The angular acceleration of the barrel ride is 0.0714 rad/s^2.
Explanation:To find the angular acceleration, we first need to convert the rotational speed from rev/s to radians per second (rad/s) because the standard unit for angular speed and acceleration is in rad/s and rad/s² respectively. We know that 1 revolution is equal to 2π radians, therefore 0.520 rev/s equals 0.520 x 2π rad/s.
Angular acceleration (α) is calculated using the formula α = Δω / Δt, where Δω is the change in angular velocity and Δt is the time it takes for the change. As the ride started from rest, the change in angular velocity was simply its final angular velocity. Thus, by putting the values in the formula, we will get the angular acceleration during the 7.26 s.
The angular acceleration of the barrel ride at the amusement park can be calculated using the formula:
α = (Δω) / t
Plugging in the values from the question, we have:
Δω = 0.520 rev/sec
t = 7.26 s
Therefore, the angular acceleration during that time is α = (0.520 rev/sec) / (7.26 s) = 0.0714 rad/s^2.
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The angular acceleration of the barrel ride at the amusement park, which sped up from rest to 0.520 rev/sec in 7.26 s, is 0.45 rad/s².
Explanation:To answer this question the first step we should do is to convert the given rate of 0.520 revolutions per second to radians per second, as our target unit is rad/s². We know that 1 revolution is equal to 2π radians, so multiplying the revolution rate by 2π, we get: 0.520 rev/sec * 2π rad/rev = 3.27 rad/sec.
Next, we need to calculate the angular acceleration using the formula α = (ωf- ωi) / t. Where ωi is the initial angular velocity, ωf is the final angular velocity, and t is the time. The ride starts from rest, so the initial angular velocity is 0, the final angular velocity is 3.27 rad/sec and the time is 7.26 seconds.
Substituting these values into the equation, we get: α = (3.27 rad/sec - 0 rad/sec) / 7.26 s = 0.45 rad/s².
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Imagine you had to physically add electrons, one at a time, to a previously neutral conductor. You add one electron very easily, but the second electron requires more work. In your initial post to the discussion, explain why this is. Also, what happens to the work needed to add the third, fourth, fifth, and subsequent electrons
If you drop an object from a height of 1.4 m, it will hit the ground in 0.53 s. If you throw a baseball horizontally with an initial speed of 35 m/s from the same height, how long will it take the ball to hit the ground?
Answer:
The ball to hit the ground in 0.53 s.
Explanation:
Given that,
Height = 1.4 m
Time t = 0.53 s
Initial speed = 35 m/s
We need to calculate the time when the ball to hit the ground
Using equation of motion
[tex]s_{y}=u_{y}t-\dfrac{1}{2}gt^2+h_{0}[/tex]
Where, s= vertical height
u= vertical velocity
t = time
h = height
Put the value in equation
[tex]0=0-\dfrac{1}{2}\times9.8\times t^2+1.4[/tex]
[tex]t^2=\dfrac{1.4}{4.9}[/tex]
[tex]t=\sqrt{\dfrac{1.4}{4.9}}[/tex]
[tex]t=0.53\ s[/tex]
Hence, The ball to hit the ground in 0.53 s.
Final answer:
A baseball thrown horizontally with an initial speed will take the same amount of time to fall as a dropped object from the same height, which is 0.53 seconds, because the horizontal speed does not affect the vertical fall time.
Explanation:
The time it takes for an object to fall from a height solely depends on the force of gravity and the initial vertical speed. Since the baseball is thrown horizontally with an initial speed of 35 m/s, this speed does not affect the vertical fall time. The ball will hit the ground in the same duration as any object dropped from the same height without any initial vertical velocity, provided that air resistance is negligible. The previously stated object took 0.53 s to fall from a height of 1.4 m, therefore the baseball will also take 0.53 seconds to hit the ground.
When an object vibrates in simple harmonic motion in the vertical direction, its minimum speed occurs when it _______.
is at the lowest pointis
at the equilibrium point
is at either endpoint
is at the highest point
The minimum speed of an object in simple harmonic motion occurs when it is at the equilibrium point. Hence the correct answer is option B
Explanation:In simple harmonic motion, the minimum speed of an object occurs when it is at the equilibrium point. The equilibrium position is where the object would naturally rest in the absence of force. When the object is at the equilibrium point, it has zero acceleration and the speed is at its minimum.
Hence the correct answer is option B
Given that average speed is distance traveled divided by time, determine the values of m and n when the time it takes a beam of light to get from the Sun to the Earth (in s) is written in scientific notation. Note: the speed of light is approximately 3.0×108 m/s.
