(a) The force constant for each elastic band is approximately 303.28 N/m.
(b) The time for one complete bounce of the child is approximately 1.043 seconds.
(c) The child's maximum velocity during the bounce is approximately 1.63 m/s.
(a) The force constant for each elastic band can be determined using Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. Mathematically, this can be expressed as F = -kx, where F is the force, k is the force constant, and x is the displacement.
Given that each elastic band stretches 0.270 m while supporting an 8.35 kg child, we can set up the equation as follows:
F = -kx
m * g = k * x
Where m is the mass of the child (8.35 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), k is the force constant (to be determined), and x is the displacement (0.270 m).
Substituting the known values, we have:
(8.35 kg) * (9.8 m/s²) = k * (0.270 m)
Solving for k, we get:
k = (8.35 kg * 9.8 m/s²) / (0.270 m)
Calculating this expression gives us:
k ≈ 303.28 N/m
Therefore, the force constant for each elastic band is approximately 303.28 N/m.
(b) To find the time for one complete bounce of the child, we can use the formula for the period of oscillation of a mass-spring system. The period (T) is the time it takes for one complete cycle of motion. It can be calculated using the equation:
T = 2π * √(m / k)
Where m is the mass of the child (8.35 kg) and k is the force constant (303.28 N/m) determined in part (a).
Plugging in the values, we have:
T = 2π * √(8.35 kg / 303.28 N/m)
Calculating this expression gives us:
T ≈ 2π * √(0.0275 kg⋅m / N)
T ≈ 2π * 0.166
T ≈ 1.043 s
Therefore, the time for one complete bounce of the child is approximately 1.043 seconds.
(c) The child's maximum velocity can be determined using the equation for simple harmonic motion. In this case, the child's bounce can be approximated as simple harmonic motion because the child is subjected to a restoring force provided by the elastic bands.
The maximum velocity (v_max) of an object undergoing simple harmonic motion can be calculated using the equation:
v_max = A * ω
Where A is the amplitude of the motion (0.270 m) and ω is the angular frequency. The angular frequency can be calculated using the equation:
ω = √(k / m)
Where k is the force constant (303.28 N/m) and m is the mass of the child (8.35 kg).
Plugging in the values, we have:
ω = √(303.28 N/m / 8.35 kg)
Calculating this expression gives us:
ω ≈ √(36.359 N/m⋅kg)
ω ≈ 6.03 rad/s
Substituting the angular frequency and the amplitude into the equation for maximum velocity, we get:
v_max = (0.270 m) * (6.03 rad/s)
Calculating this expression gives us:
v_max ≈ 1.63 m/s
Therefore, the child's maximum velocity during the bounce is approximately 1.63 m/s.
(a) The force constant for each elastic band is approximately 303.28 N/m.
(b) The time for one complete bounce of the child is approximately 1.043 seconds.
(c) The child's maximum velocity during the bounce is approximately 1.63 m/s.
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What is the maximum flow rate of water in a smooth pipe 8.0 cm diameter if the flow is to be laminar
Answer:
0.05 m/s
Explanation:
We start by finding the average velocity of water in the pipe. This is done by saying
R(e) = ρv(avg)d/μ
Where,
R(e) = Reynolds number, and that's 2000
ρ = Density of water, 1000 kg/m³
μ = Viscosity of water, 10^-3
d = diameter of pipe
v(avg) = average velocity
Since we're interested in average velocity, we make v(avg) the subject of formula. So that
V(avg) = R(e).μ/ρ.d
V(avg) = 2000 * 10^-3 / 1000 * 0.08
V(avg) = 2 / 80
V(avg) = 0.025 m/s
The maximum flow rate of water in the pipe usually is twice the average velocity, and as such
V(max) = 2 * V(avg)
V(max) = 2 * 0.025
V(max) = 0.05 m/s
LOTS OF BRAINLIST WILL BE GIVING TO THOSE WHO HELP
chemical reaction for fossil fuels:combustion of fuels.
Difference between biomass and fossil fuels:how much carbon dioxide is produced
Comparing biomass with other renewable energy sources:does not have as much energy potential as fossil fuels.
