must be greater than 0 to satisfy the second law of thermodynamics.
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carbon 14 has a half-life of 5715 years. how much carbon 14 is left after 6,451 years, given that the initial mass is q0 = 492 grams? (write the answer with 2 exact decimals).
After 6,451 years, there would be approximately 124.05 grams of carbon 14 left, the time elapsed since the start of the half-life (in this case, 736 years), T is the half-life (5,715 years), and q0 is the initial mass (492 grams.
calculated as follows:
First, we need to determine how many half-lives have passed during the 6,451 years. To do this, we divide the time elapsed by the half-life:
6,451 years / 5,715 years per half-life = 1.13 half-lives
This means that 1 half-life has fully elapsed, and we're partway through the second half-life.
To calculate how much carbon 14 is left after 1 half-life, we use the formula:
q = q0 / 2
where q is the amount of carbon 14 remaining and q0 is the initial mass. In this case, q0 = 492 grams, so after 1 half-life (5,715 years), we have:
q = 492 / 2 = 246 grams
Now we need to calculate how much further decay occurs during the remaining 1/13th of a half-life. To do this, we use the formula:
q = q0 * (1/2)^(t/T)
where t is the time elapsed since the start of the half-life (in this case, 736 years), T is the half-life (5,715 years), and q0 is the initial mass (492 grams). Plugging in these values, we get:
q = 492 * (1/2)^(736/5,715) = 124.05 grams
Therefore, after 6,451 years, approximately 124.05 grams of carbon 14 would remain, assuming an initial mass of 492 grams.
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A current loop is placed in a magnetic field as shown. If It is released from rest, what will the current loop do? TO B Select one: a. It will move upwardb. It will move downward c. It will rotate clockwise d. It will rotate counter clockwise e. None of the above
The answer is c. It will rotate clockwise. A current loop is placed in magnetic field as shown. If It is released from rest, it will rotate clockwise.
What is the magnetic field's effect on the current loop?With a magnetic field that is homogenous, there is no net force acting on a current loop. With a magnetic field that weakens to the right, a current loop with a magnetic moment pointing left is present.
What does a magnetic field generated by a circular loop of electricity look like?Every location along a circular loop carrying electricity has magnetic field lines that are concentric circles. The right-hand thumb rule may be used to determine the magnetic field direction of each segment of the circular loop.
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The answer is c. It will rotate clockwise. A current loop is placed in magnetic field as shown. If It is released from rest, it will rotate clockwise.
What is the magnetic field's effect on the current loop?With a magnetic field that is homogenous, there is no net force acting on a current loop. With a magnetic field that weakens to the right, a current loop with a magnetic moment pointing left is present.
What does a magnetic field generated by a circular loop of electricity look like?Every location along a circular loop carrying electricity has magnetic field lines that are concentric circles. The right-hand thumb rule may be used to determine the magnetic field direction of each segment of the circular loop.
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A'B'C' is the image of ABC, if the distance between ABC and the mirror is 80 cm, what is distance between the object and it's mirror (it's not 160)
Answer:
If A'B'C' is the image of ABC in the mirror, then the distance between the object (ABC) and its mirror is equal to the distance between A'B'C' and the mirror.
Let's call the distance between A'B'C' and the mirror "d". According to the problem, we know that:
d = 80 cm
However, we need to find the distance between ABC and its mirror, which we can call "x". We know that:
x + d = 2x
Simplifying this equation, we get:
d = x
Substituting the value of "d" from the first equation, we get:
x = 80 cm
Therefore, the distance between the object (ABC) and its mirror is also 80 cm, which is the same as the distance between A'B'C' and the mirror.
Explanation:
Suppose you start an antique car by exerting a force of 290 N on its crank for 0.13 s.
What angular momentum is given to the engine if the handle of the crank is 0.38 m from the pivot and the force is exerted to create maximum torque the entire time?
The angular momentum given to the engine is 44.2 Nms.
Angular momentum (L) is given by the equation L = r * F * Δt, where r is the distance from the pivot (0.38 m), F is the force exerted (290 N), and Δt is the time duration for which the force is applied (0.13 s).