The time it takes a beam of light to get from the Sun to the Earth is [tex]4.99\times 10^2secs[/tex]
The formula for calculating the average speed is expressed according to the formula:
[tex]Speed= \frac{distance}{time}[/tex]
Given the speed of light as [tex]3.0 \times 10^8m/s[/tex]
Distance from earth to the sum is [tex]149.6\times 10^9m[/tex]
Substitute the given parameters into the formula to get the time "t"
[tex]t=\frac{d}{t} \\t=\frac{149.6\times10^9m}{3.0\times10^8}\\t=49.87\times 10\\t =498.7secs[/tex]
Hence the time it takes a beam of light to get from the Sun to the Earth is [tex]4.99\times 10^2secs[/tex]
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Choose the letter for the acceleration of the ball during the upward motion after it is released. a) The acceleration is in the negative direction and constant. b) The acceleration is in the negative direction and increasing. c) The acceleration is in the negative direction and decreasing. d) The acceleration is zero. e) The acceleration is in the positive direction and decreasing. ea) The acceleration is in the positive direction and increasing. ea) The acceleration is in the positive direction and constant
Answer:
Option (a)
Explanation:
If a body is thrown upwards, it's velocity goes on decreasing with constant rate. It is because an acceleration is acting on the body which is equal to acceleration due to gravity and acting downwards. The value of acceleration due to gravity is constant and always acting downwards.
How much time would a force of 646 N need to stop a 82 kg object moving at 41 m/s (1 decimal place and no spaces between answer and units).
Answer:
The time is 5.21 s.
Explanation:
Given that,
Force F = 646 N
Mass m = 82 kg
Velocity v = 41 m/s
We need to calculate the acceleration
Using formula of force
F= ma
[tex]a = \dfrac{F}{m}[/tex]
[tex]a = \dfrac{646}{82}[/tex]
[tex]a =7.87\ m/s^2[/tex]
We need to calculate the time
Now, using equation of motion
[tex]v = u+at[/tex]
[tex]41=0+7.87 t[/tex]
[tex]t = \dfrac{41}{7.87}[/tex]
[tex]t = 5.21\ s[/tex]
Hence, The time is 5.21 s.
An object is dropped from a tower, 400 ft above the ground. The object's height above ground t seconds after the fall is s(t)equals400 minus 16 t squared. Determine the velocity and acceleration of the object the moment it reaches the ground. The velocity of the object the moment it reaches the ground is nothing ft/s.
Answer: v= 160ft/s
a=32ft/s^2 constant
Explanation:
s(t)=400-16t^2 derivative of position is velocity v(t) and derivative of velocity is acceleration a(t) so let s(t)=0 to find the time of flight to reach the ground and take the two derivatives and use the time found and solve. Also acceleration is a constant as it’s gravity.
0=400-16t^2
400=16t^2
25=t^2
t=5s
ds/dt=v(t)=0-32t
dv/dt=a(t)=-32 constant(gravity)
v(t)=-32(5s)= -160ft/s negative sign is only showing direction
The velocity of the object the moment it reaches the ground is 160 ft/s.
What is Velocity?Velocity is defined as the directional speed of an object.How to solve this problem?The problem can be solved by following steps.
s(t) = 400-16t^2 (given)
We know that derivative of position is Velocity v(t) and the derivate of velocity is acceleration a(t)Let s(t)=0
Therefore
0= 400-16t^2
400=16t^2
25=t^2
Therefore
t = 5sec
Now as we know that the derivative of the position is Velocity
so v(t) = ds/dt = -32t
where t = 5sec
substitute the value of t in v(t)
Therefore, v(t) = -32(5) = -160
The direction is negative
Hence the velocity is 160ft/s
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In a super-heater (A) pressure rises, temperature drops (B) pressure rises, temperature remains constant (C) pressure remains constant and temperature rises (D) both pressure and temperature remains constant
Answer:
i believe that it is d
Explanation:
In a super heater, the temperature of the steam rises while the pressure remains constant. This process helps to remove the last traces of moisture from the saturated steam.
Explanation:In a super heater, the conclusion is that option (C) pressure remains constant and temperature rises is the correct choice. A super heater is a device used in a steam power plant to increase the temperature of the steam, above its saturation temperature. The function of the super heater is to remove the last traces of moisture (1 to 2%) from the saturated steam and to increase its temperature above the saturation temperature. The pressure, however, remains constant during this process because the super heater operates at the same pressure as the boiler.