Making energy choices locally: biomass
Is this right. Please help me ITS SOCIOLOGY
Answer:
Yes
Explanation:
sorry if im wrong
some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is _____________.
A. 1 B. Less than 1
C. Between 0 and 1 D. Less than or equal to 0
Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities isThe correct answer is C. Between 0 and 1.
Diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is between 0 and 1. Correlation measures the degree to which two securities move in relation to each other. A correlation of 1 indicates a perfect positive correlation, where the securities move in perfect tandem. A correlation of less than 1 indicates a less than perfect positive correlation, where the securities move somewhat together but not completely. When the correlation is between 0 and 1, it means that the securities have some degree of independence and tend to move differently from each other. This allows for diversification benefits as losses in one security may be offset by gains in another, reducing overall portfolio risk.
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The water droplets appear to be causing patterns of black and bright blue fringes. in terms of water in the real world (in a bowl, sink or pond), what do the bright blue and black colors mean?
Answer:
The bright blue and black colors represent the following:
Constructive and destructive interference are represented by the blue and black colors, respectively. When two water waves collide constructively, the resultant wave is bright blue, while when they collide destructively, the resultant wave is black in color.
Explanation:
When two propagating waves with the same frequency (say, [tex]\nu[/tex]) and wavelength (say,[tex]\lambda[/tex]) but slightly different amplitudes (say, A 1 and A 2) traveling in the same direction interfere or are superimposed on each other (that is incident at the same point or object), a third resultant wave with a different amplitude (increased or decreased) but same wavelength and frequency is generated.
The direction difference between the two waves determines whether they intervene constructively (increasing the amplitude of the resultant wave) or destructively (increasing the amplitude of the resultant wave) (decreased amplitude of the resultant wave). To put it another way, when the difference in direction between the two waves is of the form -
[tex]\Delta x = n\lambda , n=0,1,2,.....[/tex] is the order of interference.
The two waves are then assumed to be in phase, and the interference is constructive, resulting in the resultant wave having a larger amplitude (which is the sum of the two amplitudes [tex]A_1 +A_2[/tex] also known as a maxima). When the difference in direction between the two waves is in the form -
[tex]\Delta x = (2n-1)\frac{\lambda}{2} , n=0,1,2,.....[/tex] is the order of interference.
The two intervening waves are then said to be out of phase, and the interference is disruptive, resulting in the resultant wave having a lower amplitude (which is the difference between the two amplitudes [tex]A_1+A_2[/tex], also known as a minima).
Hence , the graphical representation of constructive (blue )and destructive (black) is attached.
Rita is a salon owner. She notices that her salon charged one of her clients, Linda, extra for a service that the clent did not request. What do you think Rita should do? Α. Remaln qulet about the extra money. B. Distribute the money equally among the staff. C. Call the client and Inform her that she was incorrectly charged. D. Try overcharging the next client too and check if it goes unnoticed.
Answer:
C hope it helps
call the client and inform her that she was incorrectly charged.
Answer:
The answer is C. call the client and inform her that she was incorrectky charged
Explanation:
an automobile engine slows down from 4,087 rpm to 1,830 rpm in 1,419 revolutions. calculate the magnitude of its angular acceleration in rad/s2. (assume a uniform deceleration.)
An automobile engine slows down from 4,087 rpm to 1,830 rpm in 1,419 revolutions the magnitude of the angular acceleration of the automobile engine is approximately 77.75 rad/s².
To calculate the magnitude of the angular acceleration, we can use the formula:
Angular acceleration (α) = (ω2 - ω1) / (t2 - t1)
where:
ω1 and ω2 are the initial and final angular velocities, respectively, and
t1 and t2 are the initial and final times, respectively.
