Answers
Answer:
Explanation:
The plane travels a distance of 200 m/s(20.0 s) = 4000 m
A 90° turn is π/2 radians
4000 = (π/2)R
R = 8000/π m
a = v²/R = 200²/8000/π = 5π m/s² ≈ 15.7 m/s²
When a airplane makes the graduall 90 turn at constant speed the average acceleration is 14.14 m/s.
What is acceleration?Acceleration equals the change in velocity. The rate of change of velocity per unit time is called acceleration. The unit of acceleration is m/s². It represents the speed of the object along with direction.
Acceleration(a) = dv/dt, dv represents change in velocity and dt represents change in time. Velocity is defined as rate of change of position with time. Acceleration has both magnitude and direction and it is a vector quantity.
Acceleration is of two types- Instantaneous acceleration and average acceleration. Instantaneos acceleration gives the acceleration at that instant where as the average acceleration is obtained by rate of change of velocity with elapsed time.
Average acceleration = Δv / Δt. Δv is the change in velocity and Δt is the elapsed time.
From the given,
An airplane makes 90° turn,
v₁ = 200 i^ (before 90 turn)
v₂ = 200 j^ (after 90 turn)
Δt = change in time
Average acceleration = Δv / Δt
= v₂ - v₁ / 20
= 200 i^ - 200 j^ /20
avg.acc = 10(-i) + 10 (j)
| avg.acc | = √ 10(-i) + 10 (j)
= √2×10
= 14.14 m/s²
Hence, the average accleration is 14.14 m/s².
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Related Questions
A sphere or cylinder of mass M, radius R, and moment of inertia I rolls without slipping down a hill of height h, starting from rest. If there is no slipping w = Vcm/R.(a) In terms of the given variables (M , R , I , and h ), what is vCM at the bottom of the hill? (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)
Answers
vCM at the bottom of the hill is \(\sqrt{2Mgh}\) / \(\sqrt{M+(1/R^{2}) }\). One of the most famous physics rules is the law of conservation of momentum. The overall momentum of a system is always conserved for an isolated system, according to the conservation of momentum law principle.
By the law of conservation of momentum
E₁ = E₂
U₁ + K₁ = U₁ + K₁
U₁ + \(K_{t}\) = \(u_{f}\) + \(K_{uf}\) +k
The object is initially at rest hence the initial kinetic energy is zero. Finally, the object is at the bottom of the hill. That is the height is zero. Hence the final potential energy is zero.
Mgh = 1/2 MV² + 1/2 1ω²
Velocity is
Mgh = ( 1/2MV² + 1/2 l [v²/R])
Mgh = \(\sqrt{2Mgh\frac}\) /\(\sqrt{M+(1/R^{2} } )}\)
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We can easily tell that a bowling ball rolling down an ally has energy of motion. But why would a scientist say that a white-hot piece of iron also has the energy of motion within it?
Answers
A white-hot iron piece has internal motion energy due to constant particle movement at the atomic and molecular levels, as per scientists. Thermal energy or heat energy is motion. Higher temperature means more kinetic energy and faster motion of atoms and molecules.
What is the energy of motion?White-hot iron vibrates atoms and molecules at high temperatures. Kinetic theory states that all matter is made up of moving particles. Motion occurs at the microscopic level, beyond eye view. Higher temperature = greater particle energy.
When a scientist refers to white-hot iron, they recognize its high temperature corresponds to increased kinetic energy and motion. Motion and energy at the atomic level are not visible like a bowling ball, but are fundamental traits of matter.
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Which of the following elements have the same amount of valence electrons as Sulfur (5)?
O N. Br, and Xe
O F, As, and Sn
O Si, P, and CI
O O, Se, and Te
Answers
Answer:
Explanation:
it's c
Your class goes on a field trip to observe drilling machinery. The geologists at the drill site show you displays of drilled rocks to compare different types of drills and methods. The drilled holes in one rock display are significantly larger than the holes drilled in the display next to it. Given this information, which statement is correct?
