Answer:
C. her moment of inertia increases and her angular speed decreases
D. her moment of inertia increases and her angular speed decreases
Explanation:
The moment of inertia of a body is the sum of the products of an increment of mass and the square of its distance from the center of rotation. When a spinning person extends her arms, part of her mass increases its distance from the center of rotation, so increases the moment of inertia.
The kinetic energy of a spinning body is jointly proportional to the moment of inertia and the square of the angular speed. Hence an increase in moment of inertia will result in a decrease in angular speed unless there is a change in the rotational kinetic energy.
This effect is used by figure skaters to increase their spin rate by drawing their arms and legs closer to the axis of rotation. Similarly, they can slow the spin by extending arms and legs.
When the person extends her arms, her moment of inertia increases and her angular speed decreases.
_____
Note to those looking for a letter answer
Both choices C and D have identical (correct) wording the way the problem is presented here. You will need to check carefully the wording in any problem you may think is similar.
a 15-nC point charge is at the center of a thin spherical shell of radius 10cm, carrying -22nC of charge distributed uniformly over its surface. find the magnitude and direction of the electric field (a) 2.2cm,(b)5.6cm,and (c)14 cm from the point charge.
Answer:
A) E = 278925.62 N/C with direction; radially out.
B) E = 43048.47 N/C with direction radially out.
C) E = -3214.29 N/C with direction radially in.
Explanation:
From Gauss' Law, the Electric field for any spherically symmetric charge or charge distribution is the same as the point charge formula. Thus;
E = kQ/r²
where;
Q is the net charge within the distance r.
We are given the charge Q = 15-nC and
spherical shell of radius 10cm
A) The distance r = 2.2 cm = 0.022 m is between the surface and the point charge, so only the point charge lies within this distance and Q = 15 nC = 15 x 10^(-9) C
While k is coulombs constant with a value of 9 × 10^(9) N.m²/C²
E = ((9 x 10^(9) × (15 x 10^(-9)))/(0.022)²
E = 278925.62 N/C
This will be radially out ,since the net charge is positive.
B) The distance r = 5.6 cm = 0.056 m is between the surface and the point charge, so only the point charge lies within this distance and Q = 15 nC = 15 x 10^(-9) C
While k is coulombs constant with a value of 9 × 10^(9) N.m²/C²
E = ((9 x 10^(9) × (15 x 10^(-9)))/(0.056)²
E = 43048.47 N/C
This will be radially out ,since the net charge is positive.
C) The distance r = 14 cm = 0.14 m is outside the sphere so the "net" charge within this distance is due to both given charges. Thus;
Q = 15 nC - 22 nC
Q = -7 nC = -7 x 10^(-9) C
and;
E = (9 x 10^(9)*(-7 x 10^(-9))/(0.14)²
E = -3214.29 N/C
This will be radially in, since the net charge is negative. You can indicate this with a negative answer.
A) When The distance r is = 2.2 cm = 0.022 m is between the surface and also the point charge, also that so only the point charge lies within this distance and also Q = 15 NC = 15 x 10^(-9) C
Then While k is coulombs constant with a value of 9 × 10^(9) N.m²/C²When E = ((9 x 10^(9) × (15 x 10^(-9)))/(0.022)²Then E = 278925.62 N/CThen This will be radially out since the net charge is positive.
B) When The distance r = 5.6 cm = 0.056 m is between the surface and also the point charge, so only the point charge lies within this distance and also Q = 15 nC = 15 x 10^(-9) C
then While k is coulombs constant with a value of 9 × 10^(9) N.m²/C²When E = ((9 x 10^(9) × (15 x 10^(-9)))/(0.056)²Then E = 43048.47 N/CAfter that This will be radially out since the net charge is positive.
C) Then when The distance r = 14 cm = 0.14 m is outside the sphere so the "net" charge within this distance is due to both given charges. Thus;
Then Q = 15 nC - 22 nCAfter that Q = -7 nC = -7 x 10^(-9) CWhen E = (9 x 10^(9)*(-7 x 10^(-9))/(0.14)²Then E = -3214.29 N/C Thus, This will be radially in, since the net charge is negative.Find out more information about magnitude here:
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In a 2 dimensional Cartesian system, the x-component of a vector is known, and the angle between vector and x-axis is known. Which operation is used to calculate the magnitude of the vector? (taken with respect to the x-component)
a. dividing by cosine
b. dividing by sine
c. multiplying by cosine
d. multiplying by sine
Answer:
The correct answer is a
Explanation:
The cosine function is
cos θ = ca / H
done ca is the adjacent leg (x-axis) and H is the hypotenuse (vector module)
we clear
H = ca / cos θ
therefore, to find the magnitude of the vector, the cathete is divided into the cosine.
