(a) The ball will accelerate at a speed of 9.81 m/s² while it is in flight.
(b) The ball will be moving at a speed of 0 m/sec when it reaches its highest point.
(c) The ball's initial upward velocity is 20.30 m/s.
(d) It will reach a maximum height of 21.0 m.
What is speed?Speed is defined as the change in distance with regard to time. A scalar quantity, speed. It is a temporal element, m/sec is its unit.
The information provided in the issue is;
u is the fall's beginning speed in m/sec;
h is the fall's distance
g is the fall's acceleration or 9.81 m/sec²
a. The ball's speed while in flight is equal to the acceleration caused by gravity, which is 9.81 m/s².
b. When the ball reaches its highest point, its velocity will be zero.
c. The ball's starting velocity is;
v=u-gt
0=u-gt
u=gt
u=9.81 m/s² × 2.07 sec
u=20.30 m/s
d. The formula is used to determine the highest height it can reach.
[tex]\rm u^2 = - 2gh \\\\ (20.30)^2 = -2 \times (-9.8) \times h \\\\ 412.09 = 19.6 \times h\\\\ h = 412.09/19.6\\\\ h = 21.00 m[/tex]
As a result, the ball's greatest height, beginning velocity, and acceleration are all 9.81 meters per second, zero meters per second, 20.30 meters per second, and 21 meters accordingly.
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16. 1 800 cm³ of fresh water of density
1 000 kgm is mixed with
2 200 cm³ of sea water of density
1 025 kgm. Calculate the density of
the mixture.
The density of the mixture is determined as 1,013.75 kg/m³.
Density of the mixtureThe density of the mixture is calculated as follows;
density = total mass of the mixture / total volume of the mixture
mass of the fresh water = density x volume
= 1000 kg/m³ x 0.0018 m³
= 1.8 kg
mass of the sea water = 1025 kg/m³ x 0.0022 m³
= 2.255 kg
Total mass = 1.8 kg + 2.255 kg = 4.055 kg
Total volume = 0.0018 m³ + 0.0022 m³ = 0.004 m³
Density = 4.055 kg/0.004 m³ = 1,013.75 kg/m³
Thus, the density of the mixture is determined as 1,013.75 kg/m³.
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A long rope is fixed at one end, and the free end is made to oscillate in one plane at right angles to the rope with frequency 5Hz. The successive crests are 60cm apart. What is the speed of the waves? For what frequency would the wavelength be 0.4m?
Answer:
See below
Explanation:
speed = freq * wavelength
= 5 Hz * .6 m = 3 m/s
speed = freq * wavelength
3 = freq * .4 m freq = 7.5 hz
1. The speed of the waves is 3 m/s. 2. for a wavelength of 0.4 m, the frequency would be 7.5 Hz.
To find the speed of the waves, we can use the equation:
[tex]\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \][/tex]
Given that the frequency is 5 Hz and the distance between successive crests (wavelength) is 60 cm, we need to convert the wavelength to meters:
[tex]\[ \text{Wavelength} = 60 \, \text{cm} = 0.6 \, \text{m} \][/tex]
Plugging in the values, we have:
[tex]\[ \text{Speed} = 5 \, \text{Hz} \times 0.6 \, \text{m} = 3 \, \text{m/s} \][/tex]
Therefore, the speed of the waves is 3 m/s.
Now, to find the frequency at which the wavelength is 0.4 m, we rearrange the equation:
[tex]\[ \text{Frequency} = \frac{\text{Speed}}{\text{Wavelength}} \][/tex]
Substituting the given values:
[tex]\[ \text{Frequency} = \frac{3 \, \text{m/s}}{0.4 \, \text{m}} = 7.5 \, \text{Hz} \][/tex]
Thus, for a wavelength of 0.4 m, the frequency would be 7.5 Hz.
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A tennis player tosses a tennis ball straight up and then catches it after 2.07 s at the same height as the point of release.
(a) What is the acceleration of the ball while it is in flight?
magnitude
m/s2
direction
---Select---
(b) What is the velocity of the ball when it reaches its maximum height?
magnitude
m/s
direction
---Select---
(c) Find the initial velocity of the ball.
m/s upward
(d) Find the maximum height it reaches.
m
(a)The acceleration of the ball, while it is in flight, will be 9.81 m/s².
