a mass-less spring of length 31 cm is laid out on a table, with the left side firmly attached to a support, and a mass of 1 kg attached to the right end. the value of the spring constant is 164 n/m. the mass is pulled by a distance 6 cm to the right, and released. the table is friction-less, and the spring-mass executes simple harmonic motion. how many complete vibrations will the mass undergo in a time 60 s. round your answer to the nearest whole number
Answers
The number of vibrations are 122
as per the question given,
the length of the mass less string (l) is 31cm
a mass attached to the right end of spring (m) is 1kg
the value of the spring constant is (k) is 164 n/m
the mass is pulled by a distance (d) is 3cm
time (t) is 60s
the time period of the mass-less spring system is
\(T=2\pi \sqrt{\frac{m}{k} }\) ----(1)
where
the value of (m) is 1kg
the value of spring constant (k) is 164 n/m
let the value of \(\pi\) is 3.14
now substitute the values in the time period equation
\(T=2\pi \sqrt{\frac{1}{164} }\)
=> \(T= 2\times (3.14) \sqrt{\frac{1}{164} }\)
=> T = \(2\times (3.14) \times 0.07803\)
=> T =0.49002
the time period T is 0.49002,
therefore the number of oscillations in 60s is
n = time/Time period
\(n=\frac{60}{T}\)
=>n = \(\frac{60}{0.49002}\)
=> n= 122.43
=> n = 122
the number of vibrations are 122
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Related Questions
The basic principle behind the simple DC motor is that wires that carry experience when placed in regions of space that have
Answers
The principle of DC motor is based on Fleming’s left hand rule. i.e., the current carrying wires experiences a force when placed in region of space that have magnetic field.
According to Fleming’s left hand rule Stretch the thumb, forefinger, and middle finger of the left hand until they are parallel to one another. If the thumb is pointing in the direction of motion, or the force acting on the conductor, and the middle finger is pointing in the direction of the magnetic field, the forefinger is pointing in the direction of current flow.
An armature revolves inside a magnetic field of a DC motor. A DC motor's fundamental operating concept is based on the idea that whenever a current-carrying conductor is positioned inside a magnetic field, that conductor will experience mechanical force.
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You walk to school every day. It is 0.5 miles. After school you walk to Kroger, which is 1.3 miles. You leave Kroger to go all back home, which is 0.8 miles. What is the total distance you have walker today?
Answers
A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later at the bottom of the slope, its speed is 22 m/s. what is the average acceleration?
Answers
\(a_avg = (22 m/s - 4 m/s) / 3 s = 18 m/s / 3 s = 6 m/s^2,\) Therefore, the average acceleration of the roller coaster car is \(6 m/s^2\).
Which of Newton's principles of motion is best illustrated by how friction causes a rolling ball to slow down and come to a stop?Newton's first law states that each change in velocity (a change in either magnitude or direction) must have a cause. The law of inertia is another name for this rule. An external force called friction slows down an object.
a_avg = (v_f - v_i) / t
So, the average acceleration is:
a_avg = (22 m/s - 4 m/s) / 3 s
= 18 m/s / 3 s
\(= 6 m/s^2\)
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if released from the inner wall, what would be the kinetic energy of a negative 9fc charge at the outer wall? 1fc
Answers
The kinetic energy would be \(3*10^{-17} J.\)An object's kinetic energy is the energy it has as a result of its motion. It is defined as the amount of work required to accelerate a body of a given mass from rest to a given velocity. The body retains its kinetic energy after gaining it during acceleration unless its speed changes.
An object's kinetic energy is the energy it has as a result of its motion. It is defined as the amount of work required to accelerate a body of a given mass from rest to a given velocity. The body retains its kinetic energy after gaining it during acceleration unless its speed changes.
When it moves from inner wall to outer wall:-
K.E= qΔqΔv (where, delta v is the potential difference between plates= \(1*10^{-2} V.\)
K.E. gained by charge, \(q= 3*10^{-15} C.\)
Therefore, kinetic energy= \(3*10^{-15} * 1*10^{-2} = 3*10^{-17} J.\)
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power is function of time . give reason
Answers
Reason: The quantity work has to do with a force causing a displacement. Work has nothing to do with the amount of time that this force acts to cause the displacement. Sometimes, the work is done very quickly and other times the work is done rather slowly. For example, a rock climber takes an abnormally long time to elevate her body up a few meters along the side of a cliff. On the other hand, a trail hiker (who selects the easier path up the mountain) might elevate her body a few meters in a short amount of time. The two people might do the same amount of work, yet the hiker does the work in considerably less time than the rock climber. The quantity that has to do with the rate at which a certain amount of work is done is known as the power. The hiker has a greater power rating than the rock climber.