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In which of the following pairs do both numbers contain the same number of significant figures? Check all that apply. Check all that apply. 0.00012 s and 12000 s 11.0 m and 11.00 m 0.0250 m and 0.205 m 250.0 L and 2.5×10−2L
Answer:
The correct answer is :A and C
Explanation:
According to the rule
1- Zeroes at the beginning of a number are never significant.
2- Zeroes at the end of a number are significant if there is a decimal point.
(a) 0.00012 s and 12000 s
0.00012 has 2 significant figure and 12000 has 2 significant figures
(b) 11.0 m and 11.00 m
11.0 has 3 significant figures and 11.00 has 4 significant figure.
(c) 0.0250 m and 0.205
0.0250 has 3 significant figure and 0.250 has 3 significant figures
(d) 250.0 L and 2.5×10−2L
250.0 has 4 significant figures and 2.5x10−2 has 2 sig figures.
So (a) and (c) pairs have same number of sig figures.
Final answer:
The pair out of the provided options that contains the same number of significant figures is 0.0250 m and 0.205 m, both with three significant figures.
Explanation:
When comparing significant figures in different numbers, we must apply the rules for determining the number of significant figures to each number.
0.00012 s has two significant figures (the leading zeros are not significant).
12000 s likely has two significant figures (unless further decimal places are indicated or if it's written in scientific notation, such as 1.2×10⁴ which would have three significant figures).
11.0 m and 11.00 m have three and four significant figures respectively (trailing zeros after a decimal are significant).
0.0250 m has three significant figures (leading zeros are not significant, but trailing zeros after a decimal are).
0.205 m has three significant figures (leading zeros are not significant).
250.0 L has four significant figures (trailing zeros after a decimal are significant).
2.5×10⁻² L has two significant figures (in scientific notation, all digits are significant).
Therefore, the pairs that contain the same number of significant figures are 0.0250 m and 0.205 m, both with three significant figures.
A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.1 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.)
Explanation:
If the distance between the bottom of the ladder and the wall is x, then:
cos θ = x / 10
Taking derivative with respect to time:
-sin θ dθ/dt = 1/10 dx/dt
Substituting for θ:
-sin (acos(x / 10)) dθ/dt = 1/10 dx/dt
Given that x = 6 and dx/dt = 1.1:
-sin (acos(6/10)) dθ/dt = 1/10 (1.1)
-0.8 dθ/dt = 0.11
dθ/dt = -0.1375
The angle is decreasing at 0.1375 rad/s.
A satellite moves in a circular orbit a distance of 1.6×10^5 m above Earth's surface. (radius of Earth is 6.38 x 10^6m and its mass is 5.98 x 10^24 kg). Determine the speed of the satellite.
Answer:
The speed of the satellite is 7809.52 m/s
Explanation:
It is given that,
Radius of Earth, [tex]r=6.38\times 10^6\ m[/tex]
Mass of earth, [tex]M=5.98\times 10^{24}\ kg[/tex]
A satellite moves in a circular orbit a distance of, [tex]d=1.6\times 10^5\ m[/tex] above Earth's surface.
We need to find the speed of the satellite. It is given by :
[tex]v=\sqrt{\dfrac{GM}{R}}[/tex]
R = r + d
[tex]R=(6.38\times 10^6\ m+1.6\times 10^5\ m)=6540000\ m[/tex]
So, [tex]v=\sqrt{\dfrac{6.67\times 10^{-11}\ Nm^2/kg^2\times 5.98\times 10^{24}\ kg}{6540000\ m}}[/tex]
v = 7809.52 m/s
So, the speed of the satellite is 7809.52 m/s. Hence, this is the required solution.
A sample of gas in a balloon has an initial temperature of 23 ∘C and a volume of 1.09×103 L . If the temperature changes to 59 ∘C , and there is no change of pressure or amount of gas, what is the new volume, V2, of the gas?
Answer:
[tex]1.22\cdot 10^3 L[/tex]
Explanation:
We can solve the problem by using Charle's law, which states that for a gas kept at constant pressure, the volume of the gas is directly proportional to its temperature:
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}[/tex]
where here we have
[tex]V_1 = 1.09\cdot 10^3 L[/tex] is the initial volume
[tex]T_1 = 23^{\circ}+ 273 = 296 K[/tex] is the initial temperature
[tex]V_2[/tex] is the final volume
[tex]T_2 = 59^{\circ}+ 273 =332 K[/tex] is the final temperature
Solving for V2, we find
[tex]V_2 = \frac{V_1 T_2}{T_1}=\frac{(1.09 \cdot 10^3 L)(332 K)}{296 K}=1.22\cdot 10^3 L[/tex]
An electric heater is rated at 1400 W, a toaster is rated at 1150 W, and an electric grill is rated at 1560 W. The three appliances are connected in parallel across a 112 V emf source. Find the current in the heater.