(b) The velocity of the ball when it reaches its maximum height will be 0 m/sec.
(c) The initial velocity of the ball is 20.30 m/s upward.
(d) The maximum height it reaches will be 21.00 m
What is velocity?The change of displacement with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The given data in the problem is;
u is the initial velocity of fall = ? m/sec
h is the distance of fall = ? m
g is the acceleration of free fall = 9.81 m/sec²
a.
The acceleration of the ball, while it is in flight, is equal to the acceleration due to gravity,g=9.81 m/s².
b.
The ball's velocity will be zero when it has reached its highest point.
c.
The initial velocity of the ball is;
v=u-gt
0=u-gt
u=gt
u=9.81 m/s² × 2.07 sec
u=20.30 m/s
d.
The maximum height it reaches is found by the formula as;
[tex]\rm u^2 = - 2gh \\\\ (20.30)^2 = -2 \times (-9.8) \times h \\\\ 412.09 = 19.6 \times h\\\\ h = 412.09/19.6\\\\ h = 21.00 m[/tex]
Hence the acceleration of the ball,s the velocity of the ball when it reaches its maximum height, the initial velocity of the ball, and the maximum height it reaches will be 9.81 m/s²,0 m/sec,20.30 m/s, and 21.00 m respectively.
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The cost of gas is $1.27 per liter. How much does a gallon of gas costs?
The cost of gas is $1.27 per liter and the gallon of gas costs $4.80. where 1 gallon is equal to 3.78541 liters.
To convert the cost of gas from dollars per liter to dollars per gallon, The conversion factor between liters and gallons.
1 gallon is equal to 3.78541 liters (the exact conversion factor is 3.785411784).
Given the cost of gas is $1.27 per liter, let's calculate the cost per gallon:
Cost per gallon = Cost per liter × Liters per gallon
Cost per gallon = $1.27 × 3.78541
Cost per gallon = $4.80
So, a gallon of gas costs $4.80.
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which of these are lost when the body repairs?
oxygen and calcium
calcium and sodium
sodium and potassium
potassium and oxygen
c. Sodium and potassium
What is called perspiration?Perspiration, water given off by the intact skin, either as vapor by simple evaporation from the epidermis or as sweat, a form of cooling in which liquid actively secreted from sweat glands evaporates from the body surface.
When our body is sweating sodium and potassium is lost from the body along with water.
In order to maintain the integrity of the cells in the body ,Sodium and potassium are very important.
Sweat is also known as perspiration.
So,
By maintaining the proper cell functioning and cell vitality optimum level of sodium and potassium should be maintained in the body.
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Many television sets show 25 images, called 'frames, each second. What is the time interval between one
frame and the next?
Answer:
Given,
Frame rate = 25 frames per second
To find,
Time interval between one frame and the next.
Solution,
We can simply solve this numerical problem by using the following process.
Now,
Number of frames = 25
Total time taken to display the given number of frames (ie. 25 frames) = 1 second
To calculate the time interval between one frame and next, we need to divide the time taken to display total number of frames by total number of frames.
So,
Time interval between one frame and next :
= Time taken to display total number of frames / Total frames
= 1/25
= 0.04 second
Hence, time interval between one frame and next is 0.04 second.
two object of masses 80kg and 50kg are separated by a distance 0.2m. If the gravitational constant is 6.6 × 10^-11 Nm^2 kg^-2, calculate the gravitational attraction between them.
The gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.
What is Newton's law of gravitation?Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.
Given data
Mass of object 1,m = 80 kg
Mass of object 2,M = 50 kg
Gravitational constant,G = 6.6 × 10⁻¹¹ kg⁻² m²
Distance of seperation,R = 0.2 m
The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.
[tex]\rm F = G\frac{mM}{R^ 2} \\\\ F = 6.6 \times 10^{-11 }\times \frac{80 \times 50 }{(0.2)^2} \\\\F = 6.6 \times 10^{-6 } \ N[/tex]
Hence the gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.
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Abdou was explaining to a classmate that graphite is a good lubricant
because it is bonded in layers that easily slip over each other. Which image
shows this quality?
The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other.