The correct answer is a
The Gulf Stream off the east coast of the United States can flow at a rapid 3.8 m/s to the north. A ship in this current has a cruising speed of 8.0 m/s . The captain would like to reach land at a point due west from the current position.
At this heading, what is the ship's speed with respect to land?
Answer:
61.6° west of South
Explanation:
The ship goes to the south at an equal rate just like water flows to the north. Thus, the velocities would balance making the ship move towards the west.
Since we're dealing with water, the ship goes 3.8 m / s to the South, but a lot still remains to the west. Finding this would require us drawing a triangle. 3.8 m/s point down side and the hypotenuse is 8
cos(θ) = [adjacent/hypotenuse]
Cos θ = 3.8/8
Cos θ = 0.475
θ = cos^-1 (0.475)
θ = 61.6°
Therefore the angle is 61.6° west of South.
Find the equivalent resistance from the indicated terminal pair of the networks in the attached doc
Answer:
a) R = 2.5 Ω, b) R = 1 Ω, c) R = 2R / 3 Ω
Explanation:
The resistance configuration can be in series or in parallel, for each one the equivalent resistance can be calculated
series, the equivalent resistance is the sum of the resistances
parallel, the inverse of the equivalent resistance is the inverse of the sum of the resistances
let's apply these principles to each case
case a)
equivalent series resistance
R₁ = 1 +4 = 5 ohm
R₂ = 2 +3 = 5 ohn
these two are in parallel
1 / R = 1/5 +1/5
1 / R = 2/5
R = 2.5 Ω
case B
we solve the parallel
1 / R₁ = ½ + ½ = 1
R₁ = 1 Ω
we solve the resistors in series
R₂ = 1 + 1
R₂ = 2 Ω
finally we solve the last parallel
1 / R = ½ +1/2 = 1
R = 1 Ω
case C
we solve house resistance pair in series
R₁ = R + 2R = 3R
we go to the next mesh
R₂ = R + 2R = 3R
R₃ = R + 2R = 3R
last mesh
R₄ = R + R = 2R
now we solve the parallel of this equivalent resistance
1 / R = 1 / R₁ + 1 / R₂ + 1 / R₃ + 1 / R₄
1 / R = 1 / 3R + 1 / 3R + 1 / 3R + 1 / 2R
1 / R = 3 / 3R + 1 / 2R = 1 / R + 1 / 2R
1 / R = 3 / 2R
R = 2R / 3 Ω
Espresso is a coffee beverage made by forcing steam through finely ground coffee beans. Modern espresso makers generate steam at very high pressures and temperatures, but in this problem we'll consider a low-tech espresso machine that only generates steam at 100?C and atomospheric pressure--not much good for making your favorite coffee beverage.The amount of heat Q needed to turn a mass m of room temperature ( T1) water into steam at 100?C ( T2) can be found using the specific heat c of water and the heat of vaporization Hv of water at 1 atmosphere of pressure.Suppose that a commercial espresso machine in a coffee shop turns 1.50 kg of water at 22.0?C into steam at 100?C. If c=4187J/(kg??C) and Hv=2,258kJ/kg, how much heat Q is absorbed by the water from the heating resistor inside the machine?Assume that this is a closed and isolated system.Express your answer in joules to three significant figures.Q = _________________ J
Answer:
Q = 3877 KJ
Explanation:
Since, the system is closed and isolated. Therefore, the law of conservation of energy can be written as:
Heat Absorbed By Water (Q) = Heat required to raise the temperature of water (Q₁) + Heat required to convert water to steam (Q₂)
Q = Q₁ + Q₂ ----- equation (1)
Now, for Q₁:
Q₁ = m C ΔT
where,
m = Mass of Water = 1.5 kg
C = Specific Heat of Water = 4187 J/kg.°C
ΔT = Change in Temperature of Water = T₂ - T₁ = 100°C - 22°C = 78°C
Therefore,
Q₁ = (1.5 kg)(4187 J/kg.°C)(78°C)
Q₁ = 490 x 10³ J =490 KJ
Now, for Q₂:
Q₂ = m H
where,