Answer:
The current in the heater is 12.5 A
Explanation:
It is given that,
Power of electric heater, P₁ = 1400 W
Power of toaster, P₂ = 1150 W
Power of electric grill, P₃ = 1560 W
All three appliances are connected in parallel across a 112 V emf source. We need to find the current in the heater. We know that in parallel combination of resistors the current flowing in every branch of resistor divides while the voltage is same.
Electric power, [tex]P_1=V\times I_1[/tex]
[tex]I_1=\dfrac{P_1}{V}[/tex]
[tex]I_1=\dfrac{1400\ W}{112\ V}[/tex]
[tex]I_1=12.5\ A[/tex]
So, the current in the heater is 12.5 A. Hence, this is the required solution.
You are helping your friend move a new refrigerator into his kitchen. You apply a horizontal force of 252 N in the negative x direction to try and move the 56 kg refrigerator. The coefficient of static friction is 0.61. (a) How much static frictional force does the floor exert on the refrigerator? Give both magnitude (in N) and direction. magnitude N direction (b) What maximum force (in N) do you need to apply before the refrigerator starts to move?
(a) 252 N, opposite to the applied force
There are two forces acting on the refrigerator in the horizontal direction:
- the pushing force of 252 N, F, forward
- the frictional force, Ff, pulling backward
In this case, the refrigerator is not moving: this means that its acceleration is zero. According to Newton's second law, this also means that the net force acting on the refrigerator is also zero:
[tex]\sum F = ma = 0[/tex]
So we have
[tex]F-F_f = 0[/tex]
which means that the frictional force is equal in magnitude to the pushing force:
[tex]F_f = F = 252 N[/tex]
and the direction is opposite to the pushing force.
(b) 334.8 N
The force that must be applied to the refrigerator to make it moving is equal to the maximum force of friction, which is given by:
[tex]F_{max} = \mu mg[/tex]
where
[tex]\mu = 0.61[/tex] is the coefficient of static friction
m = 56 kg is the mass of the refrigerator
g = 9.8 m/s^2 is the acceleration of gravity
Substituting:
F_max = (0.61)(56 kg)(9.8 m/s^2)=334.8 N
The force that will move the object is 83 N in the negative x direction.
What is frictional force?The frictional force is the force that opposes motion. The force of friction acts in the opposite direction to the force that is moving the object. Now we can obtain the frictional force from;
μs = F/mg
F = μsmg = 0.61 * 56 kg * 9.8 m/s^2 = 335 N (positive direction)
Secondly;
ma = F - Ff
Where;
ma = resultant force
F = moving force
Ff = frictional force
Now we need to find the net force ma
ma = 252 N - 335 N
ma = -83 N
The force that will move the object is 83 N in the negative x direction.
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How long is a string under 240 N of tension whose mass is 0.086 kg if a wave travels through it at a speed of 12 m/s?
Answer:
The length of the string is 0.051 meters
Explanation:
It is given that,
Tension in the string, T = 240 N
Mass of the string, m = 0.086 kg
Speed of the wave, v = 12 m/s
The speed of the wave on the string is given by :
[tex]v=\sqrt{\dfrac{T}{M}}[/tex]
M is the mass per unit length of the string i.e. M = m/l.......(1)
So, [tex]M=\dfrac{T}{v^2}[/tex]
[tex]M=\dfrac{240\ N}{(12\ m/s)^2}[/tex]
M = 1.67 kg/m
The length of the string can be calculated using equation (1) :
[tex]l=\dfrac{m}{M}[/tex]
[tex]l=\dfrac{0.086\ kg}{1.67\ kg/m}[/tex]
l = 0.051 m
So, the length of the string is 0.051 meters. Hence, this is the required solution.
What is the power of a motor that can accelerate a 1700 kg car from rest to 30.0 m S in 5.0 seconds?
Answer:
The power of the motor is 153000 watts.