Power is the rate at which work is done. It is the work/time ratio. Mathematically, it is computed using the following equation.
Power = Work / time
or
P = W / t
A 2. 9 kg model rocket accelerates at 15. 3 m/s2 with a force of 44 N. Before launch, the model rocket was not moving. After the solid rocket engine ignited, hot gases were pushed out from the rocket engine nozzle and propelled the rocket toward the sky. Which of Newton’s laws apply in this example? Select three options. The first law the second law the third law the fourth law the fifth law.
Answers
Answer:
The first law: the law of Inertia.
Explanation:
Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.
Answer:
1st, 2nd, & 3rd law
Explanation:
there is no 5th/4th law ppl
I did this question and it says SELECT 3 OPTIONS not 1 (This answer isn’t meant to be rude but just stating what the question says.)
How do you determine the height of a wave?
Answers
Answer:
Wave height is the vertical distance between the crest (peak) and the trough of a wave. Some other definitions: Still-Water Line is the level of the lake surface if it were perfectly calm and flat. Crest is the highest point on the wave above the still-water line.
Explanation:
Write S if the given quantity is scalar and V if the quantity is a vector
_100° Celsius
_50 m/s²
_300 s
_250 m/s, northwest
_1m, to the right
_10 cm,upwards
_525 600 mins.
_90 km/h,east
_5 000 kg
_1.5 L
Answers
Answer:
1. Scalar_100° Celsius
2. Vector_50 m/s²
3. Scalar_300 s
4. Vector_250 m/s, northwest
5. Vector_1m, to the right
6. Vector_10 cm, upwards
7. Scalar_525 600 mins.
8. Vector_90 km/h,east
8. Scalar_5 000 kg
10. Scalar_1.5 L
Explanation:
A scalar quantity can be defined as a quantity that has magnitude but no direction. Some examples of scalar quantities are speed, mass, temperature, volume, length, etc.
On the other hand, a vector quantity has both magnitude and direction. Some examples of vector quantities are acceleration, velocity, displacement, etc.
1. Scalar_100° Celsius (Temperature).
2. Vector_50 m/s² (Acceleration).
3. Scalar_300 s (Time).
4. Vector_250 m/s, northwest (Velocity).
5. Vector_1m, to the right (Displacement).
6. Vector_10 cm, upwards (Displacement).
7. Scalar_525 600 mins. (Time).
8. Vector_90 km/h,east (Velocity).
8. Scalar_5 000 kg (Mass).
10. Scalar_1.5 L (Volume).
what are forces that two objects apply on each other
Answers
HOPE IT HELPED:) HAVE A NICE DAY
The Voyager 1 space probe was launched by NASA in 1977. It's now the most distant spacecraft from Earth, as it hurtles into space at over 60,000 km/h. It has run out of fuel, so it can't change its own motion.
One of your friends says, "If Voyager 1 doesn't collide with anything and is too far from anything to be affected by gravity, it will gradually slow down and stop."
I have to either agree or disagree with my friend, then i have to explain.
Answers
The statement, "The Voyager 1 space probe can't change its own motion" is correct and true. The Voyager 1 space probe was launched by NASA in 1977, and since then it has traveled over 14 billion miles away from Earth. It's the most distant spacecraft from Earth.
The Voyager 1 was designed to study the outer solar system and it sent valuable data back to Earth. But, now it has run out of fuel and cannot change its own motion as the thrusters that are responsible for keeping the spacecraft’s antenna pointed toward Earth have to be continuously fired to compensate for the small natural imbalances in its motion. Therefore, the statement is correct that Voyager 1 cannot change its own motion. It is still continuing its journey into space at a speed of over 60,000 km/h and is expected to keep traveling until it reaches other stars and the next galaxy beyond our Milky Way. So, I agree with the statement that the Voyager 1 space probe can't change its own motion.For such more question on motion
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2. Use delta to wye resistance. transformation to find the total Also, determine the total current. 100 V (+ 2002 N 40 M 1965 120V I₁ 50 3.0 100 92 M- W Io 302 10 N 270 3.Reduce the circuit to a single loop network using source transformation then find lo. N62 $452 N 82 182 4022 3A
Answers
The total resistance in the circuit is 144Ω, and the total current is approximately 0.694A.