Initial angular velocity ω1 = 4087 rpm
Final angular velocity ω2 = 1830 rpm
Number of revolutions (n) = 1419
First, we need to convert the angular velocities from rpm to radians per second (rad/s):
ω1 = (4087 rpm) * (2π rad/1 min) * (1 min/60 s) ≈ 426.97 rad/s
ω2 = (1830 rpm) * (2π rad/1 min) * (1 min/60 s) ≈ 191.46 rad/s
Next, we can calculate the time interval (t2 - t1) using the number of revolutions and the initial and final angular velocities:
t2 - t1 = (n / ω2) - (n / ω1)
t2 - t1 = (1419 / 191.46) - (1419 / 426.97) ≈ 3.3 s
Finally, we can calculate the magnitude of the angular acceleration:
α = (ω2 - ω1) / (t2 - t1)
α = (191.46 rad/s - 426.97 rad/s) / (3.3 s)
α ≈ -77.75 rad/s²
Therefore, the magnitude of the angular acceleration of the automobile engine is approximately 77.75 rad/s².
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Which of the following correctly defines the speed of a wave?
O A. v=1
B. A = vf
O C. v= f 2
OD. =v2
Answer:
V = f x λ
Explanation:
The options are confusing
A carbon resistor is 8 mm long and has a constant cross section of 0.3 mm2. The conductivity of carbon at room temperature is σ = 3 ✕ 104 per ohm·m. In a circuit its potential at one end of the resistor is 15 volts relative to ground, and at the other end the potential is 21 volts. A thin copper wire in the same circuit is 8 mm long and has a constant cross section of 0.3 mm2. The conductivity of copper at room temperature is σ = 6 ✕ 107 ohm-1m-1. The copper wire is in series with the carbon resistor in the same circuit mentioned above, with one end connected to the 21 volt end of the carbon resistor. Calculate the resistance R of the copper wire and the potential Vat end at the other end of the wire.
R =___ ohms
V at end = ____V
You can see that for most purposes a thick copper wire in a circuit would have practically a uniform potential. This is because the small drift speed in a thick, high-conductivity copper wire requires only a very small electric field, and the integral of this very small field creates a very small potential difference along the wire.
The resistance (R) of the copper wire in the circuit is 1600 ohms, and the potential (V) at the other end of the wire is 21 volts.
To calculate the resistance of the copper wire (R), we use the formula R = (ρ * L) / A, where ρ represents the resistivity of the material, L is the length of the wire, and A is the cross-sectional area. In this case, the length of the copper wire is 8 mm (0.008 m), and the cross-sectional area is 0.3 mm^2 (0.3 * 10^(-6) m^2). With the resistivity of copper being 6 * 10^7 ohm^(-1) m^(-1), we can calculate the resistance as follows: R = (6 * 10^7 ohm^(-1) m^(-1) * 0.008 m) / (0.3 * 10^(-6) m^2), which gives us 1600 ohms. Since the copper wire and the carbon resistor are connected in series in the circuit, the potential difference (V) across each component is the same. In the case of a thick, high-conductivity copper wire, the small drift speed of electrons requires only a very small electric field, resulting in a negligible potential difference along the wire. As a result, the potential throughout the thick copper wire remains practically uniform.
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  do batteries produce or make energy
Answer:
Batteries are intended to store chemical energy and then it converts into electricidal energy. So overall, batteries produce energy.
Explanation:
What is the magnitude of the electrostatic force between two electrons each having a charge of 1.6 x 10-19 C separated by a distance of 1.00 × l0– 8 meter?
A)
2.56 × 10–22 N
B)
2.30 × 10–20 N
C)
2.30 × 10–12 N
D)
1.44 × 10–1 N
Answer:
The correct option is (C).
Explanation:
The distance between two charges, [tex]d=10^{-8}\ m[/tex]
We need to find the magnitude of the electrostatic force between two electrons. The formula for the electric force between charges is given by :
[tex]F=\dfrac{kq^2}{r^2}\\\\=\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{(10^{-8})^2}\\\\=2.304\times 10^{-12}\ N[/tex]
So, the magnitude of force is equal to [tex]2.30\times 10^{-12}\ N[/tex].
n2 Find a linear homogeneous recurrence relation with constant coefficients that the sequence An = (n-3) (2") + NEN 2n satisfies. Do not forget to specify initial values.
The linear homogeneous recurrence relation with constant coefficients that the sequence is: An = -(-1)n + (3)n or An = (1)n + (3)n
The sequence An = (n-3)(2n) + n(2n) satisfies the linear homogeneous recurrence relation with constant coefficients. In order to prove this, we need to first find the general formula of the sequence.