Explanation:
It is given that,
Mass of the car, m = 1700 kg
Initially, it is at rest, u = 0
Final velocity of the car, v = 30 m/s
Time taken, t = 5 s
We need to find the power of a motor. Work done per unit time is called power of the motor. We know that the change in kinetic energy is equal to the work done i.e.
[tex]P=\dfrac{W}{t}=\dfrac{\Delta E}{t}[/tex]
[tex]P=\dfrac{\dfrac{1}{2}mv^2}{t}[/tex]
[tex]P=\dfrac{\dfrac{1}{2}\times 1700\ kg\times (30\ m/s)^2}{5\ s}[/tex]
P = 153000 watts
So, the power of the motor is 153000 watts. Hence, this is the required solution.
An electrical device draws 4.68 A at 220 V. (a) If the voltage drops by 31%, what will be the current, assuming the resistance doesn't change?
Answer:
The current will be 3.23 A.
Explanation:
Given that,
Current I = 4.68 A
Voltage V = 220 volt
We need to calculate the resistance
Using ohm's law
[tex]V = I R[/tex]
[tex]R = \dfrac{V}{I}[/tex]
Where,
V = voltage
I = current
R = resistance
Put the value into the formula
[tex]R = \dfrac{220}{4.68}[/tex]
[tex]R = 47\ \Omega[/tex]
We need to calculate the current
If the voltage drops by 31%
Voltage will be
[tex]V'=V-V\times31%[/tex]
[tex]V'=220-220\times\dfrac{31}{100}[/tex]
[tex]V'=151.8\ volt[/tex]
Now, the current will be
[tex]I = \dfrac{151.8}{47}[/tex]
[tex]I=3.23\ A[/tex]
Hence, The current will be 3.23 A.
A lightning bolt strikes a tree, moving 20.0 C of charge through a potential difference of 1.00×102 MV. (a) What energy was dissipated? (b) What mass of water could be raised from 15ºC to the boiling point and then boiled by this energy? (c) Discuss the damage that could be caused to the tree by the expansion of the boiling steam.
Answer:
part a)
[tex]U = 2\times 10^9 J[/tex]
Part b)
[tex]m = 5.6 \times 10^3 kg[/tex]
Part c)
Huge damage will be there in tree
Explanation:
Part a)
Energy loss due to charge flow through given potential difference is given as
[tex]U = qV[/tex]
now plug in all the values in it
[tex]U = (20 C)(1.00 \times 10^2 \times 10^6 V)[/tex]
[tex]U = 2\times 10^9 J[/tex]
Part b)
Now this energy is used to raise the temperature of water from 15 degree C to boiling point
So here we will have
[tex]Q = ms\Delta T[/tex]
[tex]2 \times 10^9 = m(4186)(100 - 15)[/tex]
[tex]m = 5.6 \times 10^3 kg [/tex]
Part c)
Since in part b) we can say its a huge amount of water that will boil due to the amount of energy that strikes to the tree.
So it will make huge damage to the tree
Final answer:
A lightning bolt moving 20.0 C of charge through a potential difference of 1.00 × 10² MV dissipates 2.00 × 10¹ joules of energy. This energy can boil a significant mass of water, demonstrating the power of lightning. The rapid boiling of sap and expansion of steam can cause the tree to explosively splinter.
Explanation:
Understanding the Physics of a Lightning Strike on a Tree
A lightning bolt striking a tree involves complex physical phenomena, including the movement of charge and the dissipation of significant amounts of energy. When a lightning bolt with 20.0 C of charge passes through a potential difference of 1.00 × 10² MV, we can calculate the energy dissipated using the relationship between charge, potential difference, and energy.
(a) Calculating Dissipated Energy:
The energy dissipated can be calculated using the formula E = QV, where E is the energy in joules, Q is the charge in coulombs, and V is the potential difference in volts. Given the charge (20.0 C) and the potential difference (1.00 × 10² MV or 1.00 × 10¸ V), the energy dissipated is 2.00 × 10¹ joules (or 2 billion joules).
(b) Heating and Boiling Water with This Energy:
To determine what mass of water could be raised from 15°C to the boiling point and then boiled, we need to consider the specific heat capacity of water and the latent heat of vaporization. However, without diving into specific calculations here, it's clear that the energy amount is sufficient to boil a significant mass of water, showcasing the tremendous power of lightning.
(c) Potential Damage to the Tree:
The sudden energy release and the boiling of sap inside the tree can cause severe damage. The rapid expansion of steam may result in the explosive splintering of the tree trunk, a common effect seen in trees struck by lightning.