To find the total resistance and total current in the given circuit, let's break down the steps:
1. Delta to Wye Transformation:
- Identify the resistors in the delta configuration: 200Ω, 40Ω, and 120Ω.
- Apply the delta to wye transformation to convert the resistors into a wye configuration:
- R₁ = (Rb * Rc) / (Ra + Rb + Rc) = (40 * 120) / (200 + 40 + 120) = 16Ω
- R₂ = (Ra * Rc) / (Ra + Rb + Rc) = (200 * 120) / (200 + 40 + 120) = 96Ω
- R₃ = (Ra * Rb) / (Ra + Rb + Rc) = (200 * 40) / (200 + 40 + 120) = 32Ω
- Replace the delta configuration with the wye configuration using the calculated values: R₁ = 16Ω, R₂ = 96Ω, R₃ = 32Ω.
2. Total Resistance Calculation:
- The total resistance (RT) in the circuit is the sum of the individual resistances:
- RT = R₁ + R₂ + R₃ = 16Ω + 96Ω + 32Ω = 144Ω.
3. Total Current Calculation:
- The total current (I) can be calculated using Ohm's Law: I = V / RT, where V is the voltage across the circuit.
- Given that the voltage (V) is 100V, the total current (I) is: I = 100V / 144Ω = 0.694A.
Therefore, the total resistance in the circuit is 144Ω, and the total current is approximately 0.694A.
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Near the critical point of a pure fluid, the Gibbs energy obeys the scaling function λG(t,p)=G(λ a
⋅t,λ a
p) where the reduced temperature, pressure, and volume displacements are t= T c
T c
−T
p= P c
P c
−P
v= V
ˉ
c
V
ˉ
− V
ˉ
c
(a) Differentiation of G with respect to pressure gives the volume displacement, v=( ∂p
∂G
) Use Eqs.(1) and (3) to derive the scaling law for v(t,p) in terms of a t
and a p
. (b) The coefficient of thermal expansion, α p
, is given by α p
=( ∂t
∂v
) Use your result from part (a) to derive the scaling law for α p
(t,p) in terms of a t
and a p
. (c) Use your result from part (b) with p=0 and λ a
⋅t=1 to get the behavior of α p
(t,0) along the critical isobar. (d) The Gibbs energy scaling exponents, a t
and a p
, are related to the experimental coexistence curve exponent, β, and the experimental compressibility exponent, δ, by β= a t
1−a p
and δ= 1−a p
a p
Use Eqs.(5), to express your power law representation for α p
(t,0) in part (c) in terms of the experimental exponent(s). Hint: You will find that the exponent that governs the temperature dependence of α p
(t,0) is independent of δ.
Answers
The scaling law for volume displacement, v(t, p), in terms of scaling exponents aₜ and aₚ is given by v(t, p) = aᵥ / (∂G/∂(λₐ⋅t)).