The formula can be found by replacing n with n+1 as follows:
An+1 = (n+1-3)(2n+2) + (n+1)(2n+2)
An+1 = n(2n+4) + (n+1)(2n+2)
An+1 = 2n² + 4n + 2n² + 4n + n + 2n + 2
An+1 = 4n² + 7n + 2
The characteristic equation of the linear homogeneous recurrence relation is given by:
r² - 2r - 3 = 0
Solving this quadratic equation, we get:r = -1 or r = 3
Hence, the general formula of the sequence is given by:An = A(-1)n + B(3)n
Now, we need to find the values of A and B using the initial values of the sequence. The first two terms of the sequence are given by:
A0 = -6 and A1 = 2
Substituting these values in the general formula, we get:
-6 = A + B2 = -A + 3B
From the above two equations, we can solve for A and B to get:
A = -1 and B = 1
Hence, the linear homogeneous recurrence relation with constant coefficients that the sequence An = (n-3)(2n) + n(2n) satisfies is given by:
An = -(-1)n + (3)n or An = (1)n + (3)n
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Which one of the following items contains matter in the plasma state?
Stars
liquid water
ice cubes
Answer:
Stars i think
Explanation:
1) longer storms should print in the correct order, with 200ms between each event in the array and 400ms between each flash! and boom!
For accurate printing of longer storms, it is important to ensure that the events in the array are arranged in the correct order, with a 200ms delay between each event and a 400ms delay between each flash and boom.
When printing longer storms, it is crucial to maintain the correct order of events in the array. By arranging the events in the correct sequence, the storm will be printed accurately, providing a realistic representation. To achieve this, a delay of 200ms should be implemented between each event in the array. This delay ensures that each event is printed with the appropriate timing, creating a smooth and coherent storm simulation.
Additionally, it is necessary to introduce a 400ms delay between each "flash" and "boom" in the storm. This delay creates a distinct gap between these two elements, mimicking the natural occurrence of a lightning flash followed by the accompanying thunder. By allowing sufficient time between the flash and boom, the printed storm will convey a more realistic and immersive experience.
In summary, to accurately print longer storms, it is essential to maintain the correct order of events in the array and introduce appropriate delays. A 200ms delay between each event ensures accurate timing, while a 400ms delay between each flash and boom replicates the natural occurrence of lightning and thunder. Following these guidelines will result in a more realistic representation of storms when printing them.
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If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping?
Express your answer in terms of the variables R, r, and the constant g.
The speed οf the ball when it reaches the lοwest pοint οf the track, rοlling withοut slipping is √10/7g(R-r).
What is speed?Speed is a scalar quantity that measures hοw fast an οbject is mοving, withοut cοnsidering its directiοn. Speed is typically expressed in units such as meters per secοnd (m/s), kilοmeters per hοur (km/h), οr miles per hοur (mph).
Given:
The radius οf the ball is r.
The radius οf the track is R.
The acceleratiοn due tο gravity is 9.18 m/s².
The mοment οf inertia οf the spherical ball can be expressed as:
I=2/5m/r²
It is given that the ball is rοlling withοut slipping. The speed οf the ball can be expressed as:
v=rω
At the lοwest pοsitiοn οf the track, the ball has bοth types οf speed, namely angular and linear speed.
The tοtal energy οf the ball in the vertical circle can be expressed as:
cEₜ= Eᵦ+ K.Eₜ+ K.Eᵣ
mgR= mgr+ (1/2)mv²+ (1/2)Iω²
mg(R-r)= (1/2)mv²+ (1/2)* (2/5) mr²ω²
g(R-r)= (1/2)v²+ (1/5)v²
Here,
Eₜ is the tοtal energy οf the ball οn the track,
Eᵦ is the ball's energy in the vertical circle at the highest pοint,
K.Eₜ is the translatiοnal kinetic energy οf the ball,
K.Eᵣ is the rοtatiοnal kinetic energy οf the ball, and g is the acceleratiοn due tο gravity.
