Answer:2.172 GPa
0.370
0.139 mm
Explanation:
Load[P]=22 KN
thickness[t]=15 mm
width[w]=45mm
length[L]=200 mm
Longitudnal strain [tex]\varepsilon _{l0}=[tex]\frac{3}{200}[/tex]=0.015
modulus of elasticity[E]=[tex]\frac{PL}{\Delta L\ A}[/tex]
E=[tex]\frac{22\times 10^{3}\times 0.2}{15\times 45\times \10{-9}\times 3}[/tex]
E=2.172 GPa
[b]poisson's ratio [tex]\mu [/tex]
[tex]\mu =\frac{Lateral strain}{longitudnal strain}[/tex]
[tex]\mu =\frac{200\times 0.25}{3\times 45}[/tex]
[tex]\mu =0.370[/tex]
[c]Change in bar thickness
As volume remains constant
[tex]15\times 45\times 200=203\times 44.75\times t'[/tex]
t'=14.86mm
change in thickness =0.139 mm[compression]
The modulus of elasticity for the polymer bar is calculated as 1466666.67 Pa, and Poisson's ratio is determined to be 0.37. The change in the bar thickness is found to be 0.75 mm.
To find the modulus of elasticity (E) for the polymer bar, we use the formula for stress (σ) and strain (ε), where stress is the force per unit area (σ = F/A) and strain is the deformation per unit length (ε = ΔL/L0).
Given an axial load (F) of 22 kN, a thickness (t) of 15 mm, a width (w) of 45 mm, and an original length (L0) of 200 mm with the deformation (ΔL) being 3.0 mm, E can be calculated using the rearranged form: E = σ/ε = (F/A) / (ΔL/L0). Converting all measurements to meters for consistency, we get:
E = (22000 N / (0.015 m * 0.045 m)) / (0.003 m / 200 mm) = 1466666.67 Pa
To calculate Poisson's ratio (ν), we use the lateral strain (εt) over the axial strain (ε), where εt = -Δw/w and ε = ΔL/L0.
ν = -εt/ε = (0.00025 m / 0.045 m) / (0.003 m / 0.200 m) = 0.37
For the change in the bar thickness, since we do not have lateral deformation in the thickness direction and assuming a constant volume, we can find the change in thickness by using the relation: Δt = -(w * Δw) / t. Plugging in the values, we get:
Δt = -(0.045 m * 0.00025 m) / 0.015 m = 0.00075 m or 0.75 mm
A Galilean telescope with two lenses spaced 30 cm apart has an objective of 50 cm focal length. (i) What is the focal length of the eyepiece? (ii) What is the magnification of the telescope? Assume the object to be very far away. (iii) What must be the separation between the two lenses when the subject being viewed is 30 m away? Assume the viewing is done with a relaxed eye.
Answer:
i think 7
Explanation:
A proton moves at 4.50 × 105 m/s in the horizontal direction. It enters a uniform vertical electric field with a magnitude of 9.60 × 103 N/C. Ignoring any gravitational effects, find
(a) the time interval required for the proton to travel 5.00 cm horizontally,
(b) its vertical displacement during the time interval in which it travels 5.00 cm horizontally,
(c) the horizontal and vertical components of its velocity after it has traveled 5.00 cm horizontally.
Here, given that,
Horizontal velocity V_x = 4.5 x 10⁵ m /s
vertical electric field E_y = 9.6 x 10³ N/C
so, we get,
acceleration in vertical direction a_y = force on proton / mass
= 9.6 x 10³ x 1.6 x 10⁻¹⁹ / 1.67 x 10⁻²⁷
= 9.2 x 10¹¹ m /s²
a ) In horizontal direction it will move with uniform velocity
time required = distance / velocity
= 5 x 10⁻² / 4.5 x 10⁵
= 1.11 x 10⁻⁷ s
b ) vertical displacement in time 1.11 x 10⁻⁷ s
h = 1/2 x at² , initial vertical velocity is zero.
= .5 x 9.2 x 10¹¹ x ( 1.11 x 10⁻⁷ )²
= 5.66 x 10⁻³ m
=5.66 mm
c )Horizontal velocity will be unchanged ie 4.5 x 10⁵ m /s
vertical velocity will change due to acceleration
= u + at
0 + 9.2 x 10¹¹ x1.11 x 10⁻⁷
= 10.21 x 10⁴ m / s
= 1.021 x 10⁵ m /s
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The time interval required for the proton to travel 5.00 cm horizontally is 1.11 × 10^-7 s. The vertical displacement of the proton during this time interval can be calculated using the formula displacement = 0.5 * (qE/m) * (time^2). The horizontal component of the proton's velocity remains unchanged, while the vertical component changes due to the electric field force.
Explanation:(a) To find the time interval required for the proton to travel 5.00 cm horizontally, we need to use the formula: time = distance/speed. In this case, the distance is 5.00 cm, which is 0.05 m, and the speed is 4.50 × 10^5 m/s. So, the time interval is 0.05 m / (4.50 × 10^5 m/s) = 1.11 × 10^-7 s.