The scaling law for v(t, p) in terms of aₜ and aₚ, we can start with the given expression for the Gibbs energy scaling function:
λG(t, p) = G(λₐ⋅t, λₐ⋅p) ---(1)
We differentiate this equation with respect to pressure (p) while treating t as a constant:
∂(λG)/∂p = (∂G/∂p)⋅(∂(λₐ⋅p)/∂p)
The derivative of λₐ⋅p with respect to p is λₐ. Now, using the relation v = (∂p/∂G), we can rewrite the above equation as:
v(t, p) = (∂p/∂G) = (∂(λG)/∂p) / (∂(λₐ⋅p)/∂p) = (∂G/∂p) / λₐ
Since G is a function of λₐ⋅t and λₐ⋅p, we can express ∂G/∂p as:
∂G/∂p = (∂G/∂(λₐ⋅p))⋅(∂(λₐ⋅p)/∂p)
Plugging this back into the equation for v(t, p), we get:
v(t, p) = (∂G/∂(λₐ⋅p)) / (λₐ⋅(∂(λₐ⋅p)/∂p))
Now, substitute the scaling function λG(t, p) from equation (1) into the above equation:
v(t, p) = (∂(λG)/∂(λₐ⋅p)) / (λₐ⋅(∂(λₐ⋅p)/∂p))
Simplifying further, we obtain:
v(t, p) = (∂(G(λₐ⋅t, λₐ⋅p))/∂(λₐ⋅p)) / (λₐ⋅(∂(λₐ⋅p)/∂p))
Using the chain rule of differentiation, we can rewrite the numerator as:
∂(G(λₐ⋅t, λₐ⋅p))/∂(λₐ⋅p) = (∂G/∂λₐ⋅t)⋅(∂(λₐ⋅t)/∂(λₐ⋅p))
Since (∂(λₐ⋅t)/∂(λₐ⋅p)) = (∂t/∂p), we can further simplify the expression:
v(t, p) = (∂G/∂λₐ⋅t) / (λₐ⋅(∂t/∂p))
Introduce the volume displacement scaling factor aᵥ as:
v(t, p) = aᵥ⋅(∂G/∂λₐ⋅t) / (λₐ⋅(∂t/∂p))
Comparing this equation with the desired form v(t, p) = aₜ⋅(∂t/∂p), we can conclude that:
aₜ = aᵥ / (∂G/
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a 1.8-kg mass attached to a spring oscillates with an amplitude of 9.3 cm and a frequency of 2.8 hz.
Answers
The frequency is 5.9 jules.
we have been given that the mass is equal to 2.4 kgs and the amplitude others 9.3 and returned to the power -2 m. Yeah. So he can write The angular frequency is two pi f. That is To buy into 3.8 Hz. That is equal to 23.87. Ready for a 2nd. Now to find the first concert,
we can write Omega Square. Um that is 23.87 reading perspective, but you didn't one second. We square this into 2.4 gauges. That is equal to 1,36, newtons per meter. How to find the total energy we laid half. Okay, A square that is equal to one by two and 21368.26 into 9.3 to 10 to the minus two squared. That is equality 5.9 Jules.
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where m1o, m2o form a complete and orthonormal basis; e is a real constant having the dimensions of energy. (a) is h hermitian? calculate the trace of h
Answers
The trace of h is 0
The given matrix h is:
$$h = \begin{bmatrix}
e & 0\\
0 & -e
\end{bmatrix}$$
(a) To determine if h is hermitian, we need to check if the conjugate transpose of h is equal to h. The conjugate transpose of a matrix is obtained by taking the transpose of the matrix and then taking the complex conjugate of each element.
The transpose of h is:
$$h^T = \begin{bmatrix}
e & 0\\
0 & -e
\end{bmatrix}$$
Since all the elements of h are real, the complex conjugate of each element is the same as the element itself. Therefore, the conjugate transpose of h is:
$$h^\dagger = \begin{bmatrix}
e & 0\\
0 & -e
\end{bmatrix}$$
Since h is equal to its conjugate transpose, h is hermitian.
(b) The trace of a matrix is the sum of its diagonal elements. The trace of h is:
$$Tr(h) = e + (-e) = 0$$
Therefore, the trace of h is 0.
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Which best explains how gravity contributes to the formation of layers in protoplanets?.
Answers
The following statement best describes how gravity helps protoplanets create layers in that gravity pulls materials and generates compaction, which produces heat and causes materials to melt, sink, and rise. Option A is correct.
What is gravity?Gravitation is a natural law by which all things with all matter are attracted towards one another. gravity causes weight to all matter and the gravity of the moon causes the ocean tides.
The force that draws massed bodies toward one another is known as gravity. Gravitatithus
According to the alternatives, gravity pulls things together and causes compaction, which generates heat and causes things to melt,
Thus, we may draw the conclusion that gravity draws materials and creates compaction, which generates heat and causes materials to melt, sink, and rise.
Hence option A is correct,
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Answer:
its A
Explanation:
Can someone please help
Answers
99.16 Newtons is the new force of attraction between the particles.
What causes an atoms to attract one another?The forces that hold atoms together to create molecules and solids are referred to as chemical bonds. The attraction between the electrons of one atom and the nuclei of another atom as a result of this electric force is what is known as a chemical bond.
