Answer:
The angle is 3.95 rad.
Explanation:
The angle can be calculated as follows:
[tex] \omega_{f}^{2} = \omega_{0}^{2} + 2\alpha \theta [/tex]
Where:
[tex]\omega_{f}[/tex]: is the final angular speed
ω₀: is the initial angular speed = 0 (it starts from rest)
α: is the angular acceleration
θ: is the angle=?
The centripetal acceleration is:
[tex]a_{c} = \omega_{f}^{2}*r[/tex]
And the tangential acceleration is:
[tex] a_{T} = \alpha*r [/tex]
Since the magnitude of the centripetal acceleration is 7.9 times the magnitude of the tangential acceleration:
[tex]a_{c} = 7.9a_{T}[/tex]
[tex]\omega_{f}^{2}*r = 7.9*\alpha*r \rightarrow \alpha = \frac{\omega_{f}^{2}}{7.9}[/tex]
Now, the angle is:
[tex]\omega_{f}^{2} = 2(\frac{\omega_{f}^{2}}{7.9})\theta[/tex]
[tex] \theta = \frac{7.9}{2} = 3.95 rad [/tex]
Therefore, the angle is 3.95 rad.
I hope it helps you!
The angular distance traveled by the electric drill is 3.95 radians.
The given parameters;
initial angular speed, [tex]\omega_i[/tex] = 0centripetal acceleration, [tex]a_c[/tex] = 7.9aThe angular distance traveled by the electric drill is calculated as follows;
[tex]\omega_f^2 = \omega_i^2 + 2\alpha \theta[/tex]
The relationship between centripetal acceleration, tangential acceleration and angular speed is given as;
[tex]a_c = \omega ^2 r\\\\a = \alpha r\\\\a_c = 7.9a= 7.9\alpha r\\\\7.9\alpha r = \omega^2 r\\\\\alpha = \frac{\omega ^2}{7.9}[/tex]
Substitute the value of angular acceleration into the first equation;
[tex]\omega _f^2 = 0 + 2(\a (\frac{\omega _f^2}{7.9})\theta\\\\2\theta \omega_f^2 = 7.9\omega_f ^2\\\\\theta = \frac{7.9}{2} \\\\\theta = 3.95 \ rad[/tex]
Thus, the angular distance traveled by the electric drill is 3.95 radians.
Learn more about angular distance here: https://brainly.com/question/12680957
The emf of the battery is 1.5 V. In Nichrome there are 9 × 1028 mobile electrons per m3, and the mobility of mobile electrons is 7 × 10−5 (m/s)/(N/C). Each thick wire has length 29 cm = 0.29 m and cross-sectional area 9 × 10−8 m2. The thin wire has length 6 cm = 0.06 m and cross-sectional area 1.3 × 10−8 m2. (The total length of the three wires is 64 cm.) In the steady state, calculate the number of electrons entering the thin wire every second. Do not make any approximations, and do not use Ohm's law or series-resistance equations.
Answer:
The number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
Explanation:
Given;
emf of the battery, V = 1.5 V
electron density, = 9 × 10²⁸ mobile electrons per m³
mobility of electron, u = 7 × 10⁻⁵ (m/s)/(N/C)
length of thin wire, L = 6 cm = 0.06 m
cross sectional area of the thin wire, A = 1.3 x 10⁻⁸ m²
The magnitude of the electric field in the thin wire is given by;
E = V/L
E = (1.5) / (0.06)
E = 25 N/C
the number of electrons entering the thin wire every second is given by;
[tex]e/s = mobility \ x \ Electric \ field\\\\number \ of \ electrons \ per \ second =\frac{7*10^{-5} (m/s)}{N/C} *25 (N/C)\\\\number \ of \ electrons \ per \ second = 1.75*10^{-3} \ m/s[/tex]
Therefore, the number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
The number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
Calculation of the number of electrons:Since
emf of the battery, V = 1.5 V
electron density, = 9 × 10²⁸ mobile electrons per m³
mobility of electron, u = 7 × 10⁻⁵ (m/s)/(N/C)
length of thin wire, L = 6 cm = 0.06 m
cross sectional area of the thin wire, A = 1.3 x 10⁻⁸ m²
So here the magnitude should be
E = V/L
E = (1.5) / (0.06)
E = 25 N/C
Now the number of electrons should be
= 7 × 10⁻⁵ *25
= 1.75 x 10⁻³ mobile
hence, The number of electrons entering the thin wire every second is 1.75 x 10⁻³ mobile electrons / second
Learn more about electron here: https://brainly.com/question/24701476
A lamp of mass m hangs from a spring scale which is attached to the ceiling of an elevator. When the elevator is stopped at the fortieth floor, the scale reads mg. What does it read as the elevator slows down to stop at the ground floor?