Answers
We can see here that the statement that is correct will be: B. The rock display with larger holes shows petroleum drilling, which is deep underground.
Who is a geologist?A geologist is a scientist who focuses on the solid components of the Earth, such as minerals and rocks, as well as the processes that shape the planet's surface.
Geologists study the make-up, structure, and past of the Earth's crust in order to comprehend geological processes including mountain creation, earthquake and volcanic activity, and the exploitation of natural resources. They frequently perform fieldwork, gathering samples, running surveys, and researching geological formations.
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The complete question is that:
Your class goes on a field trip to observe drilling machinery. The geologists at the drill site show you displays of drilled rocks to compare different types of drills and methods. The drilled holes in one rock display are significantly larger than the holes drilled in the display next to it. Given this information, which statement is correct? (1 point)
A. The rock display with smaller holes shows copper drilling, which is deep underground.
B. The rock display with larger holes shows petroleum drilling, which is deep underground.
C. The rock display with smaller holes shows petroleum drilling, which is closer to the surface.
D. The rock display with larger holes shows copper drilling, which is closer to the surface.
(a)Find the force (in N) of electrical attraction between a proton and an electron that are 7.4 ✕ 10−11 m apart.
(b)Compare this to the gravitational force between these particles. (Enter the gravitational force, in N.
Answers
The electrostatic force of attraction between the proton and electron is 4.2 x 10⁻⁸N.
The gravitational force between the proton and electron is 1.9 x 10⁻⁴⁷N.
a) Charge on proton = charge on electron = q = 1.6 x 10⁻¹⁹C
Distance between the proton and electron, r = 7.4 x 10⁻¹¹m
The electrostatic force of attraction between the proton and electron is given by,
F = 1/4πε₀(q²/r²)
F = 9 x 10⁹ x (1.6 x 10⁻¹⁹)²/(7.4 x 10⁻¹¹)²
F = 9 x 10⁹ x 2.56 x 10⁻³⁸/54.76 x 10⁻²²
F = 4.2 x 10⁻⁸N
b) Mass of the electron, m₁ = 9.1 x 10⁻³¹kg
Mass of the proton, m₂ = 1.67 x 10⁻²⁷kg
Distance between the proton and electron, r = 7.4 x 10⁻¹¹m
The gravitational force between the proton and electron is given by,
F = Gm₁m₂/r²
F = 6.67 x 10⁻¹¹x 9.1 x 10⁻³¹x 1.67 x 10⁻²⁷/(7.4 x 10⁻¹¹)²
F = 1.9 x 10⁻⁴⁷N
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If magnet A can pick up 3 steel paperclips and magnet B can pick up 5 paperclips, which one is stronger
Answers
Answer:4
Explanation:
The clips are not affected by magnet strength
May someone please give me a hand?
Answers
circuit diagram
this is a circuit diagram
1.) A potato is shot off a 20 meter high rooftop. The potato leaves the cannon traveling 50
m/s horizontally. How far did the potato fly?
Answers
Answer:
Explanation:
Find the time it is in the air.
See the comments below. I'm going to restrict the question to horizontal distance.
If you just drop the potato, then the height is 20 meters
The acceleration due to gravity is 9.81
The starting speed (vi ) = 0
Formula
d = vi * t + 1/2 a t ^2
Solution
20 = 0 + 1/2 9.81 * t^2
20 = 1/2 9.81 * t^2
20 = 4.905 t^2
20/4.905 = t^2
t^2 = 4.077
sqr(t^2)= sqr(4.077)
t = 2.02
Find the distance travelled horizontally
There is no acceleration horizontally so you use d = r * t
r = 50 m/s
t = 2.02
d = 50 * 2.02
d = 101 meters.
An electric heater uses 0,5 MJ when connected to a 220 V supply for 30 minutes. Calculate the power rating of the heater and the current drawn from the supply.
Answers
The power rating of the heater is 277.8 W and the current drawn from the supply is 0.07015mA.
The power is obtained from the ratio of work and time and the power is measured in watts(W). The current is defined as the flow of electrons in the circuit and it is measured in ampere(A).