m = Mass of Water = 1.5 kg
H = Heat of Vaporization of Water = 2258 KJ/kg
Therefore,
Q₂ = (1.5 kg)(2258 KJ/kg)
Q₂ = 3387 KJ
Substituting the values in equation (1), we get:
Q = Q₁ + Q₂
Q = 490 KJ + 3387 KJ
Q = 3877 KJ
An object, with mass 70 kg and speed 21 m/s relative to an observer, explodes into two pieces, one 4 times as massive as the other; the explosion takes place in deep space. The less massive piece stops relative to the observer. How much kinetic energy is added to the system during the explosion, as measured in the observer's reference frame
Answer:
K = 3.9 kJ
Explanation:
The kinetic energy ([tex]K_{T}[/tex]) added is given by the difference between the final kinetic energy and the initial kinetic energy:
[tex] K_{T} = K_{f} - K_{i} [/tex]
The initial kinetic energy is:
[tex] K_{i} = \frac{1}{2}m_{1}v_{1}^{2} [/tex]
Where m₁ is the mass of the object before the explosion and v₁ is its velocity
[tex] K_{i} = \frac{1}{2}m_{1}v_{1}^{2} = \frac{1}{2}70 kg*(21 m/s)^{2} = 1.54 \cdot 10^{4} J [/tex]
Now, the final kinetic energy is:
[tex] K_{f} = \frac{1}{2}m_{2}v_{2}^{2} + \frac{1}{2}m_{3}v_{3}^{2} [/tex]
Where m₂ and m₃ are the masses of the 2 pieces produced by the explosion and v₁ and v₂ are the speeds of these pieces
Since m₂ is 4 times as massive as m₃ and v₃ = 0, we have:
[tex] K_{f} = \frac{1}{2}*\frac{4}{5}m_{1}v_{2}^{2} + \frac{1}{2}*\frac{1}{5}m_{1}*0 [/tex] (1)
By conservation of momentum we have:
[tex] p_{i} = p_{f} [/tex]
[tex] m_{1}v_{1} = m_{2}v_{2} + m_{3}v_{3} [/tex]
[tex] m_{1}v_{1} = \frac{4}{5}m_{1}v_{2} + \frac{1}{5}m_{1}*0 [/tex]
[tex] v_{2} = \frac{5}{4}v_{1} [/tex] (2)
By entering (2) into (1) we have:
[tex] K_{f} = \frac{1}{2}*\frac{4}{5}m_{1}(\frac{5}{4}v_{1})^{2} = \frac{1}{2}*\frac{4}{5}70 kg(\frac{5}{4}*21 m/s)^{2} = 1.93 \cdot 10^{4} J [/tex]
Hence, the kinetic energy added is:
[tex] K_{T} = K_{f} - K_{i} = 1.93 \cdot 10^{4} J - 1.54 \cdot 10^{4} J = 3.9 \cdot 10^{3} J [/tex]
Therefore, the kinetic energy added to the system during the explosion is 3.9 kJ.
I hope it helps you!
cellus
An object ends up at a position of
327 m after a displacement of -144 m.
What was its initial position?
(Unit = m)
Answer:
Its initial position was 471 m.
Explanation:
We have,
Final position of the object is 327 m
Displacement of the object is -144 m
It is required to find its initial position. The difference of final and initial position is equal to the displacement of the object. So,
[tex]d=\text{final position}-\text{initial position}\\\\-144=327-\text{initial position}\\\\\text{initial position}=327+144\\\\\text{initial position}=471\ m[/tex]
So, its initial position was 471 m.
the heat capacity of 0.125Kg of water is measured to be 523j/k at a room temperature.Hence, calculate the heat capacity of water
(a) per unit mass
(b) per unit volume
Answer:
A. 4148 J/K/Kg
B. 4148 J/K/L
Explanation:
A. Heat capacity per unit mass is known as the specific heat capacity, c.
C = Heat capacity/mass(kg)
C = (523 J/K) / 0.125 Kg = 4148 J/K/Kg
B. Volume of water = mass/density
Density of water = 1 Kg/L
Volume of water = 0.125 Kg/ 1Kg/L
Volume of water = 0.125 L
Heat capacity per unit volume = (523 J/K) / 0.125 L
Heat capacity per unit volume = 4148 J/K/L
Two identical charges,2.0m apart,exert forces of magnitude 4.0 N on each other.What is the value of either charge?
Answer:
[tex]\large \boxed{42\, \mu \text{C}}$[/tex]
Explanation:
The formula for the force exerted between two charges is
[tex]F=k \dfrac{ q_1q_2}{r^2}[/tex]
where k is the Coulomb constant.