\(F = (kq1q2)/r^2\)
\(9,916 = (kq1q2)/r^2\)
\(F = (k*(q1/5)*(q2/5))/(2r)^2\)
\(F = (1/100)((kq1*q2)/(r^2))\)
So, the new force of attraction is:
\(F = (1/100)*9,916 = 99.16\)Newtons (rounded to 4 decimal places)
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A common activity like cooking a meal can use many natural _________.
Answers
A common activity like cooking a meal can use many natural Ingredients
Ingredients
Ingredients are substances combined to make a particular mixture such as a meal. most of the ingredients used for the preparation of a meal are sourced naturally.
In cooking different recipes of a meal the use of specific ingredients for each recipe differentiates the recipes.
Therefore we can conclude that cooking a meal requires the use of natural ingredients.
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The light beam shown in the figure below makes an angle of? = 15.5° with the normal line NN' in the linseedoil. Determine the angles θ and θ'.(The refractive index for linseed oil is 1.48.)
θ = 1
°
θ' = 2
°
Answers
The angle θ is approximately 0.688°, and the angle θ' is approximately 1.988°.
To determine the angles θ and θ' in the given scenario, we can use Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the media involved. Snell's Law can be stated as follows:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ is the refractive index of the medium of incidence (in this case, air with a refractive index close to 1),
θ₁ is the angle of incidence,
n₂ is the refractive index of the medium of refraction (in this case, linseed oil with a refractive index of 1.48), and
θ₂ is the angle of refraction.
Let's solve for the unknown angles θ and θ' using the given information.
Given:
Angle of incidence θ = 1°
Refractive index of linseed oil n₂ = 1.48
We need to find the angle of refraction θ₂.
Using Snell's Law, we have:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Since the refractive index of air (n₁) is approximately 1, we can simplify the equation to:
sin(θ₁) = n₂ * sin(θ₂)
Plugging in the values:
sin(1°) = 1.48 * sin(θ₂)
We can now solve for θ₂:
θ₂ = arcsin(sin(1°) / 1.48)
Calculating this value, we find:
θ₂ ≈ 0.688°
Now, let's determine the angle θ'.
Given:
Angle of refraction θ₂ = 0.688°
Refractive index of linseed oil n₂ = 1.48
We need to find the angle of incidence θ'.
Using Snell's Law, we have:
n₂ * sin(θ₂) = n₁ * sin(θ')
Since the refractive index of air (n₁) is approximately 1, we can simplify the equation to:
n₂ * sin(θ₂) = sin(θ')
Plugging in the values:
1.48 * sin(0.688°) = sin(θ')
Solving for θ', we find:
θ' = arcsin(1.48 * sin(0.688°))
Calculating this value, we get:
θ' ≈ 1.988°
Therefore, the angle θ is approximately 0.688°, and the angle θ' is approximately 1.988°.
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Question: How do static and sliding friction affect the speed of a paperback book, a flat
eraser and a key?
Answers
Answer:
How do static and sliding friction affect the speed of a paperback book, a flat eraser and a key?
Prediction: Which item (paperback book, flat eraser, or key) will have the most static friction and which item will have the most sliding friction? Make sure your prediction gives an explanation of your reasoning.
Explanation:
13. A glass of water left in the sun becomes warm. Estella adds ice to the water to make
it cool. What energy change occurs when ice is added to the warm drink?
Answers
Answer:
second
Explanation:
second
You rub an inflated balloon on the carpet and it acquires a potential that is 1560 V lower than its potential before it became charged. If the charge is uniformly distributed over the surface of the balloon and if the radius of the balloon is 15 cm, what is the net charge on the balloon
Answers
This question involves the concepts of charge and potential difference.
The net charge on the balloon is "2.6 x 10⁻⁸ C".
Net Charge on BalloonThe balloon has a shape of a sphere. Therefore, the formula for the charge on the surface of a sphere can be used here, as follows:
\(V=\frac{Q}{4\pi \epsilon_o r}\\\\Q=4\pi \epsilon_orV\)
where,
Q = net charge = ?r = radius of balloon = 15 cm = 0.15 mV = potential difference = 1560 V\(\epsilon_o\) = permittivity of free space = 8.85 x 10⁻¹² C²/N.m²Therefore,
Q = (4π)(8.85 x 10⁻¹² C²/N.m²)(0.15 m)(1560 V)
Q = 2.6 x 10⁻⁸ C = 26 nC
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Answer:
Explanation:
50% of the kVp set on the control panel. The voltage actually used in three-phase, 12-pulse units is about:
Answers
In three-phase, 12-pulse units, the voltage used is typically determined by the relationship between the kilovolt peak (kVp) set on the control panel and the actual voltage used. According to the given information, the voltage used is 50% of the kVp set.