The abοve equatiοn can be further sοlved as:
cg(R-r)= (7/10)v²
v²= (10/7)g (R-r)
v= √(10/7)g (R-r)
Therefοre, the speed οf the ball when it reaches the lοwest pοint οf the track is √10/7g(R-r).
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A wagon wheel is a ring (hoop) of mass 77.1 kg and radius 0.630 m. The wagon is moving at 1.22 m/s. What is the TOTAL kinetic energy of the wheel? [?] Remember v = wr Enter
Kinetic energy is the energy that an object possesses due to its motion. Hence, the correct option is [109.5 J].
The formula to calculate kinetic energy is KE = 1/2 mv², where m is the mass of the object and v is its velocity or speed. In this question, the wagon wheel is a ring of mass 77.1 kg and radius 0.630 m. The wagon is moving at 1.22 m/s. We have to calculate the total kinetic energy of the wheel.The velocity of the wagon can be converted into the angular velocity of the wheel by using the formula v = wr. The angular velocity w is calculated as:w = v/rw = 1.22 m/s ÷ 0.630 m ≈ 1.936 rad/sNow that we know the angular velocity of the wheel, we can calculate its total kinetic energy using the formula KE = 1/2 Iw², where I is the moment of inertia of the wheel. For a ring-shaped object, the moment of inertia is given by I = mr².KE = 1/2 Iw²KE = 1/2 (mr²) (w²)KE = 1/2 (77.1 kg) (0.630 m)² (1.936 rad/s)²KE ≈ 109.5 J. Therefore, the total kinetic energy of the wagon wheel is approximately 109.5 J. Note: As per the question, the total kinetic energy of the wheel is required, not of the wagon.
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which of these is an impossible set of quantum numbers? a. n = 3, ℓ = 2, mℓ = 1, ms = –½ b. n = 3, ℓ = 1, mℓ = 1, ms = –1 c. n = 2, ℓ = 0, mℓ = 0, ms = –½ d. n = 1, ℓ = 0, mℓ = 0, ms = –½
n = 3, ℓ = 1, mℓ = 1, ms = -1 is an impossible set of quantum numbers.
What are quantum numbers?
Quantum numbers are a set of values used to describe the unique energy states and properties of electrons in an atom. They provide a way to distinguish and characterize the different electron orbitals within an atom.
Among the given options:
a. n = 3, ℓ = 2, mℓ = 1, ms = -½
b. n = 3, ℓ = 1, mℓ = 1, ms = -1
c. n = 2, ℓ = 0, mℓ = 0, ms = -½
d. n = 1, ℓ = 0, mℓ = 0, ms = -½
Option (a) represents a valid set of quantum numbers. However, options (b), (c), and (d) are impossible sets of quantum numbers.
For option (b), the value of mℓ is not within the allowed range for the given ℓ value. In this case, ℓ = 1, which means that mℓ can have values -1, 0, or 1. The value of mℓ = 1 is outside this range.
For options (c) and (d), the values of n and ℓ are not consistent. According to the rules of quantum numbers, the principal quantum number (n) should be greater than or equal to the azimuthal quantum number (ℓ). However, in both options (c) and (d), the value of n is lower than ℓ, which is not possible.
Therefore, the correct answer is option (b), as it represents an impossible set of quantum numbers.
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a thermodynamic cycle is a series of steps that ultimately returns to its beginning point. compute the total work performed around the thermodynamic cycle of quasi-static processes in the figure 7.
The total work performed around the thermodynamic cycle in Figure 7 is 350 Joules.
In a thermodynamic cycle, the total work performed is equal to the net area enclosed by the cycle on a pressure-volume (PV) diagram. From the given figure, we can observe that the cycle consists of two quasi-static processes: Process 1-2 and Process 2-3.
In Process 1-2, the system undergoes an expansion at constant pressure, represented by the horizontal line between points 1 and 2 on the PV diagram. As the volume increases, work is done by the system, and the work done in this process is given by the equation W_1-2 = PΔV = 2 * 50 = 100 Joules (where P is the constant pressure and ΔV is the change in volume).