Why is graphite a solid lubricant?We know that graphite is composed of layers. These hexagonal layers are held together by weak Van Der Walls forces and as such are able to slide over each other. The carbon atom in each layer are held together by strong covalent bonds.
The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other and as such make the graphite fluid.
Thus, the image that shows these layers of graphite is attached to this an answer
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Answer:it’s B
Explanation:
Example No. 10
In a worst-case design scenario, a 2000 kg elevator with broken cables is
falling at 8.0 m/s when it first contact a cushioning spring at the bottom
of the shaft. The spring is supposed to stop the elevator, compressing 3.0
m as it does so. Determine what the force constant of the spring should
be.
The force constant of the spring is determined as 14,222.2 N/m.
Force constant of the springApply the principle of conservation of energy,
K.E = U
where;
K.E kinetic energy of the elevatorU is elastic potential energy of the spring¹/₂mv² = ¹/₂kx²
mv² = kx²
k = mv²/x²
Where;
m is mass of the elevatorv is speedx is compression of the springk = (2000 x 8²)/(3²)
k = 14,222.2 N/m
Thus, the force constant of the spring is determined as 14,222.2 N/m.
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21. An AC generator has an rms output voltage of 274 V at a frequency of 57.0 Hz.
The generator is connected across a 0.900-H inductor.
(a) Determine the inductive reactance.
(b) Determine the maximum voltage across the inductor.
(c) Determine the rms and maximum currents in the inductor
The answers are as follows;
a) the inductive reactance is 322 ohm
b) The maximum voltage is 387.5 V
c) The rms and maximum currents in the inductor are 1.2 A and 0.85 A.
What is the reactance?The reactance is obtained from;
XL = 2πfL
XL = 2 * 3.14 * 57.0 * 0.900
XL = 322 ohm
The maximum voltage is obtained as;
Vo = Vrms * √2
Vo = 274 V * √2
Vo = 387.5 V
Io = Vo/XL
Io = 387.5 V/ 322 ohm
Io = 1.2 A
Irms = 274 V/322 ohm
Irms = 0.85 A
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A ball starts rolling down a ramp. What is the value of the change in its kinetic energy, ΔEk?
Positive
Zero
Negative
For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive
Meaning of Kinetic energyKinetic energy can be defined as the ability assumed by an object in motion.
Kinetic energy is also said to be a form of mechanical energy that is possessed by an object to be in motion.
In conclusion, For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive
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which of the following examples is not considered a pure substance?
Answer asap
Answer:
Fruit Punch
Explanation:
A pure substance is whereby there is only one type of element or a compound in the periodic table in the substance.
Carbon: Well its just C in the periodic table, so this is definitely pure.
Water Molecule: What makes water? H2O right? Contains Hydrogen and Oxygen, and as we all know H2O is a compound, therefore this is a pure substance.
Fruit Punch: What makes fruit punch, water and fruits. Fruits may contain citric acid(a compound itself), and is mixed with water with already has a compound, so having 2 different compounds will result in a mixture and therefore it will not be pure.
A car moves with an average speed of 75 kmh^-1 from town P to town Q in 2 hours. By using information, you may calculate the distance between two towns. convert the value 75kmh ^-1 to S.I unit
The distance car moves with an average speed of 75 km/hr from town P to town Q in 2 hours is 149,760 m.
Given:
Speed = 75 km/hr
Time = 2 hr
The distance can be calculated from the product of velocity and time.
The standard unit of distance is a meter.
Convert speed and time into meters per second and seconds:
v = 75×5/18
v = 20.8 m/s
t = 3600×2
t = 7200 s
The distance is computed as:
v = d/t
d = vt
d = 20.8×7200
d = 149,760 m
Hence, the distance car moves with an average speed of 75 km/hr from town P to town Q in 2 hours is 149,760 m.
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M, a solid cylinder (M=2.15 kg, R=0.111 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.730 kg mass, i.e., F = 7.161 N.
1. Calculate the angular acceleration of the cylinder.
2. If instead of the force F an actual mass m = 0.730 kg is hung from the string, find the angular acceleration of the cylinder.
3. How far does m travel downward between 0.390 s and 0.590 s after the motion begins?
4. The cylinder is changed to one with the same mass and radius, but a different moment of inertia. Starting from rest, the mass now moves a distance 0.450 m in a time of 0.490 s. Find I[tex]_{cm}[/tex] of the new cylinder.