Therefore, if the kVp set on the control panel is V, the voltage actually used in three-phase, 12-pulse units would be 50% of V, or 0.5V.
To calculate the actual voltage used, you would need to know the specific value of the kVp set on the control panel. Once you have that value, you can multiply it by 0.5 to find the voltage actually used in the three-phase, 12-pulse units.
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Need help fast *20 points*
satellites are not typically used for _____ signals.
a. cell phone
b. am
c. global positioning
d. fm
Answers
Satellites are not typically used for cell phone and global positioning signals.
A satellite is an artificial object that is intentionally placed into orbit around a planet, moon or other celestial body. Satellites are typically designed to perform a specific task, such as communication, weather monitoring, scientific research, or navigation.
Satellites are used for global positioning signals (c) and, in some cases, for cell phone signals (a). They are not typically used for AM (b) or FM (d) radio signals, which are generally transmitted via ground-based radio towers.
However, there are some satellite radio services that provide digital radio programming to subscribers, which use satellite communication to deliver their signals.
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2. What is the total voltage drop across
the first and second resistor?
8v
10v
0 12v
Answers
Answer: 8v
Explanation:
The total voltage drop across the first and second resistor is 8 V, hence option A is correct.
What is Voltage?Voltage is the fluctuation in electric potential between the two places. It is sometimes produced by electric pressure, electric tension, or voltage source. The work required to move a test charge between two places in a static electric field corresponds to this. The derived measure for voltage in the International System of Units is called a volt. Work per unit energy is expressed in SI units as joules per coulomb, with 1 volt equaling 1 joule per 1 coulomb.
To detect the voltages between two locations in a circuit, use a voltmeter. A common reference point, like the system's foundation, is frequently utilized as one of the points.
A voltage can indicate either a supply of energy or its loss, dissipation, or storage.
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A simple pendulum consisting of a mass on a string of length L is undergoing small oscillations with amplitude. If the pendulum is taken to the moon? What happens to the time period?
Answers
A simple pendulum consisting of mass on a string of length L is undergoing small oscillations with amplitude and if the pendulum is taken to the moon, then the time period increases.
What happens to the time period when pendulum is taken on moon?As we know that,
Time period of simple pendulum is :
T = 2π√(L/g)
Gravity of moon is 1/6th of the earth's gravity. And gravity is inversely proportional to time period, therefore time period increases. Since, the pendulum takes more time to complete one vibration, therefore it will lose time.
The mass of the Moon is about 1/80th of the Earth's mass, so the gravity of Moon is less than the Earth's gravity.
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For a flat mirror, when there’s a ray that travels parallel to the surface where the object sits and it hits the surface of the mirror, the ray will then be reflected back in the opposite direction like the following diagram. Why can’t it be the same for a concave or convex mirror when the light ray travels parallel to the principle axis?
Answers
When a light ray travels parallel to the principal axis of a curved mirror, the ray will not be reflected back in the opposite direction like in the case of a flat mirror.
What is a ray diagram?The reason why this does not occur is because the surface of a curved mirror is not a flat surface and it has a varying curvature, which causes the reflected rays to behave differently compared to the flat mirror.
In the case of a concave mirror, when a light ray travels parallel to the principal axis and strikes the mirror, it is reflected back towards the focus of the mirror. This is because the concave mirror surface curves inward, causing the reflected light rays to converge towards the focus.
In the case of a convex mirror, when a light ray travels parallel to the principal axis and strikes the mirror, it is reflected back in a direction away from the focus of the mirror. This is because the convex mirror surface curves outward, causing the reflected light rays to diverge away from the focus.
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If a rock is thrown
with an initial velocity of 5.4 m/s in the y-
direction and 8.2 m/s in the x-direction.
At what angle was the rock thrown?
Answers
The angle at which the rock was thrown is 33.37°.