From the given,
The energy of the electric heater = 0.5MJ = 0.5×10⁶ J
Voltage (V) = 220 V
time (t) = 30 minutes = 30×60 s = 1800 s.
To find power (P):
Power = Energy / Time
= 0.5×10⁶ / 1800
= 277.77 W
Power of the electric heater = 277.8 W
To find current from the given:
Power (P) = V×I×t
Current (I) = P/(V×t)
= 277.8 / (220×1800)
= 0.7015 mA
The current drawn from the supply is 0.7015 mA.
Hence, the power rating of the heater is 277.8 W and the current drawn from the supply is 0.7015 mA.
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Jibari walks 40.0 meters east in 120.0 seconds. He then walks 30.0 meters west in 60.0 seconds. What is his average velocity for the trip?
Answers
Answer:
0.1667 meters/second.
Explanation:
To find Jibari's average velocity for the trip, we need to first calculate his average velocity for each leg of the trip. To do this, we need to divide the distance he traveled by the time it took him to travel that distance.
For the first leg of the trip, Jibari walked 40.0 meters east in 120.0 seconds. His average velocity for this leg of the trip is therefore 40.0 meters / 120.0 seconds = 0.3333 meters/second east.
For the second leg of the trip, Jibari walked 30.0 meters west in 60.0 seconds. His average velocity for this leg of the trip is therefore 30.0 meters / 60.0 seconds = 0.5000 meters/second west.
To find Jibari's average velocity for the entire trip, we need to add the velocities for each leg of the trip, taking into account their direction. Since the first leg of the trip was east and the second leg was west, we can simply add the two velocities together to find the overall average velocity.
Jibari's overall average velocity for the trip is therefore 0.3333 meters/second east + 0.5000 meters/second west = 0.1667 meters/second.
Therefore, Jibari's average velocity for the trip was 0.1667 meters/second.
Jibari's average velocity for the trip is 0.7 m/s east.
To solve for Jibari's average velocity, we will first need to find his total displacement. We can do this by adding the magnitudes of his eastward and westward displacements. The magnitude of Jibari's eastward displacement is 40.0 meters, and the magnitude of his westward displacement is 30.0 meters. So, his total displacement is
40.0 - 30.0 = 10.0 meters east.
We can then find Jibari's average velocity by dividing his total displacement by the total time it took him to complete the trip. The total time it took Jibari to complete the trip is
120.0 + 60.0 = 180.0 seconds.
So, his average velocity is
10.0 / 180.0 = 0.7 m/s east.
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2. Sarah is a 54-year-old woman who is in excellent shape. She goes to the gym every
morning at 5 AM before work. This morning, she is a little stressed out. She overslept
by about 15 minutes, she couldn't find any clean socks, she spilled her coffee all over
the kitchen floor, and her gas light went on while she was on the way to the gym, and
there are no gas stations open this early. She is hoping that a workout will help her
clear her head. As she parks her car in the almost-empty parking lot, she hears
breaking glass. She turns around and sees some figures hastily getting into a car,
and a minute later they speed away. She calls 911 and the police take her in for
Avalitness fortimanu
Answers
Answer:
The Police take her in for questioning
Explanation:
Because she was an eye witness to the incident
A ball hangs on a rope of 0.30 m. The ball is pushed horizontally so that it has a speed of 1.1 m/s. What angle does the rope make with the vertical when the ball's kinetic energy is halved
Answers
This question involves the concepts of the law of conservation of energy, Pythagora's Theorem, kinetic energy, and potential energy.
The rope makes an angle of "26.2°" with the vertical when the ball's kinetic energy is halved.