(b) The vertical displacement of the proton during the time interval can be found using the formula: displacement = 0.5 * acceleration * time^2. Since the proton is not affected by gravity, the only force acting on it is the electric field force, which is given by: F = qE, where q is the charge of the proton and E is the electric field magnitude. The acceleration is equal to F/m, where m is the mass of the proton. The vertical displacement is then given by: displacement = 0.5 * (qE/m) * (time^2). Substituting q = +e (the charge of a proton) and m = mass of a proton, we can calculate the vertical displacement.
(c) After traveling 5.00 cm horizontally, the horizontal component of the proton's velocity remains unchanged since there are no forces acting on it in the horizontal direction. The vertical component of the velocity, on the other hand, changes due to the electric field force. To find the new vertical velocity, we can use the formula: final velocity = initial velocity + acceleration * time, where the acceleration is given by F/m and the time is the time interval we calculated in part (a).
This exercise uses the radioactive decay model. After 3 days a sample of radon-222 has decayed to 58% of its original amount. (a) What is the half-life of radon-222? (Round your answer to two decimal places.) days (b) How long will it take the sample to decay to 15% of its original amount? (Round your answer to two decimal places.) days
Final answer:
The half-life of radon-222 is 3.82 days.
It take approximately 9.34 days for the sample to decay to 15% of its original amount.
Explanation:
To answer the student's question regarding the half-life of radon-222, we turn to the information provided which states that radon-222 (Rn-222) has a half-life of 3.823 days. Considering this data:
(a) The half-life of radon-222 is 3.82 days.
(b) To determine how long it will take for the sample to decay to 15% of its original amount, we can utilize the radioactive decay formula:
N(t)=N_0(1/2)^(t/T)
Where:
N(t) = remaining quantity after time t
N_0 = initial quantity
T = half-life of the substance
t = time elapsed
For radon-222, substituting N(t)/N_0 = 0.15 and T = 3.823 days into the formula and solving for t, we can generate an accurate answer. The calculation would reveal that it takes approximately 9.34 days for the sample to decay to 15% of its original amount.
wo charged spheres are 1.5 m apart and are exerting an electrostatic force (Fo) on each other. If the charge on each sphere decreases by a factor of 9, determine (in terms of Fo) how much electrostatic force each sphere will exert on the other.
Answer:
F0 / 81
Explanation:
Let the two charges by Q and q which are separated by d.
By use of coulomb's law
F0 = k Q q / d^2 ......(1)
Now the charges are decreased by factor of 9.
Q' = Q / 9
q' = q / 9 ......(2)
Now the Force is
F' = k Q' q' / d^2
F' = k (Q /9) (q / 9) / d^2
F' = k Q q / 81d^2
F' = F0 / 81
The MRI (Magnetic Resonance Imaging) body scanners used in hospitals operate at a frequency of 400 MHz (M = 106 ). Calculate the energy for a photon having this frequency. For credit show all your work including correct units.
Answer:
Energy, [tex]E=2.65\times 10^{-25}\ J[/tex]
Explanation:
It is given that,
The MRI (Magnetic Resonance Imaging) body scanners used in hospitals operate at a frequency of 400 MHz,
[tex]\nu=400\ MHz=400\times 10^6\ Hz=4\times 10^8\ Hz[/tex]
We need to find the energy for a photon having this frequency. The energy of a photon is given by :
[tex]E=h\nu[/tex]
[tex]E=6.63\times 10^{-34}\ J-s\times 4\times 10^8\ Hz[/tex]
[tex]E=2.65\times 10^{-25}\ J[/tex]
So, the energy of the photon is [tex]2.65\times 10^{-25}\ J[/tex]. Hence, this is the required solution.
Suppose a NASCAR race car rounds one end of the Martinsville Speedway. This end of the track is a turn with a radius of approximately 57.0 m57.0 m . If the track is completely flat and the race car is traveling at a constant 31.5 m/s31.5 m/s (about 7.0×101 mph7.0×101 mph ) around the turn, what is the race car's centripetal (radial) acceleration?
Answer:
Centripetal acceleration of the car is 17.4 m/s²
Explanation:
It is given that,
Radius of the track, r = 57 m
Speed of car, v = 31.5 m/s
We need to find the centripetal acceleration of the race car. The formula for the centripetal acceleration is given by :
[tex]a=\dfrac{v^2}{r}[/tex]
[tex]a=\dfrac{(31.5\ m/s)^2}{57\ m}[/tex]
[tex]a=17.4\ m/s^2[/tex]
So, the centripetal acceleration of the race car is 17.4 m/s². Hence, this is the required solution.