What is angle?An angle is formed when two rays are joined together at a common point.
To calculate the angle at which the rock was thrown, we use the formula below.
Formula:
∅ = tan⁻¹(Vy/Vx)................ Equation 1Where:
∅ = Angle at which the rock was thrownVy = Velocity of the rock in y- directionVx = Velocity of the rock in x-directionFrom the question,
Given:
Vy = 5.4 m/sVx = 8.2 m/sSubstitute these values into equation 1
∅ = tan⁻¹(5.4/8.2)∅ = tan⁻¹(0.6585)∅ = 33.37°Hence, the angle is 33.37°.
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4) A basketball is launched at a velocity of 25 m/s in a direction making an angle of 50° upward with the
horizontal. What is the maximum height reached by the object?
Answers
Answer:
As Per Provided Information
Velocity of projection u is 25m/sAngle made by ball ∅ is 50°We have been asked to determine the maximum height reached by the object .
here we will take acceleration due to gravity g is 9.8 m/s².
For calculating the maximum height attained by the object we will use the following formula .
\( \boxed{\bf \:H_{(max)} \: = \cfrac{u {}^{2} {sin}^{2} \theta }{2g}}\)
Substituting all the value in above equation we obtain
\(\sf \qquad \: \longrightarrow\:H_{(max)} \: = \cfrac{ {25}^{2} {sin}^{2} {50}^{ \circ} }{2 \times 9.8} \\ \\ \\ \sf \qquad \: \longrightarrow\:H_{(max)} = \cfrac{625 \times(0.766) {}^{2} }{19.6} \\ \\ \\ \sf \qquad \: \longrightarrow\:H_{(max)} = \cfrac{625 \times 0.586756}{19.6} \\ \\ \\ \sf \qquad \: \longrightarrow\:H_{(max)} = \cfrac{366.7225}{19.6} \\ \\ \\ \sf \qquad \: \longrightarrow\:H_{(max)} = \cancel \cfrac{366.7225}{19.6} \\ \\ \\ \sf \qquad \: \longrightarrow\:H_{(max)} =18.71 \: m\)
Therefore,
Maximum height reached by the object is 18.71 meters.
suppose a motor connected to a 120 v source draws 10.0 a when it first starts. (b) what current does it draw at its normal operating speed when it develops a 100 v back emf? (answer in a)
Answers
Since the motor develops a 100 V back emf (electromotive force) at its normal operating speed, its current is 1.67 A.
The relation between current (I), voltage(V), and resistor (R) in a direct current circuit is:
V = I . R
At start:
V = 120 V
I = 10 A
Hence, we can find the equivalent resistor:
R = V/ I = 120 / 10 = 12 Ohm
When the motor is running, it develops 100 V back emf.
Therefore, the net voltage is
= 120 V - 100 V = 20 V
and hence, the current:
I = 20 / 12 = 1.67 A
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A block of unknown mass is attached to a spring with a spring constant of 6.50 N/m and undergoes simple harmonic motion with an amplitude of 10.0 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 30.0 cm/s. Calculate (a) the mass of the block, (b) the period of the motion, and (c) the maximum acceleration of the block.
Answers
A.) The mass of the block is 0.722 kg.
B.) The period of the motion is 0.853 s.
C.) The maximum acceleration of the block is 0.903 m/s^2.
(a) We may use the equation for the kinetic energy of a simple harmonic oscillator to calculate the mass of the block:
(1/2)mv2 = (1/2)kA2 = KE
where m is the block's mass, v is its velocity, k is the spring constant, and A is the motion's amplitude. Substituting the provided values yields:
\((1/2)m(0.3^2) = (1/2)(6.50)(0.10^2)\)
When we solve for m, we get:
m = (6.50 x 0.01) / 0.09 = 0.722 kg
As a result, the block's mass is 0.722 kg.
(b) The period of the motion can be calculated using the following equation:
T = 2π√(m/k)
Substituting the values from part (a), we get:
T = 2π√(0.722/6.50) = 0.853 s
As a result, the motion's period is 0.853 s.
(c) The maximum acceleration of the block can be calculated using the following equation:
max a = kA/m
Substituting the provided values yields:
\(a_max = (6.50 x 0.10) / 0.722 m/s2\)
As a result, the block's maximum acceleration is 0.903 m/s2.
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