First, we will find the initial kinetic energy of the ball:
\(K.E = \frac{1}{2}mv^2\\\\K.E=\frac{1}{2}(m)(1.1\ m/s)^2\\\\K.E = (0.605\ m^2/s^2) m\)
Now, half of this kinetic energy is left at the final point. Therefore, according to the law of conservation of energy, the other half must be converted to the potential energy of the ball:
\(P.E=\frac{1}{2}K.E\\mgh'=\frac{1}{2}(0.605\ m^2/s^2)m\\\\h'=\frac{0.3025\ m^2/s^2}{9.81\ m/s^2}\\\\h' = 0.031\ m\)
This h' is the height of the ball above the ground the final position, as shown in the picture attached.
Applying Pythagora's Theorem to the right angled triangle shown in the attached picture we have:
\(Cos\theta = \frac{Base}{Hypotenuse}=\frac{h}{l}\)
where,
θ = angle of rope with vertical = ?
l = legth of rope = 0.3 m
h = l - h' = 0.3 m - 0.031 m = 0.27 m
Therefore,
\(Cos\theta=\frac{0.27\ m}{0.3\ m}\\\\\theta = Cos^{-1}(0.89721)\)
θ = 26.2°
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Which type of force is used by your legs to pedal a bicycle?
Answers
Answer:
kinetic energy
Explanation:
Laasya is lifting a table and moving it to another room to expand the space in her room. What mode of
strength-training
is Laasya performing?
Answers
Laasya is performing resistance training by lifting a table and moving it to another room to expand the space in her room. The correct option to this question is D.
Strength training By putting your muscles up against resistance, resistance training builds muscle strength. Free weights, weight machines, resistance bands, and your own body weight are all used in various types of resistance training. To get the most out of their training, beginners should go two or three times per week.Resistance training is founded on the idea that, when called upon, the body's muscles will struggle to overcome a resisting force. Resistance exercise has both advantages and disadvantages.Resistance exercises include planks, sit-ups, squats, push-ups, leg raises, and leg extensions. You and a small amount of room are all that are needed for these strength training exercises.For more information on resistance training kindly visit to
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Complete question : Laasya is lifting a table and moving it to another room to expand the space in her room. What mode of strength-training is Laasya performing?
a. Endurance
b. Isometric
c. Isotonic
d. Resistance
What kind of waves can travel through empty space or a vacuum?
A.Sound
B.Light
C.Frequency
D.Wavelength
Answers
Answer:
the answer is B.
Answer:
light
Explanation:
you can see stuff in space but cant hear it
a) a drone flies 150 m to southwest (directly between south and west), then flies 85 m directly south, and finally flies 550 m in the direction 35 degrees north of east. Use the analytical method to find the resultant displacement of the drone (magnitude and direction)
you can help with a
Answers
The resultant of the displacement is 336.5m
What is resolution of vectors?The process of splitting a vector into its components is called resolution of the vector. The vectors are splitted into vertical and horizontal component.
For the first displacement;
The vertical component = - 150 sin45 = -106.1 m
The horizontal component = - 150 cos 45° = -106.1 m
For the second displacement;
The vertical displacement = - 85sin90 = -85
The horizontal component = 0
For the third displacement;
The vertical displacement = 550 sin55 = 450.5
The horizontal displacement = 550 cos 55 = 315.5
Sum of vertical component = 450.5-85-106.1 = 263.4
sum of horizontal component = 315.5 -106.1 = 209.4
Using Pythagorean theorem
R = √ 263.4² + 209.4²
R = √113227.92
R = 336.5m
The resultant angle = tan^-1( 263.4/209.4)
= tan^-1(1.26)
= 51.56°
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A spring with a spring constant of 52N/m sits on a desk. The spring is 34cm long. A block of mass 0.12kg is placed on top of the spring. How high above the desk does the block rest?
Answers
Answer:
H = 31.7 cm
Explanation:
Given:
k = 52 N/m - Spring rate
L = 34 cm = 0.34 m - Spring length
m = 0.12 kg
g = 9.8 m/s²
____________
H - ?
Block weight:
F = m*g = 0.12·9.8 ≈ 1.18 N
According to Hooke's law:
F = k·ΔL
The spring is compressed by:
ΔL = F / k = 1.18 / 52 ≈ 0.023 м
Height of the block above the table:
H = L -ΔL = 0.34 - 0.023 = 0.317 m or H = 31.7 cm
How many valence electrons do most stable atoms have?