The charges are identical, so we can write the formula as
[tex]F=k\dfrac{q^{2}}{r^2}[/tex]
[tex]\begin{array}{rcl}\text{4.0 N}& = & 8.988 \times 10^{9}\text{ N$\cdot$m$^{2}$C$^{-2}$} \times \dfrac{q^{2}}{\text{(2.0 m)}^{2}}\\\\4.0 & = & 2.25 \times 10^{9}\text{ C$^{-2}$} \times q^{2}\\\\q^{2} & = & \dfrac{4.0}{2.25 \times 10^{9}\text{ C$^{-2}$}}\\\\& = & 1.78 \times 10^{-9} \text{ C}^{2}\\q & = & 4.2 \times 10^{-5} \text{ C}\\& = & 42\, \mu \text{C}\\\end{array}\\\text{Each charge has a value of $\large \boxed{\mathbf{42\, \mu }\textbf{C}}$}[/tex]
A kicked ball rolls across the grass and eventually comes to a stop in 4.0 sec. When the ball was kicked, its initial velocity was 20 mi/ hr. What is the acceleration of the ball as it rolls across the grass?
Answer:
-2.24 m/s²
Explanation:
Given:
v₀ = 20 mi/hr = 8.94 m/s
v = 0 m/s
t = 4.0 s
Find: a
v = v₀ + at
0 m/s = 8.94 m/s + a (4.0 s)
a = -2.24 m/s²
A 1.0-m-long copper wire of diameter 0.10 cm carries a current of 50.0 A to the east. Suppose we apply to this wire a magnetic field that produces on it an upward force exactly equal in magnitude to the wire's weight, causing the wire to "levitate."
Required:
a. What is the field's magnitude?
b. What is the field's direction?
Answer:
The classification of that same issue in question is characterized below.
Explanation:
The given values are:
Current, I = 50.0 A
Diameter, d = 0.10 cm
(a)...
As we know,
⇒ Magnetic force = Copper wire's weight
So,
⇒ [tex]B\times I\times L=M\times g[/tex]
On putting the estimated values, we get
⇒ [tex]B\times 50\times 1=7.037\times 10^{-3}\times 9.81[/tex]
⇒ [tex]50B=69.03297\times 10^{-3}[/tex]
⇒ [tex]B=1.38\times 10^{-3} \ T[/tex]
(b)...
As we know,
⇒ [tex]m=\delta\times L\times \frac{\pi \ d^2}{4}[/tex]
⇒ [tex]=8960\times 1\times \frac{\pi \ (0.001)^2}{4}[/tex]
⇒ [tex]=2240\times \pi \ 0.000001[/tex]
⇒ [tex]=7.037\times 10^{-3} \ kg[/tex]
Consider a weather balloon floating in the air. There are three forces acting on this balloon: the force of gravity is FG, the force from lift towards balloon is FL, and the force from the wind is labeled Fw. The orientation of these forces along with a coordinate system is given below:
Assume that || FG || = 20 N, || FL ||= 25 N, and || Fw ll = 15 N.
Required:
Find the magnitude of the resultant force acting on the weather balloon and round your answer to two decimal places.
50 points!! please help :((
Answer:
Loudness: decreases
Amplitude: decreases
Pitch: stays the same
Frequency: stays the same
Explanation:
1.
An oscilloscope measures how much the microphone is vibrating, or how much electricity it is sending. This means that a louder noise will register higher on the oscilloscope. Since the size of the waves at Y is lower than at X, the loudness of the sound has decreased.
2.
Similarly to loudness, amplitude measures how far the crests of the waves are from the nodes. Since Y is closer to the center line than X, it has a lower amplitude.
3 and 4.
The pitch and frequency, for our purposes, are essentially the same thing here. They are dependent on how close together the waves on the oscilloscope are, or how quickly the microphone is vibrated. Since this stays the same throughout the entire sound, they both stay the same.
Hope this helps!
A ball is thrown upward from the ground with an initial speed of 19.2 m/s; at the same instant, another ball is dropped from a building 18 m high. After how long will the balls be at the same height above the ground?