Hi there!
1.
Let's use the rotational equivalent of Newton's Second Law.
[tex]\Sigma \tau = I\alpha[/tex]
τ = Torque (Nm)
I = Moment of Inertia (1/2mR² for solid cylinder)
α = Angular acceleration (rad/sec²)
The torque is equivalent to:
[tex]\tau = r \times F[/tex]
r = distance from lever arm to pivot point, aka the radius for this cylinder (0.111 m)
F = applied force (7.161 N)
We are already given various values, so let's create a working equation and solve.
[tex]rF = I\alpha \\\\\alpha = \frac{rF}{I}[/tex]
[tex]\alpha = \frac{(0.111)(7.161)}{\frac{1}{2}(2.15)(0.111^2)} = \boxed{60.013 \frac{rad}{sec^2}}[/tex]
2.
So, let's begin by doing a summation of forces acting on the block.
We have its force of gravity downward(+), and the tension from the string upward. (-), assigning signs based on the path of the falling block.
[tex]\Sigma F = F_g - T\\\\\Sigma F = m_b g - T\\\\m_b a = m_b g - T[/tex]
Solving for 'T':
[tex]T = m_b g - m_b a[/tex]
Let's now do a summation of torques on the cylinder. We only have the torque caused by the tension in the string connected to the block.
[tex]\Sigma \tau = rT\\\\I\alpha = r(T = m_b g - m_b a)[/tex]
Using the relationship between angular and translational acceleration:
[tex]a = \alpha r\\\\alpha = \frac{a}{r}[/tex]
And the equation for the moment of inertia:
[tex]I = \frac{1}{2}Mr^2[/tex]
Simplify the expression.
[tex]\frac{1}{2}Mr^2(\frac{a}{r}) = r( m_b g - m_b a)\\\\\frac{1}{2}Ma = ( m_b g - m_b a)[/tex]
Solve for 'a':
[tex]\frac{1}{2}ma + m_b a= m_b g \\\\a = \frac{m_b g}{\frac{1}{2}M + m_b} = \frac{0.730(9.81)}{\frac{1}{2}(2.15) + 0.730} = \boxed{3.97 \frac{m}{s^2}}[/tex]
3.
This is just a case of kinematics since we have a constant acceleration. To solve for this instance, however, let's use calculus.
We know that:
[tex]a(t) = 3.97[/tex]
v(t) is the integral. There is no initial velocity (block starts from rest), so:
[tex]v(t) = 3.97t + C\\C = 0 m/s \\\\v(t) = 3.97t[/tex]
Now, we can take the integral of the velocity/time equation to find the displacement between the interval.
[tex]\int\limits^{0.590}_{0.390} {3.97t} \, dt = \boxed{0.389 m}[/tex]
4.
So, let's now find the translational acceleration produced by the new cylinder. Use the kinematic equation:
[tex]\Delta x = v_0 t + \frac{1}{2}at^2[/tex]
Since the block starts from rest, we can do some simplifying and rearranging:
[tex]2\Delta x = at^2\\\\a = \frac{2\Delta x}{t^2} = \frac{2(0.450)}{0.490^2} = 3.748 \frac{m}{s}^2[/tex]
So, let's go back to our summation of torques equation. This time, however, we cannot simplify 'I'.
[tex]I(\frac{a}{r}) = r( m_b g - m_b a)[/tex]
Solving for 'I':
[tex]I = \frac{r^2( m_b g - m_b a)}{a} = \frac{(0.111^2)(7.161 - .730(3.748))}{3.748}\\\\ = \boxed{0.0145 kgm^2}[/tex]
A wooden baseball bat and an aluminum baseball bat have the exact same size, shape, and mass. Aluminum is much denser than wood. Explain how the two bats could be the same size, shape, and mass.
Due to density, the two bats have the same size, shape, and mass.
How the two bats could be the same size, shape, and mass?The two bats could be the same size, shape, and mass if they have the same density because density is directly proportional to mass so if the density same, the mass will also be the same.
So we can conclude that due to density, the two bats have the same size, shape, and mass.