A) one
B) two
C) four
D) eight
Answers
Answer:
D) 8
Explanation:
Due to the octet rule the most stable atoms will have 8 valence electrons.
In an air standard diesel cycle, the compression ratio is 16 and at the beginning of isentropic compression, the temperature is 15c and the pressure is 0.1 j\.1pa. Heat is added until the t:mperature at constant process is 1480c. Calculate cut off ratio, heat supplied per kg of arr, cycle efficiency and mean effective pressure
Answers
If Cv reduces by 2%, calculate the percentage gain in efficiency of the a diesel cycle with a bit rate of 16 and a cut-off ratio of 10% of a swept volume. Taking Cv = 0.717 & 1.4; the answer is 1.23%.
Where can I find the volume?In cubic units, the volume answer is displayed. Volume is determined by multiplying the length, breadth, and height.
What does measuring of volume entail?The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units. A derived measure called a cubic meter (m3) serves as the SI volume measurement unit.
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Sam drives her scooter 7 kilometres north. She stops for lunch and then drives
5 kilometres east. What distance did she cover? What was her displacement?
Answers
Answer:
1. Distance travelled = 12 km.
2. Displacement = 8.6 km
Explanation:
From the question given above, the following data were obtained:
Distance 1 (d₁) = 7 km
Distance 2 (d₂) = 5 km
Total distance =?
Displacement =?
1. Determination of the distance travelled.
Distance 1 (d₁) = 7 km
Distance 2 (d₂) = 5 km
Total distance (dₜ) =?
dₜ = d₁ + d₂
dₜ = 7 + 5
dₜ = 12 km
2. Determination of the displacement.
In the attached photo, R is the displacement.
We can obtain the value of R by using the pythagoras theory as illustrated below:
R² = 7² + 5²
R² = 49 + 25
R² = 74
Take the square root of both side
R = √74
R = 8.6 km
You have three jugs measuring 12 gallons, 8 gallons, 3 gallons, and a water faucet. You need to measure out exactly one gallon. What do you do?
Answers
We need to measure out exactly one gallon of water in the 12-gallon jug using the water faucet, three 12-gallon jugs, an 8-gallon jug, and a 3-gallon jug.
What is water faucet used for?The flow of a liquid or gas from a pipe or container can be controlled by a faucet. I entered the bathroom and started the faucets so the tub would fill. The word faucet, which has French roots, first appears in English manuscripts in the 1400s. It made reference to a barrel's peg or stopper. The stopper at the end of the tube where a spigot (a tube) was used to draw out liquid (beer, etc.) was referred to as a faucet.
What is the difference between tap and faucet?The most popular term in American English is faucet, which is used similarly to "tap" in British English, as in "water faucet" (although the term "tap" is also used in the US). The term "spigot" is typically used by tradespeople (such as plumbers) to describe an outside fixture.
The steps below can be used to accurately measure one gallon of water using the jugs:
The 12-gallon container should be fully filled.
Fill the 8-gallon jug to the top with water by pouring it into the 12-gallon jug. The 12-gallon jug is now left with 4 gallons of water.
Fill the 8-gallon jug to the top with water, then add the 4 gallons from the 12-gallon jug.
Fill the 12-gallon jug to the top with water from the tap, then transfer the extra liquid into the 8-gallon jug (until precisely 1 gallon is left in the 12-gallon jug).
Right now, the 12-gallon jug contains exactly 1 gallon of water.
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How much force required to displace a body through 50cm by doing 25J work on it.
Answers
Answer:
50 N
Explanation:
W = Fd
F = W/d
first convert cm → m: 50 cm x 1 m/cm = 0.50 m
F = (25 J) / (0.50 m) = 50 N
A 1.2-kg mass is projected from ground level with a velocity of 31.3 m/s at some unknown angle above the horizontal. A short time after being projected, the mass barely clears a 16-m tall fence. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass as it clears the fence
Answers
Answer:
The kinetic energy will be "399.65 J".