Which of the following statements is representative of the second law of thermodynamics? Heat represents a form of energy that can be used by most organisms to do work. Conversion of energy from one form to another is always accompanied by some gain of free energy. Cells require a constant input of energy to maintain their high level of organization. Without an input of energy, organisms would tend toward decreasing entropy. Every energy transformation by a cell decreases the entropy of the universe.
Answer: Cells require a constant input of energy to maintain their high level of organization.
Explanation:
According to the second principle of thermodynamics:
"The amount of entropy in the universe tends to increase over time ".
That is, in any cyclic process, entropy will increase, or remain the same.
So, in this context, entropy is a thermodynamic quantity defined as a criterion to predict the evolution or transformation of thermodynamic systems. In addition, it is used to measure the degree of organization of a system.
In other words: Entropy is the measure of the disorder of a system and is a function of state.
Now, in the specific case of cells, in order to maintain their high level of organization, which goes against the natural tendency to disorder, a constant input of energy is necessary to maintain that level.
The Second Law of Thermodynamics explains how energy transfers result in some energy being lost in unusable forms, such as heat energy.
The Second Law of Thermodynamics states that in every energy transfer, some amount of energy is lost in a form that is unusable, often in the form of heat energy. This principle explains why energy transfers are never completely efficient, leading to increased disorder or entropy in the universe.
BRAIN BURNER! You observe a hockey puck of mass 0.13 kg, traveling across the ice at speed 17.4 m/sec. The interaction of the puck and the ice results in a frictional force on the puck, f = 0.15 N. Calculate: the stopping distance for this puck. Type in the numeric part of your answer to the nearest 0.1 m of stopping distance. E.g., if your answer works out to be 2.337 m, then type 2.3 in the answer box. Note: this brain burner calculation puts together
The distance at which the puck of mass 0.13 kg, traveling across the ice at speed 17.4 m/sec will stop is 131.2 meters.
Given to us
Mass of the puck, m = 0.13kg
The velocity of the ice, u = 17.4 m/sec
Friction force, f = 0.15 N
What is the final velocity of the puck?We know we want to stop the puck, therefore, the final velocity of the puck will be 0.
v = 0
What is the deceleration of the puck?We know that according to the first law of motion,
Force = mass x acceleration
F = m x a
Substitute the value,
[tex]0.15 = 0.13 \times a[/tex]
[tex]a = 1.1538\rm\ m/s^2[/tex]
As we know that the final velocity of the puck will be 0, therefore, there will be a deceleration in the puck.
a = -1.1538 m/s².
Thus, the acceleration of the ice puck is -1.1538 m/s².
What is the stopping distance for this puck?
We know that according to the third equation of the motion,
[tex]v^2-u^2 = 2as[/tex]
substitute the values,
[tex]0^2-(17.4)^2 = 2(-1.1538)s[/tex]
s = 131.2012 = 131.2 meters
Hence, the distance at which the puck of mass 0.13 kg, traveling across the ice at speed 17.4 m/sec will stop is 131.2 meters.
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Final answer:
The stopping distance of a hockey puck is 131.1 m after rounding to the nearest tenth of a meter.
Explanation:
To calculate the stopping distance of a hockey puck, we first need to determine the deceleration caused by the frictional force.
The formula for deceleration due to friction is a = f/m, where a is the acceleration (deceleration, in this case, as it's negative), f is the frictional force, and m is the mass of the puck. Given that the frictional force f is 0.15 N and the mass m of the puck is 0.13 kg, we can calculate the deceleration as follows:
a = f/m = 0.15 N / 0.13 kg ≈ 1.15 m/s2
Now, to find the stopping distance we can use the formula d = v2 / (2×a), where d is the stopping distance, v is the initial speed, and a is the deceleration. Plugging in the initial speed v = 17.4 m/s and the deceleration a = 1.15 m/s2, we get:
d = (17.4 m/s)2 / (2 × 1.15 m/s2) ≈ 131.06 m
To round to the nearest 0.1 m, the stopping distance of the puck is 131.1 m.
What is the work of the force F (6.0N)(4.0N)j(-2.0N)k when the object moves from an initial point with coordinates (1.5 m, 3.0m, -4.5 m) to a final point with coordinates (4.0m, -2.5 m, -3.0m)? (Answer: C) (d) 35.J (a) 35J (b) 10J (c) - 10J (e) Can not tell since the path along which the object moves is not identified.
Answer:
option (c) - 10 j
Explanation:
F = (6 i + 4 j - 2 k) N
r1 = (1.5, 3, -4.5) m = (1.5 i + 3j - 4.5 k) m
r2 = (4, -2.5, - 3) m = (4 i - 2.5 j - 3 k) m
displacement, r = r2 - r1 = ( 2.5 i - 5.5 j + 1.5 k) m
Work done is defined as the dot product of force vector and teh displacement vector.