a. more than mg
b. mg
c. less than mg
d. zero
e. can't tell
Answer:
The correct answer is (a)
Explanation:
A spring scale measures the weight of an object not the mass because according to hooke's law the extension of a spring is directly proportional to the load or force attached/applied to it. The force of gravity acting on the mass of any substance as it goes up actually reduces and increases as it comes down.
If F = ma, as a increases, F will also increase and vice versa
Where F = force
m = mass
a = acceleration (due to gravity in this case)
From the above explanation, it can be deduced that the scale will read more than mg as it gets to the ground because of an increase in the force of gravity (which also increases a) as it approaches the ground.
A projectile is fired straight up with an initial velocity of 40.0 m/s . Approximately how high will the projectile ?
Answer:
it depends on the wind and any other conditions but if you have a controlled environment it should take 1 second to get 40 meters but it could go higher in which it could take about 5 seconds to go 200 meters
Explanation:
hope it helped
:)
While making some observations at the top of the 66 m tall Astronomy tower, Ron
accidently knocks a 0.5 kg stone over the edge. How long will a student at the bottom
have to get out of the way before being hit?
Analysing the question:
Since the stone was dropped, there was no initial velocity applied on it and hence it's initial velocity of the stone is 0 m/s
We are given:
height of the tower (h) = 66 m
mass of the stone (m) = 0.5 kg
initial velocity of the stone (u) = 0 m/s
time taken by the stone to reach the ground (t) = t seconds
acceleration due to gravity = 10 m/s²
** Neglecting air resistance**
Finding the time taken by the stone to reach the ground:
from the second equation of motion
h = ut + 1/2at²
replacing the variables
66 = (0)(t) + 1/2 (10)(t)²
66 = 5t²
t² = 13.2
t = 3.6 seconds
I initially wanted to subtract the height of the student from the height of the tower since the time i calculated is the time taken by the stone to reach the ground and that means that the stone has already hit the student before 3.6 seconds
but since we were NOT given the height of a student, the person who posed this question wants the time taken by the stone to reach the ground and that is what we solved
The forces exerted on an object are shown. (3 points)
A box has an arrow pointing up labeled F and an arrow pointing down labeled 3 N.
If the net force on the object along the vertical plane is zero, which statement is correct?
F equals 3 N and the object moves up.
F equals 3 N and the object remains stationary.
F equals 0 N and the object moves down.
F equals 0 N and the object remains stationary.
Answer:
F equals 3 N and the object remains stationary. (second option in the list)
Explanation:
For sure to cancel acting forces, F must be 3N pointing up. But with regards to the object stationary or not, the question is tricky. We could have a ZERO net force applied, and the object moving at constant speed, which could still verify Newton's Laws. But considering the first answer option that refers to vertical motion upward where the object could be gaining potential energy, the most accurate response is that the force F has to be 3 N pointing up to make the object in equilibrium, and no motion in the vertical axis.
Answer: F equals 3 N and the object remains stationary.
Explanation:
The elements in Groups 3 through 12 of the periodic table are the ______.
Answer:
Transition Metals
Explanation:
__________________________
Given a force of 10 N and an acceleration of 5 m/s2, what is the mass?
Answer:
2kg
Explanation:
i think i found it yous welcom
Two students measured the length of the same stick, each using a different 30 cm ruler. One student reported a length of 22 cm, and the other reported a length of 8 cm. The most likely explanation for the difference in the reported values is that one —
A. *student improperly read the ruler
B. ruler was metal and the other ruler was plastic
C. student viewed the ruler from a different angle
D. ruler was constructed with nonstandard cm marks
Answer:
C. student viewed the ruler from a different angle
Explanation:
It is the problem of viewing the scale from different sides or angles. If we assume the actual length of the stick to be 22 cm. Then the first student measured the length by reading the values from 1 cm towards 22 cm on the scale. While, the second student measured the length of the stick by reading the values from the other side or the other angle of the scale, that is, from 30 cm mark towards 1 cm. And in that case the the length of the 22 cm long stick will appear as:
30 cm - 22 cm = 8 cm
Therefore, the second student read 8 cm on scale. So, the correct option is:
C. student viewed the ruler from a different angle
A coin rests on a record 0.15 m from its center. The record turns on a turntable that rotates at variable speed. The coefficient of static friction between the coin and the record is 0.30.