Explanation:
Given:
Mass,
m = 1.2 kg
Velocity,
v = 31.3 m/s
The total energy of mass will be:
⇒ \(E=K+U\)
or,
⇒ \(E=.5mv^2+mgh\)
By putting the values, we get
\(=.5(1.2)(31.3)^2+0\)
\(=0.6\times 979.69+0\)
\(=587.81 \ J\)
Since,
The system's total energy is unchanged, then
⇒ \(E=K+U\)
or,
⇒ \(E=K+mgh\)
\(587.81=K+1.2(9.8)(16)\)
\(587.81=K+188.16\)
\(K=587.81-188.16\)
\(=399.65 \ J\)
Particles q₁ +8.0 μC, q2 +3.5 μC, and
93-2.5 μC are in a line. Particles q₁ and q2 are
separated by 0.10 m and particles q2 and q3 are
separated by 0.15 m. What is the net force on
particle q₂?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
+8.0μ.C
+91
0.10 m
+3.5 C
+92
0.15 m
-2.5μ C
93
Answers
The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.
To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.
The force between two charged particles can be calculated using Coulomb's law:
F = k * |q₁ * q₂| / r²
Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.
First, let's calculate the force exerted on q₂ by q₁:
F₁₂ = k * |q₁ * q₂| / r₁₂²
F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²
F₁₂ ≈ 252000 N
The force is positive because q₁ and q₂ have opposite charges.
Next, let's calculate the force exerted on q₂ by q₃:
F₂₃ = k * |q₂ * q₃| / r₂₃²
F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²
F₂₃ ≈ -63000 N
The force is negative because q₂ and q₃ have the same charge.
Finally, we can find the net force on q₂ by summing the individual forces:
Net force = F₁₂ + F₂₃
Net force = 252000 N + (-63000 N)
Net force ≈ 189000 N
The net force on particle q₂ is approximately 189000 N.
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in the figure a plane mirror MN of height h is mounted in an adjustable vertical position on vertical wall E is an observers eye which is 1 m from the wall and 1.5 above the ground PQ is a vertical post of height 3 m and is 4 m behind the observer. looking into the mirror the observer can see the whole image of the post what’s the minimum value of h
Answers
The minimum value of h is 3.75 meters.
To determine the minimum value of h, we need to consider the geometry of the situation.
From the given information, we know that the observer's eye is 1 m from the wall and 1.5 m above the ground. The vertical post-PQ is 3 m tall and located 4 m behind the observer. The observer can see the whole image of the post in the mirror.
Since the observer can see the entire image of the post, we can conclude that the line of sight from the top of the post to the observer's eye must be parallel to the line of sight from the bottom of the post to the observer's eye. This is because the mirror reflects light rays at equal angles of incidence and reflection.
Let's denote the height of the observer's eye from the ground as x. We can set up a proportion to find the height of the image of the post in the mirror:
(Height of post-PQ) / (Distance from observer to post) = (Height of the image in the mirror) / (Distance from mirror to image)
Using the given values, we have:
3 m / 4 m = h / (4 m + 1 m)
Simplifying the equation:
3/4 = h/5
Cross-multiplying:
4h = 15
h = 15/4 = 3.75 m
Therefore, the minimum value of h is 3.75 meters.
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1. The kinetic energy of a car is 8 106 J as it travels along a horizontal road. How much work is required to stop the car in 10 s? (A) zero joules (B) 8 105 J (C) 8 107 J (D)8 104 J (E) 8 106 J
Answers
The power to stop the car with kinetic energy of a car is \(8*10^{6} J\) as it travels along a horizontal road is \(8*10^{5} watt\), option B
What is Kinetic energy ?Kinetic energy can be seen as one that is been recorded when an object is able to move from a place , in a broad term we can say this is the energy that can be attributed to that of someone leaving a place and go to another place hence we can see it as the one in the motion.