Answer:
0.938 seconds
Explanation:
For the ball thrown upwards, we use the formula below to solve it:
[tex]s = ut - \frac{1}{2}gt^2[/tex]
where s = distance moved
u = initial speed = 19.2 m/s
t = time taken
g = acceleration due to gravity = 9.8 [tex]m/s^2[/tex]
Let x be the height at which both balls are level, this means that:
=> [tex]x = 19.2t - 4.9t^2[/tex]________(1)
For the ball dropped downwards, we use the formula below:
[tex]s = ut + \frac{1}{2}gt^2[/tex]
u = 0 m/s
At the point where both balls are level:
s = 18 - x
=> [tex]18 - x = 0 + 4.9t^2[/tex]
=> [tex]x = 18 - 4.9t^2[/tex]__________(2)
Equating both (1) and (2):
[tex]19.2t - 4.9t^2 = 18 - 4.9t^2\\\\=> 19.2t = 18\\\\t = 18/19.2 = 0.938 secs[/tex]
They will be level after 0.938 seconds
A camera takes a picture that is the correct brightness and the correct zoom level, but the depth-of-focus is too small. One way to increase the depth-of-focus is to increase the f-number. Assuming that we will make changes that have the overall effect to:
1. increase the f-number, and
2. keep the brightness and the zoom level the same, which changes should we make to the aperture diameter and to the shutter time? (keep in mind we're talking about the time the shutter is open; we aren't talking about the shutter speed)
a. Increase the aperture diameter, decrease the shutter time
b. Decrease the aperture diameter, increase the shutter time
c. Increase both the aperture diameter as well as the shutter time
d. Decrease both the aperture diameter as well as the shutter time
A compact disk, which has a diameter of 12.0 cm, speeds up uniformly from zero to 4.30 rev/s in 3.05 s . Part A What is the tangential acceleration of a point on the outer rim of the disk at the moment when its angular speed is 2.00 rev/s
Answer:
[tex]{0.51 \mathrm{m} / \mathrm{s}^{2}}[/tex]
Explanation:
Angular acceleration
[tex]\begin{aligned}
\alpha &=\frac{\left(\omega_{f}-\omega_{i}\right)}{t} \\
\omega_{i} &=0 \\
\omega_{f} &=4.30 \mathrm{rev} / \mathrm{s} \\
&=4.30 \times 2 \pi \mathrm{rad} / \mathrm{s} \\
&=27.02 \mathrm{rad} / \mathrm{s} \\
\alpha &=\frac{(27.02-0)}{3.15} \\
&=8.57 \mathrm{m} / \mathrm{s}^{2}
\end{aligned}[/tex]
a)Tangential acceleration
[tex]\begin{aligned}
a &=r \alpha \\
&=\frac{12}{2} \times 10^{-2} \times 8.57 \\
a &=0.51 \mathrm{m} / \mathrm{s}^{2}
\end{aligned}[/tex]
The tangential acceleration of the disc is [tex]{0.51 \mathrm{m} / \mathrm{s}^{2}}[/tex]
This question involves the concepts of the equations of motion for angular motion.
The tangential acceleration of a point on the outer rim of the disk at the moment when its angular speed reaches 2 rev/s will be "0.532 m/s²".
First, we will use the first equation of motion for the angular motion to find out the angular acceleration:
[tex]\alpha=\frac{\omega_f-\omega_i}{t}[/tex]
where,
[tex]\alpha[/tex] = angular acceleration = ?
[tex]\omega_f[/tex] = final angular speed = (4.3 rev/s)[tex](\frac{2\pi\ rad}{1\ rev})[/tex] = 27.02 rad/s
[tex]\omega_i[/tex] = initial angular speed = 0 rad/s
t = time taken = 3.05 s
Therefore,
[tex]\alpha =\frac{27.02\ rad/s-0\ rad/s}{3.05\ s}\\\\\alpha= 8.86\ rad/s^2[/tex]
Now, the tangential acceleration can be given as follows:
[tex]a=r\alpha\\a=(\frac{diameter}{2})(8.86\ rad/s^2)\\\\a=(\frac{0.12\ m}{2})(8.86\ rad/s^2)\\\\[/tex]
a = 0.532 m/s²
Learn more about the angular motion here:
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The attached picture shows the angular equations of motion.