Required:
What is the maximum coin speed at which it does not slip?
Answer:
0.66m/sExplanation:
We are expected to solve for the velocity with no slip condition
we know that the expression that relate coefficient of friction and velocity is given as
μs = v^2/rg
Given
coefficient of friction μs = 0.3
radius r= 0.15
assume g=9.81m/s^2
substituting into the expression we have
0.3= v^2/0.15*9.81
v^2=0.3*0.15*9.81
v^2=0.44145
v=√0.44145
v=0.66
therefore the velocity is 0.66m/s
Vector A has a magnitude of 6.0 m and points 30° north of east. Vector B has a magnitude of 4.0 m and points 30° west of south. The resultant vector A+ B is given by
Answer:
The resultant vector [tex]\vec R = \vec A+\vec B[/tex] is given by [tex]\vec R = 3.196\,\hat{i}-0.464\,\hat{j}\,\,\,[m][/tex].
Explanation:
Let [tex]\vec A = 6\cdot (\cos 30^{\circ}\,\hat{i}+\sin 30^{\circ}\,\hat{j})[/tex] and [tex]\vec B = 4\cdot (-\sin 30^{\circ}\,\hat{i}-\cos 30^{\circ}\,\hat{j})[/tex], both measured in meters. The resultant vector [tex]\vec R[/tex] is calculated by sum of components. That is:
[tex]\vec R = \vec A+\vec B[/tex] (Eq. 1)
[tex]\vec R = 6\cdot (\cos 30^{\circ}\,\hat{i}+\sin 30^{\circ}\,\hat{j})+4\cdot (-\sin 30^{\circ}\,\hat{i}-\cos 30^{\circ}\,\hat{j})[/tex]
[tex]\vec R = (6\cdot \cos 30^{\circ}-4\cdot \sin 30^{\circ})\,\hat{i}+(6\cdot \sin 30^{\circ}-4\cdot \cos 30^{\circ})\,\hat{j}[/tex]
[tex]\vec R = 3.196\,\hat{i}-0.464\,\hat{j}\,\,\,[m][/tex]
The resultant vector [tex]\vec R = \vec A+\vec B[/tex] is given by [tex]\vec R = 3.196\,\hat{i}-0.464\,\hat{j}\,\,\,[m][/tex].
Explain why atoms only emit certain wavelengths of light when they are excited. Check all that apply. Check all that apply. Electrons are allowed "in between" quantized energy levels, and, thus, only specific lines are observed. The energies of atoms are not quantized. When an electron moves from one energy level to another during absorption, a specific wavelength of light (with specific energy) is emitted. Electrons are not allowed "in between" quantized energy levels, and, thus, only specific lines are observed. When an electron moves from one energy level to another during emission, a specific wavelength of light (with specific energy) is emitted. The energies of atoms are quantized.
Answer:
Explanation:
Electrons are allowed "in between" quantized energy levels, and, thus, only specific lines are observed. FALSE. The specific lines are obseved because of the energy level transition of an electron in an specific level to another level of energy.
The energies of atoms are not quantized. FALSE. The energies of the atoms are in specific levels.
When an electron moves from one energy level to another during absorption, a specific wavelength of light (with specific energy) is emitted. FALSE. During absorption, a specific wavelength of light is absorbed, not emmited.
Electrons are not allowed "in between" quantized energy levels, and, thus, only specific lines are observed. TRUE. Again, you can observe just the transition due the change of energy of an electron in the quantized energy level
When an electron moves from one energy level to another during emission, a specific wavelength of light (with specific energy) is emitted. TRUE. The electron decreases its energy releasing a specific wavelength of light.
The energies of atoms are quantized. TRUE. In fact, the energy of all subatomic, atomic, and molecular particles is quantized.
The reason why atoms emit only specific wavelengths is because the energy levels in atoms are quantized.
Max Plank introduced the idea of quantization of energy in the early 1900s. He introduced the idea that energy can only take on certain specific values. This idea was later extended to atoms by Neils Bohr.