In Process 2-3, the system undergoes compression at constant volume, represented by the vertical line between points 2 and 3 on the PV diagram. Work is done on the system during this process, and the work done in this process is given by the equation W_2-3 = -PΔV = -3 * 50 = -150 Joules (where P is the constant pressure and ΔV is the change in volume).
The total work performed around the cycle is the sum of the work done in each process, i.e., 100 Joules + (-150 Joules) = -50 Joules.
The total work performed around the thermodynamic cycle in Figure 7 is -50 Joules.
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planet a exerts a force on planet b. what can be said about the magnitude and direction of the gravitational force planet b exerts on planet a?
Planet A exerts a force on planet B, the magnitude and direction of the gravitational force planet B exerts on planet A the gravitational force exerted by planet B on planet A is the same as the magnitude of the gravitational force exerted by planet A on planet B
Newton's third law states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. Hence, if planet A exerts a gravitational force on planet B, then planet B exerts an equal and opposite gravitational force on planet A.The magnitude of the gravitational force exerted by planet B on planet A is the same as the magnitude of the gravitational force exerted by planet A on planet B, this is according to the law of universal gravitation,
This law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The direction of the gravitational force exerted by planet B on planet A is towards planet B's center, just as the direction of the gravitational force exerted by planet A on planet B is towards planet A's center. Therefore, we can say that the magnitude and direction of the gravitational force planet B exerts on planet A is equal and opposite to the gravitational force planet A exerts on planet B
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A 95 kg falling trunk strikes the ground with a speed of 40 m/s. Assuming that there is no loss of energy due to air resistance, what is the height from which the trunk falls?
Answer:
80 m or 81.3 m
Explanation:
Initially it had no velocity(as at rest). Let the height be h
Using conservation of energy:
Initial KE + PE = final KE + PE
(1/2) m(0)² + mgh = (1/2) m(40)² + mg(0)
mgh = (1/2) m (1600)
2gh = 16000
h = 1600/(2*10) {for g = 10}
h = 80
80 For g = 9.8, h = 81.3 m
Using Newton's eqⁿ of motion:
v² = u² + 2aS
40² = 0² + 2(g)S
1600/2g = S
For g = 10, S = 80 m
g = 9.8, S = 81.33 m
A metal rod is 25.000 cm long at 25.0 degrees Celsius. When heated to 102.0 degrees Celsius, it is 25.054 cm long. What is the coefficient of linear expansion for this metal.
Use the drop-down menus to complete the statements. Outlook allows users to insert symbols and characters not located on the , but they can have shortcut keys. Inserting horizontal lines in the message body breaks up different sections and mostly benefits people using Outlook on .
Answer:
Keyboard and Mobile devices
Explanation:
got it right on edge 2021
Answer:
Outlook allows users to insert symbols and characters not located on the
keyboard
, but they can have shortcut keys.
Inserting horizontal lines in the message body breaks up different sections and mostly benefits people using Outlook on
mobile devices
.
Explanation:
A 13 500 N car traveling at 50.0 km/h rounds a curve of radius 2.00 × 102 m. Find the following: a. the centripetal acceleration of the car b. the centripetal force c. the minimum coefficient of static friction between the tires and the road that will allow the car to round the curve safely
Answer:
a. 0.947 m/s^2
b. 1304.54 N
c. 0.0966
Explanation:
mass of car = 13500 N = 13500/9.8 = 1377.55 kg
velocity = 50 km/h = 50,000 m/h = 13.9 m/s
raidus = 204 m
a. centripetal acceleartion = v^2/r = 13.9^2/204 = 0.947 m/s^2
b. centripetal force = m*centripetal acceleration = 1377.55 * 0.947 = 1304.54 N
c. In order for the car to round the curve safely, static friction = centripetal force
static friction = coefficient of friction (mu) * mg = mu* 1377.55*9.8 = 13500mu
13500mu = 1304.54
mu = 1304.54/13500 = 0.0966
The acceleration, force and coefficient of friction is required.