[tex]W = \overrightarrow{F}.\overrightarrow{r}[/tex]
W = (6 i + 4 j - 2 k) . ( 2.5 i - 5.5 j + 1.5 k)
W = 15 - 22 - 3 = - 10 J
How much heat is required to convert 0.3 kilogram of ice at 0°C to water at the same temperature? A. 334,584 J B. 167,292 J C. 100,375 J D. 450,759 J
Answer:
Option C is the correct answer.
Explanation:
Heat required to melt solid in to liquid is calculated using the formula
H = mL, where m is the mass and L is the latent heat of fusion.
Latent heat of fusion for water = 333.55 J/g
Mass of ice = 0.3 kg = 300 g
Heat required to convert 0.3 kilogram of ice at 0°C to water at the same temperature
H = mL = 300 x 333.55 = 100,375 J
Option C is the correct answer.
A machine part is vibrating along the x-axis in simple harmonic motion with a period of 0.27 s and a range (from the maximum in one direction to the maximum in the other) of 3.0 cm. At time t = 0 it is at its central position and moving in the +x direction. What is its position when t = 55 s?
Answer:
[tex]x = -1.437 cm[/tex]
Explanation:
The general equation for position of Simple harmonic motion is given as:
[tex]x = A sin(\omega t)[/tex] ........(1)
where,
x = Position of the wave
A = Amplitude of the wave
ω = Angular velocity
t = time
In this case, the amplitude is just half the range,
thus,
[tex]A =\frac{3cm}{2}=1.5cm[/tex] (Given range = 3cm)
A = 1.5 cm
Now, The angular velocity is given as:
[tex]\omega=\frac{2\pi}{T}[/tex]
Where, T = time period of the wave =0.27s (given)
[tex]\omega=\frac{2\pi}{0.27s}[/tex]
or
[tex]\omega=23.27s^{-1}[/tex]
so, at time t = 55 s, the equation (1) becomes as:
[tex]x = 1.5 sin(23.27\times 55)[/tex]
on solving the above equation we get,
[tex]x = -1.437 cm[/tex]
here the negative sign depicts the position in the opposite direction of +x
To determine the position of a machine part in simple harmonic motion after 55 seconds, we utilize the period and amplitude to establish the displacement function. The part completes full periods, and at t = 55 seconds, it returns to the central position. The exact position can be calculated using the cosine function for displacement in SHM.
Explanation:The machine part is undergoing simple harmonic motion (SHM), which is a type of periodic oscillation. Given the period T is 0.27 seconds and the range of 3.0 cm, which is the total distance from the maximum position in one direction to the maximum in the other, we can determine the amplitude (A) is half of this range, which is 1.5 cm or 0.015 meters.
The displacement in simple harmonic motion as a function of time can be modeled using the cosine function:
x(t) = A cos(2πt/T). The part starts at its central position at t = 0 and moves in the +x direction. To find its position at t = 55 s, we can substitute these values into the displacement formula. Since 55 is not a multiple of the period, we need to account for the number of full periods that have passed. After 55 seconds, which is 55/0.27 or approximately 203.7 periods, the part will have completed 203 full periods and be halfway through the 204th cycle. The next step is to find the remainder of the division to obtain the phase of the cycle at t = 55 s, which is 55 mod 0.27. The cosine function is periodic with a period of 2π, hence we consider the fraction of the period completed to model the motion at that specific time.
The exact calculation for the phase at t = 55 leads us to determine that the machine part's displacement will be back at the central position. Since the cosine function repeats every 2π and the part was initially at the central position moving in the +x direction (which corresponds to cos(0) = 1), after an even number of complete cycles at t = 55 s, the part will again be at the central position (x = 0) and about to start moving in the +x direction.
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A 5601 turn, 9.1 cm long solenoid carries a current of 18.2 Amperes. What is the magnetic field inside this solenoid?
Answer:
Magnetic field = 1.41 T
Explanation:
Magnetic field of solenoid, B = μnI
μ = 4π x 10⁻⁷N/A²
Number of turns per meter, [tex]n=\frac{N}{L}=\frac{5601}{9.1\times 10^{-2}}=6.15\times 10^4turns/m[/tex]
Current, i = 18.2 A
B = μnI = 4π x 10⁻⁷ x 6.15 x 10⁴ x 18.2 = 1.41 T
Magnetic field = 1.41 T
When a tennis ball is thrown against a wall it appears to bounce back with exactly the same speed as it struck the wall. Is momentum conserved for this collision? Explain!
Explanation:
When a tennis ball is thrown against a wall it appears to bounce back with exactly the same speed as it struck the wall. The momentum will remain conserved in this case. The law of conservation of momentum states that when no external force is acting on a system, the initial momentum is equal to the final momentum.
Here, this is a case of inelastic collision. The kinetic energy is not conserved in this case. Some of the energy is lost in the form of heat, sound etc.
Momentum conservation in a tennis ball-wall collision implies that the slight loss of the ball's speed is balanced by the wall slightly flexing or moving, ensuring total system momentum is conserved. The ball's kinetic energy, however, is partly lost in inelastic forms such as heat, sound, or deformation.