The following statements explain why atoms only emit certain wavelengths of light when they are excited;
When an electron moves from one energy level to another during emission, a specific wavelength of light (with specific energy) is emitted. Electrons are not allowed "in between" quantized energy levels, and, thus, only specific lines are observed. The energies of atoms are quantized.Learn more: https://brainly.com/question/24381583
A Navy Seal of mass 80 kg parachuted directly down into an enemy harbor. At one point while she was falling, the resistive force that air exerted on her was 520 N upward. What can you determine about her motion at this point in time
Answer:
The Navy Seal is accelerating downwards at the rate of 3.3 m/s²
Explanation:
Given;
mass of the Navy Seal, m = 80 kg
the upward resistive force on her, F = 520 N
Her net downward force is given by;
[tex]F_{net} = F_{down} - F_{up}\\\\F_{net} = (80*9.8) - 520\\\\F_{net} = 264 \ N[/tex]
Her downward acceleration at this time is given by;
F = ma
a = F / m
a = 264 / 80
a = 3.3 m/s²
Therefore, the Navy Seal is accelerating downwards at the rate of 3.3 m/s²
A student rides a bicycle 2400 meters in four minutes to get to school. What is the student's speed?
Answer:
10 mls2
Explanation:
speed =distance /time
A force of 41 N acts on an object which has a mass of 2.4 kg. What acceleration (in m/s2) is produced by the force
Answer:
The acceleration is [tex] a = 17.083 \ m/s^2 [/tex]
Explanation:
From the question we are told that
The force is [tex]F = 41 \ N[/tex]
The mass of the object is [tex]m = 2.4 \ kg[/tex]
Generally the force is mathematically represented as
[tex]F = m* a[/tex]
=> [tex] 41 = 2.4* a[/tex]
=> [tex] a = 17.083 \ m/s^2 [/tex]
If it takes you 5 minutes to dry your hair using a 1200-W hairdryer plugged into a 120-V power outlet, how many Coulombs of charge pass through your hair dryer
Answer:
The charge pass through your hair dryer is 3000 C.
Explanation:
Given that,
Power = 1200 W
Voltage = 120 V
Flow time = 5 min
We need to calculate the current
Using formula of power
[tex]P=VI[/tex]
[tex]I=\dfrac{P}{V}[/tex]
Put the value into the formula
[tex]I=\dfrac{1200}{120}[/tex]
[tex]I=10\ A[/tex]
We need to calculate the charge pass through your hair dryer
Using formula of current
[tex]I=\dfrac{Q}{t}[/tex]
[tex]Q=It[/tex]
Put the value into the formula
[tex]Q=10\times5\times60[/tex]
[tex]Q=3000\ C[/tex]
Hence, The charge pass through your hair dryer is 3000 C.
A small compass is held horizontally, the center of its needle has a distance of 0.270 m directly north
of a long wire that is perpendicular to the Earth's surface. When there is no current in the wire, the
compass needle points due north, which is the direction of the horizontal component of the Earth's
magnetic field at that location. This component is parallel to the Earth's surface. When the current in
the wire is 26.3 A, the needle points 22.9∘ east of north.
(a) Does the current in the wire flow toward or away from the Earth's surface? ( 2 marks)
(b) What is the magnitude of the horizontal component of the Earth's magnetic field at the location of
the compass? (3 marks)
Answer:
Explanation:
The needle is showing north south direction . when current starts flowing in the wire which is held vertical to the ground , it deflects towards east .
a )
Therefore a magnetic field towards east has been created . It is possible only if current flows towards the surface in the vertical wire .
b )
magnetic field created at the magnetic needle B = 10⁻⁷ x 2I / d where I is current and d is distance .
B = 10⁻⁷ x 2 x 26.3 / .27
= 194.81 x 10⁻⁷ T
angle of deflection of solenoid = 22.9°
Tan 22.9 = B /H
.422 = 194.81 x 10⁻⁷ / H
H = 461.63 x 10⁻⁷ T
= .46 x 10⁻⁴ T .