28 points!! please help
A CD is spinning on a CD player. In 220 radians, the cd has reached an angular speed of 92 r a d s by accelerating with a constant acceleration of 14 r a d s 2 . What was the initial angular speed of the CD
Answer:
The initial angular speed is [tex]w_i = 48 \ rad/s[/tex]
Explanation:
From the question we are told that
The angular displacement is [tex]\theta = 220 \ rad[/tex]
The angular speed is [tex]w_f = 92 \ rad/s[/tex]
The acceleration is [tex]\alpha = 14 \ rad/s^2[/tex]
Generally the initial angular speed can be evaluated as
[tex]w_f ^2 = w_i ^2 + 2 * \alpha * \theta[/tex]
=> [tex]w_i ^2 = w_f ^2 - 2 * \alpha * \theta[/tex]
substituting values
=> [tex]w_i ^2 = 92 ^2 - 2 * 14 * 220[/tex]
=> [tex]w_i ^2 = 2304[/tex]
=> [tex]w_i = 48 \ rad/s[/tex]
A small block with a mass of 0.120 kg is attached to a cord passing through a hole in a frictionless, horizontal surface (Fig. 6.34). The block is originally revolving at a distance of 0.40 m from the hole with a speed of 0.70 m/s. The cord is then pulled from below, shortening the radius of the circle in which the block revolves to 0.10 m. At this new distance, the speed of the block is observed to be 2.80 m/s.
(a) What is the tension in the cord in the original situation when the block has speed v = 0.70 m/s? (b) What is the tension in the cord in the final situation when the block has speed v = 2.80 m/s? (c) How much work was done by the person who pulled on the cord?
Answer:
a) 0.147 N
b) 9.408 N
c) 9.261 N
Explanation:
The tension on the cord is the only force keeping the block in circular motion, thus representing the entirety of its centripetal force [tex]\frac{mv^{2} }{r}[/tex]. Plugging in values for initial and final states and we get answers for a and b. The work done by the person causes the centripetal force to increase, and thus is the difference between the final tension and the initial tension.
Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.8 x 105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven-the driving force is transferred to the object, which oscillates instead of the entire building X 50%
Part (a) What effective force constant, in N/m, should the springs have to make them oscillate with a period of 1.2 s? k = 9.5 * 106 9500000 X Attempts Remain 50%
Part (b) What energy, in joules, is stored in the springs for a 1.6 m displacement from equilibrium?
Answer:
The force constant is [tex]k =1.316 *10^{7} \ N/m[/tex]
The energy stored in the spring is [tex]E = 1.68 *10^{7} \ J[/tex]
Explanation:
From the question we are told that
The mass of the object is [tex]M = 4.8*10^{5} \ kg[/tex]
The period is [tex]T = 1.2 \ s[/tex]
The period of the spring oscillation is mathematically represented as
[tex]T =2 \pi \sqrt{ \frac{M}{k}}[/tex]
where k is the force constant
So making k the subject
[tex]k = \frac{4 \pi ^2 M }{T^2}[/tex]
substituting values
[tex]k = \frac{4 (3.142) ^2 (4.8 *10^{5}) }{(1.2)^2}[/tex]
[tex]k =1.316 *10^{7} \ N/m[/tex]
The energy stored in the spring is mathematically represented as
[tex]E = \frac{1}{2} k x^2[/tex]
Where x is the spring displacement which is given as
[tex]x = 1.6 \ m[/tex]
substituting values
[tex]E = \frac{1}{2} (1.316 *10^{7}) (1.6)^2[/tex]
[tex]E = 1.68 *10^{7} \ J[/tex]
To throw the discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn with a constant angular acceleration, releasing the discus after making one complete revolution. The diameter of the circle in which the discus moves is about 1.7m. If the thrower takes 1.2s to complete one revolution, starting from rest, what will be the speed of the discus at release?
Answer:
4.437 m/s
Explanation:
Diameter of rotation d is 1.7 m
Radius of rotation = d/2 = 1.7/2 = 0.85 m
If he takes 1.2 sec to complete one revolution, then his angular speed is 1/1.2 = 0.83 rev/s
We convert to rad/s
Angular speed = 2 x pi x 0.83
= 2 x 3.142 x 0.83 = 5.22 rad/s
Speed is equal to the angular speed times the radius of rotation
Speed = 5.22 x 0.85 = 4.437 m/s
In the given case, the speed of the discus at release, If the thrower takes 1.2s to complete one revolution, starting from rest would be - 8.90 m/s.
Given:
diameter of the circle = 1.7 mradius f the circle would be = 1.7/2 = 0.85 m
time taken for one revolution t = 1.2 sThis rotation exercise can be treated using the rotation kinematics.