The definition of energy as the "power to accomplish work" refers to the capacity to apply a force that moves an object. Even if the word is vague, it is clear what energy actually means: it is the force that causes objects to move. The two types can be attributed to the one we know which are kinetic and potential energy.
\(Power \frac{Energy}{time}\)
\(Energy = 8*10^{6} J\)
\(time = 10 s\)
\(Power = \frac{8*10^{6} J}{10}\)
\(power = 8*10^{5} watt\)
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proper question;
The kinetic energy of a car is 8 × 106 J as it travels along a horizontal road. How much power is required to stop the car in 10 s? (A) zero joules (B) 8 105 J (C) 8 107 J (D)8 104 J (E) 8 106 J
A war-wolf or trebuchet is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling large vegetables and pianos as a sport. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass, d = 2.60 m long, joining particles of mass m1 = 0.115 kg and m2 = 68.5 kg at its ends. It can turn on a frictionless, horizontal axle perpendicular to the rod and 13.0 cm from the large-mass particle. The operator releases the trebuchet from rest in a horizontal orientation.
Find the maximum speed that the small-mass object attains when it leaves the trebuchet horizontally.
Answers
The maximum speed that the small-mass object attains when it leaves the trebuchet horizontally is approximately 28.3 m/s.
To find the maximum speed that the small-mass object attains when it leaves the trebuchet horizontally, we can apply the principle of conservation of mechanical energy.
Initially, the trebuchet is at rest, so its total mechanical energy is zero. As the small-mass object leaves the trebuchet horizontally, it gains kinetic energy. At this point, all of the potential energy of the system is converted into kinetic energy.
The potential energy of the system can be calculated as the sum of the gravitational potential energies of the two masses:
PE = m1 * g * h1 + m2 * g * h2
Since the trebuchet is released from rest in a horizontal orientation, the initial height h1 is zero. The height h2 can be calculated as the perpendicular distance between the pivot point and the center of mass of the larger mass m2:
h2 = 13.0 cm = 0.13 m
Therefore, the potential energy simplifies to:
PE = m2 * g * h2
The kinetic energy of the small-mass object can be calculated as:
KE = (1/2) * m1 * v^2
where v is the maximum speed of the small-mass object.
Since the total mechanical energy is conserved, we have:
PE = KE
m2 * g * h2 = (1/2) * m1 * v^2
Plugging in the given values, such as g = 9.8 m/s^2, m1 = 0.115 kg, m2 = 68.5 kg, and h2 = 0.13 m, we can solve for v:
(68.5 kg * 9.8 m/s^2 * 0.13 m) = (1/2) * 0.115 kg * v^2
Solving for v, we find:
\(v^2 = (68.5 kg * 9.8 m/s^2 * 0.13 m) / (0.115 kg)\)
\(v^2 = 800\)
v ≈ 28.3 m/s
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In an open circuit like the picture
A. the light bulb will produce light
B. a resistor controls the flow of current
C. the light bulb will be off
D. current will flow
Answers
This is due to the reason that the wire doesn’t go back to the battery :)
In an open circuit like the picture the light bulb will be off. So, option (C) is correct.
What is electric circuit?Electric circuit is a way for current to flow through electricity. An electric circuit consists of a source of energy for the charged particles that make up the current, like a battery or generator; sources of current-using equipment, like lamps, electric motors, or computers; and the connecting wires or transmission lines.
Ohm's law and Kirchhoff's rules are two of the fundamental mathematical laws that define how electric circuits function.
In the given diagram, the circuit is open. So, no current passes through it and the light bulb will be off. Hence, option (C) is correct.
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An object has the acceleration graph shown in (Figure 1). Its velocity at t=0s is vx=2.0m/s. Draw the object's velocity graph for the values of t that are separated by the step Δt = 2s.
Answers
Answer:
Explanation:
We may notice that change in velocity can be obtained by calculating areas between acceleration lines and horizontal axis ("Time"). Mathematically, we know that:
\(v_{b}-v_{a} = \int\limits^{t_{b}}_{t_{a}} {a(t)} \, dt\)
\(v_{b} = v_{a}+ \int\limits^{t_{b}}_{t_{a}} {a(t)} \, dt\)
Where:
\(v_{a}\), \(v_{b}\) - Initial and final velocities, measured in meters per second.