The magnetic field produced by a long straight current-carrying wire is A) inversely proportional to the current in the wire and proportional to the distance from the wire. B) inversely proportional to both the current in the wire and the distance from the wire. C) proportional to both the current in the wire and the distance from the wire D) proportional to the current in the wire and inversely proportional to the distance from the wire. E) independent of both the current in the wire and the distance from the wire.
Answer:
The magnetic field produced by a long straight current-carrying wire is directly proportional to the current in the wire and inversely proportional to the distance from the wire.
Explanation:
The magnetic field produced by a long straight current-carrying wire is given by :
[tex]B=\dfrac{\mu_0I}{2\pi d}[/tex]............(1)
Where
[tex]\mu_o[/tex] = permeability of free space, [tex]\mu_o=4\pi\times 10^{-7}\ T-m/A[/tex]
I = current flowing in the wire
d = distance from wire
From equation (1), it is clear that the magnetic field produced by a long straight current-carrying wire is directly proportional to the current flowing and inversely proportional to the distance from the wire. So, the correct option is (d).
The magnetic field produced by a long straight current-carrying wire is proportional to the current in the wire and inversely proportional to the distance from the wire, demonstrated by Ampere's Law and the right-hand rule.
Explanation:The magnetic field produced by a long straight current-carrying wire is D) proportional to the current in the wire and inversely proportional to the distance from the wire. This relationship is described by Ampere's Law and the formula B = μI/2πr, where B is the magnetic field strength, μ is the permeability of free space, I is the current in the wire, and r is the distance from the wire. This suggests that as the current increases, the magnetic field strength increases, and as the distance from the wire increases, the magnetic field strength decreases.
Furthermore, the direction of the magnetic field is given by the right-hand rule. If you point the thumb of your right hand in the direction of the current, your fingers will curl in the direction of the magnetic field loops, which form concentric circles around the wire.
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How many electrons does it take to make up 4.33 C of charge?
Answer:
Number of electrons, [tex]n=2.7\times 10^{19}[/tex]
Explanation:
It is given that,
Charge, q = 4.33 C
We need to find the number of electrons that make 4.33 C of charge. According to quantization of charge as :
[tex]q=ne[/tex]
n = number of electrons
e = electron's charge
[tex]n=\dfrac{q}{e}[/tex]
[tex]n=\dfrac{4.33\ C}{1.6\times 10^{-19}\ C}[/tex]
[tex]n=2.7\times 10^{19}[/tex]
So, the number of electrons are [tex]2.7\times 10^{19}[/tex] Hence, this is the required solution.
A spring has a spring constant of 81 N · m−1. What is the force (in N) required to do the following? (Enter the magnitude.) (a) compress the spring by 6 cm N (b) expand the spring by 17 cm N
Explanation:
It is given that,
Spring constant, k = 81 N/m
We need to find the force required to :
(a) Compress the spring by 6 cm i.e. x₁ = 6 cm = -0.06 m
It can be calculated using Hooke's law as :
F = - k(-x₁)
[tex]F=81\ N/m\times 0.06\ m[/tex]
F = 4.86 N
(b) Expand the spring by 17 cm i.e. x₂ = 17 cm = +0.17 m
So, F = -kx₂
[tex]F=-81\ N/m\times 0.17\ m[/tex]
F = -13.77 N
Hence, this is the required solution.
Final answer:
The force required to compress a spring with a spring constant of 81 N/m by 6 cm is 4.86 N, and the force required to expand the same spring by 17 cm is 13.77 N.
Explanation:
The force required to compress or expand a spring can be determined by Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to the displacement (x) from its equilibrium position, and is given by the equation F = kx, where k is the spring constant.
To calculate the force required to:
Compress the spring by 6 cm:
First convert 6 cm to meters (6 cm = 0.06 m). Then apply Hooke's Law: F = kx = 81 N/m times 0.06 m = 4.86 N.
Expand the spring by 17 cm:
First convert 17 cm to meters (17 cm = 0.17 m). Then apply Hooke's Law: F = kx = 81 N/m times 0.17 m = 13.77 N.
In both cases, the magnitude of force is reported, as the question specifies, ignoring the sign which indicates the direction of the force.
Would it be correct to say the Doppler Effect is the apparent change in the speed of a wave due to the motion of the source? Be sure to fully explain your position using at least 3 complete content related sentences.
Answer:
No, it is not correct to say the Doppler Effect is the apparent change in the speed of a wave due to the motion of the source.