Angular acceleration:
θ = w₀ t + ½ α t²
t = 1.2 s to give a revolution (T = 2π rad) and with part of the rest the initial angular velocity is zero (wo = 0)
=> θ = 0 + ½ α t²
=> α = 2θ / t²
=> α= 2 × 2π / 1.2²
=> α = 4π = 8.7266 rad / s²
Let's calculate the angular velocity:
=> w = wo + α t
=> w = 0 + α t
=> w = 8.7266 × 1.2
=> w = 10.47192 rad / s
The relationship between linear and angular velocity is
=> r = d / 2
=> r = 1.7 / 2 = 0.85 m
=> v = w r
=> v = 10.47192 × 0.85
=> v = 8.90 m / s
Thus, the correct speed would be - 8.90 m/s
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A 1100 kg car pushes a 1800 kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4500 N.A) What is the magnitude of the force of the car on the truck?B) What is the magnitude of the force of the truck on the car?
Answer:The answer is 3000 N.
Force (F) is the multiplication of mass (m) and acceleration (a).
F = m · a
It is given:
mc = 1000 kg
mt = 2000 kg
total force: F = 4500 N
total mass: m = mc + mt
Let's calculate acceleration which is common:
a = F/m = F/(mc + mt) = 4500/(1000 + 2000) = 4500/3000 = 1.5 m/s²
Now, when we know acceleration, let's calculate force on the truck:
Ft = mt · a = 2000 · 1.5 = 3000 N
Explanation:
b) A non-inductive load takes a current of 15 A at 125 V. An inductor is then connected
in series in order that the same current shall be supplied from 240 V, 50 Hz mains.
Ignore the resistance of the inductor and calculate:
i. the inductance of the inductor;
ii. the impedance of the circuit;
iii. the phase difference between the current and the applied voltage.
Assume the waveform to be sinusoidal.
Answer:
i. 43.5 mH ii. 16 Ω. In phasor form Z = (8.33 + j13.66) Ω iii 58.64°
Explanation:
i. The resistance , R of the non-inductive load R = 125 V/15 A = 8.33 Ω
The reactance X of the inductor is X = 2πfL where f = frequency = 50 Hz.
So, x = 2π(50)L = 100πL Ω = 314.16L Ω
Since the current is the same when the 240 V supply is applied, then
the impedance Z = √(R² + X²) = 240 V/15 A
√(R² + X²) = 16 Ω
8.33² + X² = 16²
69.3889 + X² = 256
X² = 256 - 69.3889
X² = 186.6111
X = √186.6111
X = 13.66 Ω
Since X = 314.16L = 13.66 Ω
L = 13.66/314.16
= 0.0435 H
= 43.5 mH
ii. Since the same current is supplied in both circuits, the impedance Z of the circuit is Z = 240 V/15 A = 16 Ω.
So in phasor form Z = (8.33 + j13.66) Ω
iii. The phase difference θ between the current and voltage is
θ = tan⁻¹X/R
= tan⁻¹(314.16L/R)
= tan⁻¹(314.16 × 0.0435 H/8.33 Ω)
= tan⁻¹(13.66/8.33)
= tan⁻¹(1.6406)
= 58.64°
A pendulum on a planet, where gravitational acceleration is unknown, oscillates with a time period 5 sec. If the mass is increased six times, what is the time period of the pendulum?
Explanation:
We have, a pendulum on a planet, oscillates with a time period 5 sec. The formula used to find the time period is given by :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
l is length of the pendulum
g is acceleration due to gravity on which it is placed
It is clear that, the time period of pendulum is independent of the mass. Hence, if the mass is increased six times, its time period remains the same.
Convert from standard form to scientific notation:
0.00000013
A)1.3 x 10-7
B)13 x 108
C)1.3 x 107
D)13 x 10-8
n astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a time interval 11.2 s . What are the average acceleration in each interval? Assume that the positive direction is to the right.
Answer:-
-1 m/s^2
Explanation:
The average acceleration is given by dividing the change in velocity by change in time;
[tex]a_f=\frac{v_f-v_i}{t_f-t_i}[/tex]
[tex]=\frac{(0-11.2)}{(11.2-0)}=-1 m/s^2[/tex]
the point to be noted here is if the velocity is to the left we substitute it with a negative sign and if it is to the right we substitute it with a positive sign.
A bicycle wheel has an initial angular velocity of 1.10 rad/s . Part A If its angular acceleration is constant and equal to 0.200 rad/s2 , what is its angular velocity at t = 2.50 s ? (Assume the acceleration and velocity have the same direction) Express your answer in radians per second. ω = nothing rads Request Answer Part B Through what angle has the wheel turned between t = 0 and t = 2.50 s ? Express your answer in radians. Δθ = nothing rad Request Answer Provide Feedback
Let [tex]\theta[/tex], [tex]\omega[/tex], and [tex]\alpha[/tex] denote the angular displacement, velocity, and acceleration of the wheel, respectively.