A) The current in the wire flows towards the Earth's surface
B) The magnitude of the horizontal component of the Earth's magnetic field is : 0.46 x 10⁻⁴ T
A) The compass needle held horizontally points in a North-south direction of the earth and also deflects eastwards when current is allowed to flow through it. The deflection of the needle indicates the presence/generation of a magnetic field on the earth surface. which is facilitated by the flow of the current in the wire towards the Earth's surface
B) Determine The magnitude of the horizontal component of the Earth's magnetic field
B ( magnetic field ) = 10⁻⁷ * 2I / d ---- ( 1 )
where : l = 26.3 A, d = 0.27 m
Back to equation ( 1 )
B = 10⁻⁷ * 2 * 26.3 / 0.27
= 194.81 * 10⁻⁷ T
Final step : Calculate the magnitude of horizontal component ( H )
Tan ∅ = B / H ---- ( 2 )
where : ∅ ( angle of deflection ) = 22.9°
∴ H = B / Tan ( 22.9° )
= ( 194.81 * 10⁻⁷ ) / 0.422
= 0.46 x 10⁻⁴ T
Hence we can conclude that The current in the wire flows towards the Earth's surface and The magnitude of the horizontal component of the Earth's magnetic field is : 0.46 x 10⁻⁴ T
Learn more about Earth magnetic field : https://brainly.com/question/115445
the peripheral nervous system is responsible for both sending and receiving signals to and from the brain
Answer:
its true trust me
Explanation:
Answer: true
Explanation: edge
Momentum of the 2 kg mass moving with velocity 10 m/s is *
A. 2 kg*m/s
B. 20 kg*m/s
C. 200 kg*m/s
D. 20000 kg*m/s
How much voltage (in terms of the power source voltage bV) will the capacitor have when it has started at zero volts potential difference, it is connected to the power supply and resistor and onehalf the characteristic time has passed (i.e. t= T(tau)/2)?
Answer:
The voltage is [tex]V = 0.993V_b[/tex]
Explanation:
From the question we are told that
The time that has passed is [tex]t = \frac{\tau}{2}[/tex]
Here [tex]\tau[/tex] is know as the time constant
The voltage of the power source is [tex]V_b[/tex]
Generally the voltage equation for charging a capacitor is mathematically represented as
[tex]V = V_b [1 - e^{- \frac{t}{\tau} }][/tex]
=> [tex]V = V_b [1 - e^{- \frac{\frac{\tau}{2}}{\tau} }][/tex]
=> [tex]V = V_b [1 - e^{- \frac{\tau}{2\tau} }][/tex]
=> [tex]V = V_b [1 - e^{- \frac{1}{2} }][/tex]
=> [tex]V = 0.993V_b[/tex]
If a projectile hits a stationary target, and the projectile continues to travel in the same direction, the mass of the projectile is less than the mass of the target. the mass of the projectile is equal to the mass of the target. the mass of the projectile is greater than the mass of the target. nothing can be said about the masses of the projectile and target without further information. this is an unphysical situation and will not actually happen.
The correct arrangement of the question is;
If a projectile hits a stationary target, and the projectile continues to travel in the same direction,
A) the mass of the projectile is less than the mass of the target.
B) the mass of the projectile is equal to the mass of the target.
C) the mass of the projectile is greater than the mass of the target.
D) nothing can be said about the masses of the projectile and target without further information.
E) this is an unphysical situation and will not actually happen.
Answer:
Option C: The mass of the projectile is greater than the mass of the target.
Explanation:
We want to find what will happen when a projectile continues in motion after it hits a target.
Now, for the projectile to keep moving in that direction after it hits the target, it means it had a force bigger than the force of the target to overpower it and force it to move with it.
Now, from law of inertia, Force = ma.
But in this case acceleration is 0 because the speed of the projectile is constant.
Thus, the force depends on the mass. So for a higher force, the mass of the projectile has to be more than that of the stationary object.
Thus, option C is correct
What are two ways that an object can have kinetic energy?
Answer:
The object has to have mass and speed
Explanation:
You can increase both speed and mass to increase the kinetic energy, hope this answers your question.
Happy Halloween!
A microwave oven operates at 2.50 GHzGHz . What is the wavelength of the radiation produced by this appliance? Express the wavelength numerically in nanometers.
Answer:
The wavelength is [tex]\lambda = 1.2 * 10^8 nm[/tex]
Explanation:
From the question we are told that
The frequency of operation of the microwave is [tex]f = 2.50 GHz = 2.50 *10^{9} \ Hz[/tex]
Generally the wavelength is mathematically represented as
[tex]\lambda = \frac{c}{f}[/tex]
Here c is the speed of light with value [tex]c = 3.0 *10^{8} \ m/s[/tex]
So
[tex]\lambda = \frac{3.0 *10^{8}}{ 2.50 *10^{9}}[/tex]
=> [tex]\lambda = 0.12 \ m [/tex]
converting to nanometer
[tex]\lambda = 1.2 * 10^8 nm[/tex]
. Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point? What is your displacement vector? What is the direction of your displacement? Assume the +x-axis is to the east.