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A roller coaster's velocity at the bottom of a hill is 35.0 m/s, 5.00 seconds later it reaches the top of the hill with a velocity of 10.0
m/s. What was the deceleration of the coaster?
O 5.00 m/s/s
O 7.00 m/s/s
O 2.00 m/s/s
O 25.0 m/s/s
Answer:
5 m /s^2
Explanation:
Change in velocity = 35 - 10 = 25 m/s
change in time = 5 s
decelleration = 25/5 = 5 m/s^2
A 0.145 kg ball moving in the +x direction at 14 m/s is hit by a bat. The ball's final velocity is 20.0 m/s in the -x direction. The bat acts on the ball for a duration of 0.010 s.
Find the average force exerted on the ball by the bat. Include the sign of the force to indicate the direction of the force.
Answer:
Approximately [tex](-4.9\times 10^{2}\; {\rm N})[/tex] (rounded to two significant figures.)
Explanation:
The impulse [tex]\mathbf{J}[/tex] on an object is equal to the change in the momentum [tex]\mathbf{p}[/tex] of this object. Dividing impulse by duration [tex]\Delta t[/tex] of the contact would give the average external force that was exerted on this object.
If an object of mass [tex]m[/tex] is moving at a velocity of [tex]\mathbf{v}[/tex], the momentum of that object would be [tex]\mathbf{p} = m\, \mathbf{v}[/tex].
Let [tex]m[/tex] denote the speed of this ball. Let [tex]\mathbf{v}_{0}[/tex] denote the velocity of this ball before the contact, and let [tex]\mathbf{v}_{1}[/tex] denote the velocity of the ball after the contact.
Momentum [tex]\mathbf{p}_{0}[/tex] of this ball before the contact: [tex]\mathbf{p}_{0} = m\, \mathbf{v}_{0}[/tex].
Momentum [tex]\mathbf{p}_{1}[/tex] of this ball after the contact: [tex]\mathbf{p}_{1} = m\, \mathbf{v}_{1}[/tex].
Impulse, which is equal to the change in momentum:
[tex]\mathbf{J} = \mathbf{p}_{1} - \mathbf{p}_{0} = m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}[/tex].
Since the velocity of the ball after the contact is in the [tex](-x)[/tex] direction, [tex]\mathbf{v}_{1} = -20.0\; {\rm m\cdot s^{-1}}[/tex]. The average external force on this ball would be:
[tex]\begin{aligned} \mathbf{F} &= \frac{\mathbf{J}}{\Delta t} \\ &= \frac{m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}}{\Delta t} \\ &= \frac{m\, (\mathbf{v}_{1} - \mathbf{v}_{0})}{\Delta t} \\ &= \frac{0.145\; {\rm kg} \times ((-20.0\; {\rm m\cdot s^{-1}}) - 14\; {\rm m\cdot s^{-1}})}{0.010\; {\rm s}} \\ &\approx -4.9 \times 10^{2}\; {\rm N}\end{aligned}[/tex].
(Rounded to two significant figures.)
A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.70 s later. Find the depth of the well if the air temperature is 11.0°C.
The depth of the well at the given air temperature is 456.3 m.
Depth of the wellThe depth of the well is calculated from the principle of echo.
v = 2d/t
2d = vt
d = vt/2
where;
v is speed of sound in air at 11.0°C = 338 m/sd = (338 x 2.7)/2
d = 456.3 m
Thus, the depth of the well at the given air temperature is 456.3 m.
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Find the kenetic energy of a car of mass 700kg racing with a velocity of 10m/s
Answer:
35000 KJ
Explanation:
The equation for the kinetic energy is given by the formula :
[tex]E_{k} = \frac{1}{2} mv^{2}[/tex]
[tex]E_{k} = \frac{1}{2} (700)(10)^{2}[/tex]
[tex]E_{k} = \frac{1}{2} (700)(100)[/tex]
[tex]E_{k} = (350)(100)[/tex] OR [tex]E_{k} = \frac{1}{2} (70000)[/tex]
[tex]E_{k} = 35000[/tex]
Units will be kilojoules since the units of mass was kilograms .
Our final answer is 35000 KJ
Hope this helped and have a good day
In 450 BCE, Greek philosopher Democritus first thought of the existence of tiny particles that compose everything around us. He named them 'atomos', meaning _________.