(A) The wheel has angular velocity at time [tex]t[/tex] according to
[tex]\omega=\omega_0+\alpha t[/tex]
so that after 2.50 s, the wheel will have attained an angular velocity of
[tex]\omega=1.10\dfrac{\rm rad}{\rm s}+\left(0.200\dfrac{\rm rad}{\mathrm s^2}\right)(2.50\,\mathrm s)=\boxed{1.60\dfrac{\rm rad}{\rm s}}[/tex]
(B) The angular displacement of the wheel is given by
[tex]\theta=\theta_0+\omega_0t+\dfrac\alpha2t^2\implies\Delta\theta=\omega_0t+\dfrac\alpha2t^2[/tex]
After 2.50 s, the wheel will have turned an angle [tex]\Delta\theta[/tex] equal to
[tex]\Delta\theta=\left(1.10\dfrac{\rm rad}{\rm s}\right)(2.50\,\mathrm s)+\dfrac12\left(0.200\dfrac{\rm ram}{\mathrm s^2}\right)(2.50\,\mathrm s)^2=\boxed{3.38\,\mathrm{rad}}[/tex]
b. A locomotive of a train exerts a constant force of 280KN on a train while pulling
it at 50 km/h along a level track. What is:
[4 marks)
i. Workdone in quarter an hour and
[4 marks]
Answer:
Work-done in quarter an hour = 3.5 × 10⁶ J
Explanation:
Given:
Force (F) = 280 KN = 280,000 N
Velocity (V) = 50 km / h
Time (t) = 1 / 4 = 0.25 hour
Find:
Work-done in quarter an hour
Computation:
⇒ Displacement = Velocity (V) × Time
⇒ Displacement = 50 × 0.25
⇒ Displacement = 12.5 km
⇒ Work-done = Force (F) × Displacement
⇒ Work-done in quarter an hour = 280,000 × 12.5
⇒ Work-done in quarter an hour = 3,500,000
Work-done in quarter an hour = 3.5 × 10⁶ J
A rigid tank contains 2 kg of an ideal gas at 4 atm and 40 C. Now a valve is opened, and half of the mass of the gas is allowed to escape. if the final pressure in the tank is 2.2 atm. The final temperature in the tank is: Hint: make sure you convert the units of temperature and pressure to the proper units
Answer:
Final Temperature = 71 °C
Explanation:
In this case, the ideal gas equation is written as;
PV = mRT
Where;
P is pressure
V is volume
m is mass
R is gas constant
T is temperature
We will take the volume to be constant.
So, in the initial state, we have;
P1•V = m1•R•T1 - - - eq(1)
In the final state, we have;
P2•V = m2•R•T2 - - - - eq(2)
Combining eq (1) and eq(2),we have;
P1•m2•R•T2 = P2•m1•R•T1
Dividing both sides by R gives;
P1•m2•T2 = P2•m1•T1
Making T2 the subject gives;
T2 = (P2•m1•T1)/(P1•m2)
Now, we are given;
m1 = 2kg
m2 = ½*2 = 1kg
P1 = 4 atm
P2 = 2.2 atm
T1 = 40°C = 273 + 40 K = 313K
Plugging in this values into the T2 equation, we have;
T2 = (2.2 × 2 × 313)/(4 × 1)
T2 = 344 K
Converting to °C, we have;
T2 = 344 - 273 = 71 °C
A potential difference of 71 mV is developed across the ends of a 12.0-cm-long wire as it moves through a 0.27 T uniform magnetic field at a speed of 6.0 m/s. The magnetic field is perpendicular to the axis of the wire.
Required:
What is the angle between the magnetic field and the wire's velocity?
Answer:
Explanation: please see attached file I attached the answer to your question.
The angle between the magnetic field and the wire's velocity is 33.2 degrees.
Calculation of the angle:Since the potential difference = 71mv = 71 *10 ^-3 V
The length is 12 cm = 0.12m
The magnetic field i.e. B = 0.27T
The speed or v = 4 m/s
here we assume [tex]\theta[/tex] be the angle
So,
e = Bvl sin[tex]\theta[/tex]
So,
[tex]Sin\theta[/tex] = e/bvl
= 71*10^-3 / 0.27 *4*0.12
= 0.5478
= 33.2 degrees
Therefore, the angle should be 33.2 degrees
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