To create maximum torque, the force should be applied for the entire time duration. Thus, Δt is equal to 0.13 s. Plugging in these values, we get L = 0.38 * 290 * 0.13 = 44.2 Nms as the angular momentum given to the engine.
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What things about the resistors in this circuit are the same for all three? A. Current I B. Potential difference Δ V C. Resistance R D. A and B E. B and C
The potential difference across all three resistors in a series circuit is the same, as the voltage from the battery is divided across the resistors in proportion to their resistance values. Therefore, option B (potential difference ΔV) is the same for all three resistors.
The resistance of each resistor is different, so option C is not the same for all three resistors.
The current through each resistor is the same, as there is only one path for the current to flow in a series circuit. Therefore, option A (current I) is the same for all three resistors.
So the correct answer is D, "A and B".
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a 7.000 turn coil carries has a radius of 9.800 cm and a magnetic moment of 6.500 x 10-2 am2. what is the current through the coil?
The current through the coil is 13.91mA.
What is the carrying capacity of the 18 cm diameter, 250 turn circular coil?
Current of 12a is carried through a circular coil with 250 turns and an 18 cm diameter. How Strong a Magnetic Moment Is There When the Coil Is Connected? -- Physics. Current carrying capacity is 12A in a circle with 250 turns and an 18 cm diameter.
What does a current-carrying coil of radius 10's magnetic field at its centre look like?The magnetic field at a location on the axis of a circular current-carrying coil with a 10 cm radius is 55 times greater than the magnetic field at the coil's centre.
M=I[tex]\pi r^{2}[/tex]
0.065=I3.14*9.8*9.8*7
I=13.91mA
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is it possible for an application to run slower when assigned 10 processors when assigned 8?
Yes, it is possible for an application to run slower when assigned 10 processors compared to when it is assigned 8 processors.
This is because the application may not be optimized to effectively use all 10 processors, leading to increased overhead and decreased performance. Additionally, if the system is not able to effectively manage the workload distribution across all 10 processors, it can lead to congestion and decreased performance. Therefore, it is important to consider the specific requirements of the application and the capabilities of the system before assigning a specific number of processors.
This can happen due to factors such as poor parallelization, overhead, and diminishing returns. To optimize the application's performance, it is crucial to ensure efficient use of the available processors and manage parallel tasks effectively.
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calculate the linear acceleration of a car, the 0.310-m radius tires of which have an angular acceleration of 15.5 rad/s2. assume no slippage and give your answer in m/s2.
the linear acceleration of a car, the 0.310-m radius tires of which have an angular acceleration of 15.5 rad/s2 is 4.805 m/s².
To calculate the linear acceleration of a car with 0.310-meter radius tires and an angular acceleration of 15.5 rad/s², you can use the following formula:
Linear acceleration (a) = Radius of tires (r) × Angular acceleration (α)
Step 1: Identify the given values
- Radius of tires (r) = 0.310 meters
- Angular acceleration (α) = 15.5 rad/s²
Step 2: Use the formula to calculate the linear acceleration
a = 0.310 m × 15.5 rad/s²
Step 3: Calculate the result
a = 4.805 m/s²
The linear acceleration of the car is 4.805 m/s².
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Write a general formula to describe the variation The square of T varies directly with the cube of a and inversely with the square of d: T= 3 when a = 4 and d = 2
T^2 = (Use integers or fractions for any numbers in the expression.)
The value of k, we can write the general formula:
T^2 = (9/16) * (a^3 / d^2)
To write a general formula describing the variation, we can use the given information:
The square of T varies directly with the cube of a and inversely with the square of d. We can express this relationship as:
T^2 = k * (a^3 / d^2)
Here, k is the constant of variation. Now, we'll use the given values of T, a, and d to find the value of k:
3^2 = k * (4^3 / 2^2)
9 = k * (64 / 4)
9 = k * 16
k = 9 / 16
Now that we've found the value of k, we can write the general formula:
T^2 = (9/16) * (a^3 / d^2)
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