A. None of these
B. Indivisible
C. Invisible
D. Particle
B. The meaning of 'atomos' according to Democritus in 450 BCE is indivisible.
The building block of every matter
A Greek philosopher known as Democritus first thought of the existence of tiny particles that compose everything around us.
Democritus of Abdera, named the building blocks of matter atomos, meaning literally “indivisible.
Thus, the meaning of 'atomos' according to Democritus in 450 BCE is indivisible.
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An AC voltage source is connected to a resistor R = 1.90 102 Ω. The output from an AC voltage source is given by the expression V = (2.20 102 V) sin 2ft. (a) What is the rms voltage across the resistor? V (b) What is the rms current flowing through the resistor? A
Answer:
(a) The rms voltage across the resistor is given by V = (2.20 102 V) sin 2ft.
V = (2.20 102 V) sin 2ft
V = (2.20 102 V) (0.707)
V = 1.56 102 V
(b) The rms current flowing through the resistor is given by I = V/R.
I = V/R
I = (1.56 102 V)/(1.90 102 Ω)
I = 8.21 A
Review procedures and confirm results to avoid possible errors.
Explanation:
A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k1 and k2 whose opposite ends are fixed to walls. What is angular frequency of the oscillation if k1= 9.5 N/m and k2= 5 N/m?
The angular frequency of the oscillation is determined as 2.7 rad/s.
Angular frequency of the block
ω = √k/m
With respect to spring constant k1 and k2
k1 + k2 = 9.5 N/m + 5 N/m = 14.5 N/m
ω = √14.5/2 = 2.7 rad/s
Thus, the angular frequency of the oscillation is determined as 2.7 rad/s.
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1. Is it reasonable to expect that anyone would be able to make good sense of a filing system such as this new one? Why or why not?
It reasonable to expect that anyone would be able to make good sense of a filing system as it reduces the overall storage space occupied by the records.
What is Filing?This is the process of keeping document safely and being able to easily retrieve them.
The new filing system is based on their volume which is why the space is reduced thereby reducing the ambiguity.
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What is your design for an efficient commercial vehicle chassis that incorporates as many commercial truck components into its structure as realistically possible?
The design that would be used to make an efficient commercial vehicle chassis that has many realistic truck components is:
StrengthAdequate bending stiffnessMaximum stressDeflection, etcWhat is a Chassis Frame?This refers to the main vehicle structure of a car that bears all the main stress that other components are attached to.
Hence, we can see that to make a good design for an efficient commercial vehicle chassis that has many realistic truck components, we would have to consider various factors such as handling maximum stress, maximum equilateral stress, and deflection.
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The temperature of the filament is 2500 K when the bulb is switched on. The diameter of the filament is 0.1 mm and it is made of metal of emissivity 0.35. If the emissive power is 40 W find the length of the filament.
The length of the filament is 0.2 m.
To find the answer, we need to know about the Stefan - Boltzmann law.
What's Stefan - Boltzmann law?It states that the intensity of power radiated from a body is propertional to the fourth power of temperature of the object.Mathematically, I= e×σ×T⁴I= intensity, e= emissivity, σ= a constant with value 5.67×10^(-8) W/(m²K⁴), T= temperatureAs intensity= power/area, so power= area ×e×σ×T⁴What's the length of the filament having diameter 0.1 mm, temperature 2500K, emissivity 0.35 and radiating power of 40W?Here, e= 0.35, T= 2500K, power= 40WIf L= length of the filament, its area = (2πd/2)L= πdLSo, power= π×d×L ×e×σ×T⁴L= power/(π×d×e×σ×T⁴)
= 40/(π×0.0001×0.35×5.67×10^(-8)×2500⁴)
= 0.2m
Thus, we can conclude that the length of the filament is 0.2 m.
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A Skier starting from rest rolls down a 35.0 m ramp. When he arrives at the bottom of the ramp his
speed is 10.43 m/s. (a) Determine the magnitude of his acceleration, assumed to be constant, (b) If the
ramp is inclined at 60.0 degrees with respect to the ground, what is the component of his acceleration
that is parallel to the ground. (c) Provide me with a free body diagram, one for the 35 m ramp situation.