\(t_{a}\), \(t_{b}\) - Initial and final times, measured in seconds.
\(a(t)\) - Acceleration, measured in meters per square second.
Acceleration is the slope of velocity, as we know that each line is an horizontal one, then, velocity curves are lines with slopes different of zero. There are three region where velocities should be found:
Region I (t = 0 s to t = 4 s)
\(v_{4} = 2\,\frac{m}{s} +\int\limits^{4\,s}_{0\,s} {\left(-2\,\frac{m}{s^{2}} \right)} \, dt\)
\(v_{4} = 2\,\frac{m}{s}+\left(-2\,\frac{m}{s^{2}} \right) \cdot (4\,s-0\,s)\)
\(v_{4} = -6\,\frac{m}{s}\)
Region II (t = 4 s to t = 6 s)
\(v_{6} = -6\,\frac{m}{s} +\int\limits^{6\,s}_{4\,s} {\left(1\,\frac{m}{s^{2}} \right)} \, dt\)
\(v_{6} = -6\,\frac{m}{s}+\left(1\,\frac{m}{s^{2}} \right) \cdot (6\,s-4\,s)\)
\(v_{6} = -4\,\frac{m}{s}\)
Region III (t = 6 s to t = 10 s)
\(v_{10} = -4\,\frac{m}{s} +\int\limits^{10\,s}_{6\,s} {\left(2\,\frac{m}{s^{2}} \right)} \, dt\)
\(v_{10} = -4\,\frac{m}{s}+\left(2\,\frac{m}{s^{2}} \right) \cdot (10\,s-6\,s)\)
\(v_{10} = 4\,\frac{m}{s}\)
Finally, we draw the object's velocity graph as follows. Graphic is attached below.
The velocity of a body under constant acceleration increases steadily with time
Please find attached the required velocity graph for values of t that are separated by Δt = 2s
The reasons the attached graph is correct are given as follows:
At t = 0 secondsThe initial velocity of the object at t = 0 is v = 2.0 m/s
The first point on the graph is (0, 2.0)
From t = 0 s, to t = 4 sThe acceleration from t = 0, to t = 4, a₁ = -2 m/s²
The velocity at t = 4 s, v₂ = 2.0 + (-2)×4 = -6
Therefore, the next point on the graph is (4, -6)
From t = 4 s to t = 6 sFrom t = 4 to t = 6, the acceleration, a₂ = 1 m/s²
Therefore, v₃ = -6 + 1 × 2 = -4
The third point on the velocity graph is (6, -4)
From t = 6 s to t = 10 sFrom t = 6 s to t = 10 s, we have, the acceleration, a₃ = 2 m/s²
The velocity, v₄ = -4 + 4 × 2 = 4
Therefore, the fourth point on the velocity graph is (10, 4)
With the above points, the velocity graph can be plotted using MS Excel
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3. A certain horizontal east-west lined wire has a mass of 0.2kg per meter of length and carries a current I. Impressed on the wire is northward-directed horizontal magnetic field strength of 0.4T. Find the current I if the magnetic force is to support the weight of the wire? (use: g = 10m/s?)(3pts)
Answers
Answer:
i = 4.9 A
Explanation:
The expression for the magnetic force in a wire carrying a current is
F = i L x B
bold letters indicate vectors.
The direction of the cable is towards the East, the direction of the magnetic field is towards the North, so the vector product is in the vertical direction (z-axis) upwards and the weight of the cable is vertical downwards. Let's apply the equilibrium condition
F - W = 0
i L B = m g
They indicate the linear density of the cable λ = 0.2 kg / m
λ = m / L
m = λ L
we substitute
i B = λ g
i = \(\frac{ \lambda \ g}{B}\)
let's calculate
i = 0.2 9.8 / 0.4
i = 4.9 A