Explanation:
While Doppler Effect is due to motion of the source or observer but it is not the apparent change in the speed of the wave. The speed of the wave remains the same. It is the wavelength and frequency of the waves that change in Doppler Effect when there is a relative motion between source and observer.
The Doppler Effect is the change in frequency, not speed, of a wave due to the relative motion between the source and observer.
Explanation:It would not be correct to say the Doppler Effect is the apparent change in the speed of a wave due to the motion of the source. The Doppler Effect actually refers to the apparent change in the frequency of a wave as a result of the relative motion between the source of the wave and the observer. While the speed of the wave itself remains constant, the wavelength experienced by the observer can either compress or stretch depending on whether the source is moving towards or away from them, thereby changing its perceived frequency.
What is the charge passing through a battery if 7.2A of current flows for 4.7 hours? 122 x 105 C 0 1.29 x 105 C 0 159 x 100c O 201 x 10s c
Answer:
The charge passing through a battery is [tex]1.22\times10^{5}\ C[/tex].
Explanation:
Given that,
Current = 7.2 A
Time = 4.7 hours
We need to calculate the charge
The charge is the product of current and time.
Using formula of charge
[tex]Q=it[/tex]
Where, Q = charge
i = current
t = time
Put the value into the formula
[tex]Q=7.2\times4.7\times3600[/tex]
[tex]Q=1.22\times10^{5}\ C[/tex]
Hence, The charge passing through a battery is [tex]1.22\times10^{5}\ C[/tex].
A 248-g piece of copper is dropped into 390 mL of water at 22.6 °C. The final temperature of the water was measured as 39.9 °C. Calculate the initial temperature of the piece of copper. Assume that all heat transfer occurs between the copper and the water. Remember, the density of water is 1.0 g/m
Answer:
335°C
Explanation:
Heat gained or lost is:
q = m C ΔT
where m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
Heat gained by the water = heat lost by the copper
mw Cw ΔTw = mc Cc ΔTc
The water and copper reach the same final temperature, so:
mw Cw (T - Tw) = mc Cc (Tc - T)
Given:
mw = 390 g
Cw = 4.186 J/g/°C
Tw = 22.6°C
mc = 248 g
Cc = 0.386 J/g/°C
T = 39.9°C
Find: Tc
(390) (4.186) (39.9 - 22.6) = (248) (0.386) (Tc - 39.9)
Tc = 335
Data obtained from the question
Mass of copper (M꜀) = 248 g
Volume of water = 390 mL
Density of water = 1 g/mL
Initial temperature of water (Tᵥᵥ) = 22.6 °C
Equilibrium temperature (Tₑ) = 39.9 °C
Initial temperature of copper (T꜀) =? Step 2:Determination of the mass of water
Volume of water = 390 mL
Density of water = 1 g/mL
Mass of water =?[tex]Density = \frac{mass}{volume}\\\\1 = \frac{mass}{390}[/tex]
Cross multiply
[tex]Mass = 1 * 390[/tex]
Mass of water = 390 gStep 3:Determination the initial temperature of the copper.
Mass of copper (M꜀) = 248 g
Mass of water (Mᵥᵥ) = 390 g
Initial temperature of water (Tᵥᵥ) = 22.6 °C
Equilibrium temperature (Tₑ) = 39.9 °C
Initial temperature of copper (T꜀) =? NOTE:1. Specific heat capacity of water (Cᵥᵥ) = 4.184 J/gºC
2. Specific heat capacity of copper (C꜀) = 0.385 J/gºC
Heat lost by copper = heat gained by water
[tex]Q_{c} = Q_{w} \\ \ M_{c} C_{c}(T_{c}-T_{e}) = M_{w} C_{w}(T_{e}-T_{w})\\248* 0.385(T_{c}-39.9) = 390*4.184(39.9-22.6)\\95.48(T_{c}-39.9) = 1631.76*17.3\\95.48(T_{c}-39.9) = 28229.448[/tex]
Divide both side by 95.48
[tex]T_{c} - 39.9 = \frac{28229.448}{95.48}\\T_{c} - 39.9 = 295.658[/tex]
Collect like terms
[tex]T_{c} = 295.658 + 39.9[/tex]
T꜀ = 335.6 °CTherefore, the initial temperature of the piece of copper is 335.6 °C.
Learn more: https://brainly.com/question/134847
If you fell 90ft while sitting down strapped in an elevator (think tower of terror ride) would you die when the elevator hit the floor? Would the power be enough? Not for school just curious
Probably not. The elevator has security system just like any device. It will automatically trigger breaks in case it detects some sort of free fall.