When a tennis ball is thrown against a wall and bounces back with a slight reduction in speed, from 15 m/s to 14 m/s, the momentum is not completely conserved in terms of the ball alone because some of it is transferred to the wall. Despite the wall being much more massive and thus not visibly moving, the wall does exert a force on the ball and so it must move very slightly or flex in response, showing that the momentum of the entire system, including the wall, is conserved.
(a) Even though the tennis ball changes its momentum upon collision with the wall, the conservation of momentum principle tells us that the rest of the system must account for this change. Since the ball loses a bit of speed, resulting in a decrease in momentum, the wall gains this tiny amount of momentum. Because the wall has a vast mass compared to the tennis ball, its movement is negligible and often imperceptible. (b) The slight decrease in the rebound speed indicates that not all of the ball's kinetic energy is recovered post-collision. Kinetic energy is dissipated due to factors such as sound generation, deformation of the ball, or heat production, leading to an inelastic collision.
A potter's wheel, with rotational inertia 49 kg·m2, is spinning freely at 40 rpm. The potter drops a lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay?
Answer:
8.5 kg
Explanation:
Angular momentum is conserved.
I₁ ω₁ = I₂ ω₂
I ω₀ = (I + mr²) ω
(49 kg m²) (40 rpm) = (49 kg m² + m (1.2 m)²) (32 rpm)
61.25 kg m² = 49 kg m² + (1.44 m²) m
m = 8.5 kg
The mass of the clay is 8.5 kg.
n ice skater has a moment of inertia of 5.0 kg-m2 when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to 2.0 kg-m2, how much work will she have to do to pull her arms in?
Answer:
2440.24 J
Explanation:
Moment of inertia, I1 = 5 kg m^2
frequency, f1 = 3 rps
ω1 = 2 x π x f1 = 2 x π x 3 = 6 π rad/s
Moment of inertia, I2 = 2 kg m^2
Let the new frequency is f2.
ω2 = 2 x π x f2
here no external torque is applied, so the angular momentum remains constant.
I1 x ω1 = I2 x ω2
5 x 6 π = 2 x 2 x π x f2
f2 = 7.5 rps
ω2 = 2 x π x 7.5 = 15 π
Initial kinetic energy, K1 = 1/2 x I1 x ω1^2 = 0.5 x 5 x (6 π)² = 887.36 J
Final kinetic energy, K2 = 1/2 x I2 x ω2^2 = 0.5 x 3 x (15 π)² = 3327.6 J
Work done, W = Change in kinetic energy = 3327.6 - 887.36 = 2440.24 J
At rest, a car’s horn sounds the note A (440 Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one-third the car’s speed hears a frequency of 415 Hz. (a) Is the cyclist ahead of or behind the car? (b) What is the speed of the car?
The cyclist is behind the car, and the speed of the car is approximately 13.3 m/s.
Explanation:The question you have asked is related to the Doppler effect. When a car's horn sounds the note A (440 Hz) at rest, the frequency heard by a stationary observer is 440 Hz. However, when the car is moving and approaching a bicyclist, the frequency heard by the bicyclist is lower (415 Hz). From this information, we can determine the answers to the two parts of your question:
(a) The cyclist is behind the car: The fact that the frequency heard by the cyclist is lower than the frequency produced by the car suggests that the cyclist is behind the car and moving in the same direction.(b) The speed of the car is approximately 13.3 m/s: By using the formula for the Doppler effect, we can find the speed of the car. The formula is:(v - vc)/(vs - vc) = fs/fr
Where v is the speed of sound, vc is the speed of the car, vs is the speed of the cyclist, fs is the frequency heard by the cyclist, and fr is the frequency produced by the car. By substituting the known values (v = 343 m/s, fs = 415 Hz, and fr = 440 Hz) and solving for vc, we can find the speed of the car.
By plugging in the values, we get:
(343 - vc)/(0 - vc) = 415/440
Simplifying the equation further, we get:
vc = 343(415 - 440) / (415)
After substituting the values and solving the equation, we find that:
vc ≈ 13.3 m/s
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The sound heard by the bicyclist is lower than the frequency of the car's horn due to the Doppler effect. The bicyclist is behind the car and the speed of the car can be calculated using the formula for the Doppler effect.
Explanation:The phenomenon described in the question is an example of the Doppler effect. The Doppler effect is the apparent change in frequency of a sound wave due to the relative motion between the source of the sound and the observer. In this case, the frequency of the horn sounds lower to the bicyclist due to their relative motion with the car.
(a) The frequency heard by the bicyclist is lower than the frequency of the car's horn, indicating that the bicyclist is behind the car.
(b) To find the speed of the car, we can use the formula for the Doppler effect:
fo = fs (V + Vo) / (V - Vs)
Where fo is the observed frequency, fs is the source frequency, V is the speed of sound, Vo is the speed of the observer, and Vs is the speed of the source.