Also, provide a nice sketch of the skier.
The acceleration is 1.55 m/s^2 while is component that is parallel to the ground is 0.775 m/s^2.
What is acceleration?The term acceleration is the rate of change of speed. Given that the distance covered is 35.0 m and the final velocity is 10.43 m/s it the follows that;
v^2 = u^2 + 2as
u = 0 because he started from rest
v^2 = 2as
a = v^2/2s
a = (10.43 m/s)^2/2 * 35.0 m
a = 1.55 m/s^2
The component of this acceleration which is parallel to the ground is;
ax = a sin θ
ax = 1.55 m/s^2 cos 60
ax = 0.775 m/s^2
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Two point charges q1 and q2 are located at (2.0, 0.0) cm and (8.0, 0.0) cm,
respectively. A positive point charge q3 is placed somewhere so that the net
electrostatic force acting on it due to q1 and q2 is zero. Find the position of q3 if
q1 = 2.0 μC and q2 = -8.0 μC. Sketch a figure that shows the position of all
three point charges and the forces acting on q3.
The Sketch of the figure will bear the parameters of the charge that lies at (4,0,0)
What is co-ordinate of the charge?Generally, the equation for is mathematically given as
1)
Since both of the other points, "q1"<"q2," are on the x-axis, the third one must also be on the x-axis, and it must be close to the charge of lesser magnitude. off q1 by x cm
Now, forces on q3 due to q1
[tex]\vec{F}_{1}=\frac{k q_{1} q_{3}}{x^{2}} \hat{x}[/tex]
Force on q3 due to q2
[tex]\vec{F}_{2}=\frac{k q_{2} q_{3}}{(6+x)^{2}}(-\hat{x})[/tex]
[tex]\quad \vec{F}_{1}+\vec{G}_{2}=0$[/tex]
[tex]&\frac{k q_{1} q_{3}}{x^{2}}-\frac{k q_{2} q_{3}}{(x+6)^{2}}=0 \\&\frac{2}{x^{2}}=\frac{8}{(x+6)^{2}} \Rightarrow \frac{x+6}{x}=\sqrt{\frac{8}{2}}=2 \\&x+6=2 x \Rightarrow x=6 \mathrm{~cm}[/tex]
In conclusion, the charge lies at (4,0,0)
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6.A truck is carrying a steel beam of length 13.0 m on a freeway. An accident causes the beam to be dumped off the truck and slide horizontally along the ground at a speed of 30.0 m/s. The velocity of the center of mass of the beam is northward while the length of the beam maintains an east–west orientation. The vertical component of the Earth's magnetic field at this location has a magnitude of 30.0 T. What is the magnitude of the induced emf between the ends of the beam?
The magnitude is 13.12 mV.
The steps are attached below.
How do you find the magnitude of an induced emf?The standard SI unit of the magnetic field is the tesla (T). As an end result, we can use these equations and the equation for an induced emf due to changes in magnetic flux, ϵ=−NΔϕΔt ϵ = − N Δ ϕ Δ t, to calculate the importance of a precipitated emf in a solenoid.
The magnitude of the precipitated contemporary depends on the rate of trade of magnetic flux or the fee of reducing the magnetic area strains.
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I need help with my homework
Answer:
A. the center of mass
Explanation:
[tex]C_m[/tex] is usually used to designate the center of mass of an object or system of objects.
B. is incorrect because the combined mass of a system is usually denoted by ∑m.
C. is incorrect because the momentum of a system is denoted by the letter p.
Two people are dragging a canoe on a beach using light ropes. Person 1 applies a
force of 60.0N [Forward] and person 2 applies a force of 90.0N [Forward]. The
friction exerted by the beach on the canoe is 85.0N. Determine the net force of the
canoe.
a) 50.0 N [forward]
Ob) 6.50 N [backward]
c) 6.50 N [forward]
d) 65.0 N [forward]
The net force on the canoe is obtained as 65.0 N [forward]
What is the frictional force?The frictional force is the force that opposes motion. We know that the net force is the actual force that moves the canoe in a given direction.
Hence, the total force acting in the forward direction = 60.0N + 90.0N = 150 N and the total backwards force = 85.0N
Net force = 150 N - 85.0N = 65.0 N [forward]
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