Centripetal acceleration is [tex]0.965\ \text{m/s}^2[/tex]
Centripetal force is [tex]1328\ \text{N}[/tex]
Coefficient of friction is [tex]0.1[/tex]
N = Weight of car = 13500 N
v = Velocity = [tex]50=\dfrac{50}{3.6}=13.89\ \text{m/s}[/tex]
r = Radius = [tex]2\times 10^2\ \text{m}[/tex]
m = Mass of car = [tex]\dfrac{N}{g}[/tex]
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
Centripetal acceleration is
[tex]a_c=\dfrac{v^2}{r}\\\Rightarrow a_c=\dfrac{13.89^2}{2\times 10^2}\\\Rightarrow a_c=0.965\ \text{m/s}^2[/tex]
Force is given by
[tex]F_c=ma_c\\\Rightarrow F_c=\dfrac{N}{g}a_c\\\Rightarrow F_c=\dfrac{13500}{9.81}\times 0.965\\\Rightarrow F_c=1328\ \text{N}[/tex]
Coefficient of friction is given by
[tex]\mu=\dfrac{F_c}{N}\\\Rightarrow \mu=\dfrac{1328}{13500}\\\Rightarrow \mu=0.098\approx 0.1[/tex]
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A 72.0 kg ice skater is moving at 3.1 m/s on frictionless ice throws a 0.21 kg snowball horizontally at a speed of 28.0 m/s. What is the final velocity of the skater?
Answer:
the final velocity of the skater after throwing the snowball is 3.17 m/s.
Explanation:
Given;
mass of the ice skater, m₁ = 72 kg
initial velocity of the ice skater, u₁ = 3.1 m/s
mass of the snowball, m₂ = 0.21 kg
initial speed of the snowball, u₂ = 28.0 m/s
Let the final velocity of the skater after throwing the snowball = v
Apply the principle of conservation of linear momentum to determine v;
m₁u₁ + m₂u₂ = v(m₁ + m₂)
72 x 3.1 + 0.21 x 28 = v(72 + 0.21)
229.08 = v(72.21)
v = 229.08 / 72.21
v = 3.17 m/s
Therefore, the final velocity of the skater after throwing the snowball is 3.17 m/s.
Light and Polarization: Learn from Einstein the properties of light Virtual Lab
Light is an electromagnetic wave that consists of oscillating electric and magnetic fields. It exhibits various properties, including wavelength, frequency, speed, and polarization.
Polarization refers to the orientation of the electric field vector of a light wave. Unpolarized light consists of electric field vectors oscillating in all possible directions perpendicular to the direction of propagation. Polarized light, on the other hand, has its electric field vectors confined to a specific orientation. Polarization can be achieved through various mechanisms, such as reflection, scattering, or passing light through certain materials. Polarizers, such as polarizing filters, can selectively transmit or block light waves based on their polarization orientation. The study of light and its properties, including polarization, has contributed to numerous advancements in various fields, such as optics, telecommunications, and technology.
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A helicopter's speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of this helicopter?
7 m/s
2-2.3 m/s
2-1.9 m/s
21.67 m/s2
Given, Initial speed of the helicopter = 25 m/s. Final speed of the helicopter = 60 m/s, Time taken by the helicopter to change its speed from 25 m/s to 60 m/s is 5 seconds. Therefore, the acceleration of the helicopter is 7 m/s².Hence, option (A) is correct.
To find the acceleration of the helicopter, we can use the formula:
Acceleration= (Final velocity - Initial velocity)/Time,
Acceleration = (60 m/s - 25 m/s)/5 s,
Acceleration = 35 m/s/5 s,
Acceleration = 7 m/s²
Therefore, the acceleration of the helicopter is 7 m/s².
We know that,
Acceleration = change in velocity / time taken,
Acceleration can be defined as the rate at which an object changes its velocity.
It can be measured in units such as m/s², cm/s², etc.
Here, initial velocity = 25 m/s, Final velocity = 60 m/s time = 5 s.
Hence,
Acceleration= (Final velocity - Initial velocity)/Time
Acceleration = (60 m/s - 25 m/s)/5 s
Acceleration= 35/5
Acceleration= 7 m/s²
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what is the difference between malleability and ductile ??
Please don't post invalid answer please..!!
Please post correct answer please..!!