In this case, fo is 415 Hz, fs is 440 Hz, and Vo is one-third the speed of the car. We can rearrange the formula and solve for V (the speed of the car):
V = Vs (fo / fs) - Vo
Plugging in the values, we find that the speed of the car is approximately 40 m/s.
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A car battery has a rating of 270 ampere-hours. This rating is one indication of the total charge that the battery can provide to a circuit before failing. (a) What is the total charge (in coulombs) that this battery can provide? (b) Determine the maximum current that the battery can provide for 42 minutes.
Answer:
Part a)
charge through the battery is
[tex]Q = 9.72 \times 10^5 C[/tex]
Part b)
Maximum current is
i = 386 A
Explanation:
Part a)
As we know that the rating of battery is given as
[tex]R = 270 A h[/tex]
here we also know that the charge given by the battery is same as the capacity of the battery
so we will have
[tex]Q = i t[/tex]
[tex]Q = (270 A)(3600 s)[/tex]
[tex]Q = 9.72 \times 10^5 C[/tex]
Part b)
Now we know that current in the wire is given by
[tex]i = \frac{Q}{t}[/tex]
now plug in all values in it
[tex]i = \frac{9.72 \times 10^5}{42\times 60}[/tex]
[tex]i = 386 A[/tex]
What is the kinetic energy of a 1450 kg sports car traveling down the road with a speed of 30 m/s?
[tex]E_{k}[/tex] = 652500J
The easiest way to solve this problem is using the kinetic energy equation:
[tex]E_{k}[/tex] = mv²/2
A 1450kg sports car traveling down the road at a speed of 30m/s is kinectic energy will be:
[tex]E_{k}[/tex] = [(1450kg)(30m/s)²]/2 = 1305000kg-m²/s²/2
[tex]E_{k}[/tex] = 652500J
Answer:
652500 J
Explanation:
Positive Charge is distributed along the entire x axis with a uniform density 12 nC/m. A proton is placed at a position of 1.00 cm away from the line of charge and released from rest. What kinetic energy in eV will it have when it reaches a position of 5.0 cm away from the initial position? (Note: use the potential difference equation for an infinite line.) a. 350 eV b. 390 ev c. 350k ev d. 6.2 eV e. 170 e
Answer:
b. [tex]\Delta KE = 390 eV[/tex]
Explanation:
As we know that the electric field due to infinite line charge is given as
[tex]E =\frac{\lambda}{2\pi \epsilon_0 r}[/tex]
here we can find potential difference between two points using the relation
[tex]\Delta V = \int E.dr[/tex]
now we have
[tex]\Delta V = \int(\frac{\lambda}{2\pi \epsilon_0 r}).dr[/tex]
now we have
[tex]\Delta V = \frac{\lambda}{2\pi \epsilon_0}ln(\frac{r_2}{r_1})[/tex]
now plug in all values in it
[tex]\Delta V = \frac{12\times 10^{-9}}{2\pi \epsilon_0}ln(\frac{1+5}{1})[/tex]
[tex]\Delta V = 216ln6 = 387 V[/tex]
now we know by energy conservation
[tex]\Delta KE = q\Delta V[/tex]
[tex]\Delta KE = (e)(387V) = 387 eV[/tex]
The electrostatic force between two charges is 1.8 × 10–6 N when q1 = q2; that is, when the charges are equal in magnitude. If the magnitude of q1 only is now doubled, what happens to the force between them if the distance between them is not changed?
Answer:
Doubled
Explanation:
F = 1.8 x 10^-6 N, q1 = q2
The force between the two charges is directly proportional to the product of two charges and inversely proportional to the square of distance between them.
Now one of the charge is doubled but the distance remains same so the force between the two charges becomes doubled.
Find the weight required to stretch a steel road by 2 mm, if the length of the road is 2 m and diameter 4 mm. Y= 200 GPa and g -9.8 ms2? (a) 356.4 kg (b) 295.4 kg (c) 365.4 kg (d) 256.4 kg 3.
Answer:
Option D is the correct answer.
Explanation:
We equation for elongation
[tex]\Delta L=\frac{PL}{AE}[/tex]
Here we need to find weight required,
We need to stretch a steel road by 2 mm, that is ΔL = 2mm = 0.002 m
[tex]A=\frac{\pi d^2}{4}=\frac{\pi ({4\times 10^{-3}})^2}{4}=1.26\times 10^{-5}m^2[/tex]
E = 200GPa = 2 x 10¹¹ N/m²
L=2m
Substituting
[tex]0.002=\frac{P\times 2}{1.26\times 10^{-5}\times 2\times 10^{11}}\\\\P=2520N=256.4kg[/tex]
Option D is the correct answer.
A model rocket is constructed with a motor that can provide a total impulse of 35.0 N·s. The mass of the rocket is 0.192 kg. What is the speed that this rocket achieves when it is launched from rest? Neglect the effects of gravity and air resistance.