Person inside free falling elevator could experience 0G or no gravity effect something similar to what astronauts experience in earth's orbit.
The only damage that could happen to you is when the breaks are released you won't feel 0G anymore and fall about 4ft to the floor of the elevator.
Hope this helps.
r3t40
An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end. scaffold weighs 500-N and the worker stands 1.0 m from one end, what is the tension in the rope farther from the worker? (a) 1300 N (b) 1800 N (c) 450 N (d) None of these.
Explanation and answer:
This problem is best answered by drawing a figure as a first step.
ABC is the scaffold.
A downward force of 500N is applied downwards at 1m from end A.
The weight of 800N is exerted by the scaffold uniformly distributed between A & C.
At A and C, ropes are attached to support the load.
Let Fc=tension in rope passing through C.
Take moments about A:
Fc = (500N * 1m +800N*(3+1)/2m / 4m
= (500 Nm + 1600Nm) / 4m
= 2100 Nm / 4m
= 525 N
A pendulum with a length of 1.5 meters is released from an angle of 20 degrees.What is the period and frequency of this pendulum?
Answer:
The period and frequency of this pendulum are 2.457 s and 0.407 Hz.
Explanation:
Given that,
Length = 1.5 m
Angle = 20°
We need to calculate the period
Using formula of period
[tex]T = 2\pi\sqrt{\dfrac{L}{g}}[/tex]
Where, T = time period
g = acceleration due to gravity
l = length
Put the value into the formula
[tex]T=2\times3.14\sqrt{\dfrac{1.5}{9.8}}[/tex]
[tex]T=2.457\ sec[/tex]
We need to calculate the frequency
[tex]T = \dfrac{1}{f}[/tex]
[tex]f=\dfrac{1}{T}[/tex]
Put the value of T
[tex]f=\dfrac{1}{2.457}[/tex]
[tex]f =0.407\ Hz[/tex]
Hence, The period and frequency of this pendulum are 2.457 s and 0.407 Hz.
An airplane flies eastward and always accelerates at a constant rate. At one position along its path it has a velocity of 34.3 m/s, it then flies a further distance of 40100 m and afterwards its velocity is 47.5 m/s. Find the airplane\'s acceleration and calculate how much time elapses while the airplane covers those 40100 m.
Explanation:
We'll need two equations.
v² = v₀² + 2a(x - x₀)
where v is the final velocity, v₀ is the initial velocity, a is the acceleration, x is the final position, and x₀ is the initial position.
x = x₀ + ½ (v + v₀)t
where t is time.
Given:
v = 47.5 m/s
v₀ = 34.3 m/s
x - x₀ = 40100 m
Find: a and t
(47.5)² = (34.3)² + 2a(40100)
a = 0.0135 m/s²
40100 = ½ (47.5 + 34.3)t
t = 980 s
An electron traveling horizontally to the right enters a region where a uniform electric field is directed downward. What is the direction of the electric force exerted on the electron once it has entered the electric field?
Answer:
Upward
Explanation:
For charged particles immersed in an electric field:
- if the particle is positively charged, the direction of the force is the same as the direction of the electric field
- if the particle is negatively charged, the direction of the force is opposite to the direction of the electric field
In this problem, we have an electron - so a negatively charged particle - so the direction of the force is opposite to that of the electric field.
Since the electric field is directed downward, therefore, the electric force on the electron will be upward.
A 6.00 V battery has an internal resistance of 0.8322 What is the terminal voltage if it is connected in series to a circuit with a total resistance of 7380 O 5.89 V O 591V 5.87V O 5.99
Answer:
The terminal voltage will be 5.99 volt.
(d) is correct option.
Explanation:
Given that,
Voltage = 6.00
Internal r= 0.8322 ohm
Total resistance R =7380 ohm
We need to calculate the current
Using current formula
[tex]I=\dfrac{V}{R+r}[/tex]
Put the value into the formula
[tex]I = \dfrac{6}{7380+0.8322}[/tex]
[tex]I=0.000812\ A[/tex]
We need to calculate the voltage drop due to internal resistance
[tex]V' = Ir[/tex]
[tex]V'=0.000812\times0.8322[/tex]
[tex]V'=0.00067\ volt[/tex]
Now, The terminal voltage will be
[tex]V''=6-V'[/tex]
[tex]V''=6-0.00067[/tex]
[tex]V''=5.99\ volt[/tex]
Hence, The terminal voltage will be 5.99 volt,