Answer:
A malleable material is one in which a thin sheet can be easily formed by hammering or rolling. ... In contrast, ductility is the ability of a solid material to deform under tensile stress.
a 10 kg mass slides down a flat hill that makes an angle of 10 degrees with the horizontal. If friction is negligible, what is the resultant force on the sled?
a) 98N
b) 1.7N
c) 97N
d) 17N
A 10 kg mass slides down a flat hill that makes an angle of 10 degrees with the horizontal. Therefore, the resultant force on the sled is option (c) 97N.
If friction is negligible, the resultant force on the sled will be calculated below:
We know that gravitational force can be broken into two components - force parallel to the slope and force perpendicular to the slope.
The parallel component is given by
Fg * sin θ = 10*9.8*sin10 = 16.87 N.
The perpendicular component is given by
Fg * cos θ = 10*9.8*cos10 = 96.94 N.
The total force acting on the sled is the vector sum of the two components: Resultant force = √(16.87² + 96.94²) = 97 N.
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What is specific heat capacity?
A. The amount of energy required for a unit mass of a substance to
undergo a phase change from a liquid to a gas.
B. The amount of energy required to raise the temperature of 1 kg of
a substance 1 °C.
C. The amount of energy required for a unit mass of a substance to
undergo a phase change from solid to liquid.
O D. A physical change from one form (or phase) of matter to another.
Eee A student conducts an investigation to determine how the force of gravity affects different objects dropped from different heights. The student tests each object one time and announces that all objects experienced gravity the same way. What is wrong with the student's reasoning?
Answer:
For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.
Explanation:
The force of gravity comes from Newton's second law with the force the universal attraction
F = ma
F = [tex]G \frac{m_1 M}{(R_e +h)^2}[/tex]
we substitute
[tex]G \frac{m_1 M}{ (R_e+ h)^2}[/tex] = m₁ a
where Re is the radius of the Earth 6.37 106 m
a = [tex]G\frac{M}{R_e^2} \ ( 1 + \frac{h}{R_e})^{-2}[/tex]
In general, the height is much less than the radius of the earth, therefore the term ha / Re is very small and we can use a series expansion leaving only the first fears.
(1 + x)⁻² = 1 -2x + [tex]\frac{2 \ 1}{2!}[/tex] x²
we substitute
a = g₀ ([tex]1 - 2 \frac{h}{R_e}[/tex] )
with
g₀ = [tex]G \frac{M}{R_e^2}[/tex]
let's launch the expression.
* For small height compared to the radius of the earth we can neglect the last term
g = g₀
* For height comparable to the radius of the Earth
g = g₀ [tex](1 - \frac{2h}{Re} )[/tex]
We see that the acceleration of gravity is decreasing.
For which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.
The student's reasoning gone wrong when the analysis is undertaken for the increasing heights, to drop the object.
The given problem is based on the concept of gravity and gravitational force. The force of gravity comes from Newton's second law with the force the universal attraction as,
F = ma
[tex]F=G\dfrac{mM}{(R+h)^{2}}\\\\\\ma = G\dfrac{mM}{(R+h)^{2}}[/tex]
Here, a is the linear acceleration, m is the mass of object, M is the mass of Earth, R is the radius of Earth and h is the height from where the objects will be dropped. Then,
[tex]a = \dfrac{GM}{R^{2}} \times(1+h/R)^{-2}[/tex]
In general, the height is much less than the radius of the earth, therefore the term h/ R is very small, hence can be neglected.
[tex]a = \dfrac{GM}{R^{2}}\\\\a=g = \dfrac{GM}{R^{2}}[/tex]
g is the gravitational acceleration.
For small height compared to the radius of the earth we can neglect the last term as,
a = g
And for the height comparable to radius of Earth,
[tex]a = \dfrac{GM}{R^{2}} \times(1+h/R)^{-2}\\\\a=g \times(1+h/R)^{-2}[/tex]
Clearly, the acceleration of gravity is decreasing, for which the reasoning of the boy is correct for small heights, but as height increases his analysis is not correct.
Thus, we can conclude that the student's reasoning gone wrong when the analysis is undertaken for the increasing heights, to drop the object.
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