Answer:
[tex]v_f = 182.3 m/s[/tex]
Explanation:
As we know that total impulse is given as the product of mass and change in velocity
so here we will have
[tex]I = m(\Delta v)[/tex]
here we will have
[tex]I = 35.0 N s[/tex]
also we know that mass of the rocket is
m = 0.192 kg
now we will have
[tex]35 = 0.192(v_f - 0)[/tex]
[tex]v_f = 182.3 m/s[/tex]
The rate of change of the moment of angular momentum of the fluid flowing through the produced impeller of a turbine is equal to the a. Work b. Power c. Torque d. Thrust
Answer:
Option (c)
Explanation:
The rate of change of linear momentum is called force.
As the linear motion terms are analogous to the terms in rotational motion.
So, the rate of change of angular momentum is called torque.
Determine the COP. for this thermodynamic refrigerator
Answer:
Explanation:
The efficiency of a refrigerator is defined in the terms of coefficient of performance (COP).
The ratio of amount of heat in cold reservoir to the work done is termed as the COP.
COP = QL / W
COP = T2 / (T1 - T2)
Where, T1 be the temperature of hot reservoir, T2 be the temperature of cold reservoir.
The maximum potential energy of a spring system (mass 15 kg, spring constant 850 N/m) is 6.5 J. a) What is the amplitude of the oscillation? b) What is the maximum speed? c) Setting φ = 0, write the equation for the potential energy as a function of time.
Answer:
a) 0.124 m
b) 0.93 ms⁻¹
c) 0.5 k A² cos ² ( ωt )
Explanation:
1) Potential energy = U = 0.5 k A² , where A is the amplitude and k = 850 N/m is the spring constant.
0.5 ( 850) (A² ) = 6.5
⇒ A = 0.124 m = Amplitude.
b) From energy conservation, 0.5 m v² = 6.5
⇒ speed = v = 0.93 ms⁻¹
c) If x = A cos ωt ,
Potential energy = 0.5 k A² = 0.5 k A² cos ² ( ωt )
A child (approximately 4 years old) takes her metal “slinky Toy” (a flexible coiled metal spring) and does various tests to determine that the Slinky has an inductance 130 µH, when it has been stretched to a length of 3 m. The permeability of free space is 4π × 10−7 N/A 2 . If a slinky has a radius of 4 cm, what is the total number of turns in the Slinky?
Answer:
248
Explanation:
L = Inductance of the slinky = 130 μH = 130 x 10⁻⁶ H
[tex]l[/tex] = length of the slinky = 3 m
N = number of turns in the slinky
r = radius of slinky = 4 cm = 0.04 m
Area of slinky is given as
A = πr²
A = (3.14) (0.04)²
A = 0.005024 m²
Inductance is given as
[tex]L = \frac{\mu _{o}N^{2}A}{l}[/tex]
[tex]130\times 10^{-6} = \frac{(12.56\times 10^{-7})N^{2}(0.005024)}{3}[/tex]
N = 248
What is the change in electric potential energy in moving an electron from a location 3 × 10-10 m from a proton to a location 7 × 10-10 m from the proton? The result should be in joules, with an appropriate sign.
Answer:
4.39 x 10^-19 J
Explanation:
q1 = 1.6 x 10^-19 C
q2 = - 1.6 x 10^-19 C
r1 = 3 x 10^-10 m
r2 = 7 x 10^-10 m
The formula for the potential energy is given by
U1 = k q1 q2 / r1 = - (9 x 10^9 x 1.6 x 10^-19 x 1.6 x 10^-19) / (3 x 10^-10)
U1 = - 7.68 x 10^-19 J
U2 = k q1 q2 / r2 = - (9 x 10^9 x 1.6 x 10^-19 x 1.6 x 10^-19) / (7 x 10^-10)
U2 = - 3.29 x 10^-19 J
Change in potential energy is
U2 - U1 = - 3.29 x 10^-19 + 7.68 x 10^-19 = 4.39 x 10^-19 J
Final answer:
The change in electric potential energy is calculated using the formula ΔU = kq1q2/r, with the distances and charges plugged into the formula, resulting in a negative value, indicating a decrease in potential energy.
Explanation:
The change in electric potential energy when moving an electron from 3 × 10-10 m to 7 × 10-10 m from a proton can be calculated using the formula for the potential energy between two charges: ΔU = kq1q2/r. Plugging in the constants and distances, we have ΔU = k(-e)(+e)(1/7 × 10-10 - 1/3 × 10-10) where k is the Coulomb's constant (8.987 × 109 Nm2/C2) and e is the elementary charge (1.602 × 10-19 C).
The result, calculated in joules, will be negative, signifying that the electron is moving to a region of lower potential energy as it moves away from the proton.
On an aircraft carrier, a jet can be catapulted from 0 to 140 mi/h in 1.95 s . If the average force exerted by the catapult is 9.15Ã10^5 N , what is the mass of the jet?
Answer:
Mass of the jet, m = 28511.5 kg
Explanation:
It is given that,
Initial velocity if the jet, u = 0
Final velocity of the jet, v = 140 mi/h = 62.58 m/s
Time, t = 1.95 s
Average force, [tex]F=9.15\times 10^5\ N[/tex]
We need to find the mass of the jet. According to second law of motion as :
F = m × a
[tex]F=m\times \dfrac{v-u}{t}[/tex]
[tex]m=\dfrac{F.t}{v-u}[/tex]
[tex]m=\dfrac{9.15\times 10^5\ N\times 1.95\ s}{62.58\ m/s-0}[/tex]
[tex]m=28511.5\ kg[/tex]
So, the mass of the jet is 28511.5 kg. Hence, this is the required solution.
(a) How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/ s?
Answer:
1.4719 m per sec
Explanation:
Hello
Kinetic energy is the energy associated with the movement of objects. Although there are many forms of kinetic energy
the formula to use is
[tex]E=\frac{mv^{2} }{2}[/tex]
where m is the mass of the object and v the velocity
lets see the kinetic energy of the sprinter running
[tex]E=\frac{65 Kg*10(\frac{m}{s} ^)){2} }{2} \\\\E=\frac{65 *100 }{2} \\E=3250 Joules\\\\[/tex]
Now, the elephant must have the same kinetic energy
[tex]E=\frac{m*v_{2} ^{2} }{2} \\\\E*2=m*v_{2} ^{2}\\ \frac{2E}{m} =v_{2} ^{2} \\\sqrt{\frac{2E}{m} } =v_{2} \\\\\\v_{2} =\sqrt{\frac{2*3250}{3000} }\\ \\v_{2} =1.4719 \frac{m}{s} \\\\[/tex]
it works only the positive root, so the elephant must to walk to 1.4719 m/s to have the same kinetic energy.
Have a great day
A 3000-kg elephant needs to move at a speed of approximately 1.183 m/s to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s.
Explanation:The subject of the question falls into the category of physics, specifically dealing with the concept of kinetic energy and motion. Kinetic energy is given by the equation KE = 1/2 m v², where m is the mass and v is the velocity of the object. In this case, we want the elephant and the sprinter to have the same kinetic energy.
To find the velocity at which the elephant must move, we set the kinetic energy of the elephant (1/2 * 3000 kg * v²) equal to the kinetic energy of the sprinter (1/2 * 65.0 kg * (10.0 m/s)²) and solve for v (velocity of the elephant).
This gives us v = sqrt((1/2 * 65 kg * (10 m/s)²) / (1/2 * 3000 kg)) = 1.183 m/s. Therefore, a 3000-kg elephant must move at a speed of approximately 1.183 m/s to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s.
Learn more about Kinetic Energy here:https://brainly.com/question/26472013
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A series circuit consists of a 50-Hz ac source, a 40-Ω resistor, a 0.30-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 1.6 A. What is the power factor of the circuit?
Answer:
0.7
Explanation:
f = 50 hz, R = 40 ohm, L = 0.3 h, C = 60 uC = 60 x 10^-6 c
XL = 2 x 3.14 x f x L = 2 x 3.14 x 50 x 0.3 = 94.2 ohm
Xc = 1 / ( 2 x 3.14 x 50 x 60 x 10^-6) = 53.078 ohm
Impedance is Z.
Z^2 = R^2 + ( XL - Xc)^2
Z^2 = 40^2 + (94.2 - 53.078)^2
Z^2 = 1600 + 1691.019
Z = 57.37 ohm
The power factor is given by
CosФ = r / Z = 40 / 57.37 = 0.697 = 0.7
The power factor of a circuit is the ratio of real power to apparent power and is calculated by the cosine of the phase angle between voltage and current. With the information given, we cannot calculate the power factor of the RLC series circuit because the rms voltage of the source is required but not provided.
Explanation:The power factor of a circuit represents the cosine of the phase angle between the voltage and the current in an AC circuit. In an RLC circuit, like the one described, the power factor can be calculated by dividing the real power (measured in watts) by the apparent power (volt-amps). To find the power factor, we need to first calculate the impedance (Z) of the circuit using the formula Z = √(R² + (XL - XC)²), where XL is the inductive reactance and XC is the capacitive reactance.
Inductive reactance (XL) is given by XL = 2πfL, and capacitive reactance (XC) by XC = 1/(2πfC). Since we know that f = 50 Hz, L = 0.30 H, and C = 60 μF, we can calculate XL and XC. Substituting R for the resistance in the circuit, we can find the impedance. After finding the impedance, we can calculate the real power (P) using P = I²R, where I is the rms current.
From the real power and the apparent power, which is IZ, we can find the power factor by calculating P/(IZ). However, we need the actual values of all elements, including the voltage, to complete these calculations. With the information provided in the question, we can't calculate the power factor because the rms voltage of the source isn't given.