Answer:
Explanation:
The total distance is how far you walk from the starting point.
Distance through west = 18.0m
Distance through north = 25.0m
Total distance covered = 18.0+25.0m
Total distance covered = 43.0m
This means that I am 43.0m from the starting point
Displacement is the distance covered in a specified direction. The displacement will be gotten using the Pythagoras theorem as shown:
[tex]d^2 = 25^2 + 18^2\\d^2 = 625+324\\d^2 = 949\\d = \sqrt{949}\\ d = 30.81m[/tex]
The direction of your displacement is 30.81m
Direction is gotten according to the formula;
[tex]\theta = tan ^{-1}{\frac{y}{x} }\\\theta = tan ^{-1}{\frac{25}{-18} }\\\theta = tan ^{-1}-1.3889}\\\theta = -60.27^0\\\theta = 180-60.27\\\theta = 119.7^0[/tex]
Note that the direction to the west is negative, that is why the x is -18.0m
The distance from the starting point is 43 m, the displacement vector is 30.81 m and the direction of the displacement is 119.7 degrees.
Given-
Distance travel through the west is 18 m.
Distance travel through the north is 25 m.
Distance from starting point-
To know the total distance, add both the covered distance. Thus total distance x is,
[tex]x=18+25[/tex]
[tex]x=43[/tex]
Hence, the distance from the starting point is 43 m.
The displacement vector-
Displacement is calculated as the shortest distance between starting and final point. This shortest distance can be calculated using the Pythagoras theorem which states that in a right-angled triangle, the square of the hypotenuse [tex]d[/tex] is equal to the sum of the squares of the other two sides. Therefore,
[tex]d^2=18^2+25^2[/tex]
[tex]d^2=324+625[/tex]
[tex]d^2=949[/tex]
[tex]d=\sqrt{949}[/tex]
[tex]d=30.81[/tex]
The displacement vector is 30.81 m.
The Direction of displacement-The direction of displacement [tex]\theta[/tex] with these two sides can be calculated with the formula,
[tex]\theta=tan^{-1}\dfrac{25}{-18}[/tex]
Here due to the west direction(opposite side), the sign is taken negatively.
[tex]\theta=tan^{-1}(-1.389)[/tex]
[tex]\theta=-60.27^o[/tex]
For the other quarter,
[tex]\theta=180-60.27=119.7^o[/tex]
Hence, the distance from the starting point is 43 m, the displacement vector is 30.81 m and the direction of the displacement is 119.7 degrees.
For more about the displacement, follow the link below-
https://brainly.com/question/10919017
When a parachute opens, the air exerts a large drag force on it. This upward force is initially greater than the weight of the sky diver and, thus, slows him down. Suppose the weight of the sky diver is 915 N and the drag force has a magnitude of 1061 N. The mass of the sky diver is 93.4 kg. Take upward to be the positive direction. What is his acceleration, including sign
Explanation:
According to newton's second law of motion.
[tex]\sum Fx = ma\\\\\sum Fx = 1061 - 915\\\\\sum Fx = 146N[/tex]
m is the mas of the sky diver = 93.4kg
a is the acceleration of the skydiver
From the formula above;
[tex]a = \frac{\sum Fx}{m}\\ \\a = \frac{146}{93.4}\\\\a = 1.563m/s^2[/tex]
Hence the acceleration of the sky diver is 1.563m/s²
g A hydraulic press has a safety feature which consists of a hydraulic cylinder with a piston at one end and a safety valve at the other. The cylinder has a radius of 0.0200 m and the safety valve is simply a 0.00750-m radius circular opening at one end, sealed with a disk. The disk is held in place by a spring with a spring constant of 950 N/m that has been compressed 0.0085 m from its natural length. Determine the magnitude of the minimum force that must be exerted on the piston in order to open the safety valve.
Answer:
58.32 N
Explanation:
Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]
where r is the radius of the circle.
The cylinder has a radius of 0.02 m, its area is;
[tex]A_{1}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.02)^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x 0.0004
= 1.2571 x [tex]10^{-3}[/tex]
Area of the cylinder is 0.0013 [tex]m^{2}[/tex].
The safety valve has a radius of 0.0075 m, its area is;
[tex]A_{2}[/tex] = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x [tex](0.0075)^{2}[/tex]
= [tex]\frac{22}{7}[/tex] x 5.625 x [tex]10^{-5}[/tex]
= 1.7679 x [tex]10^{-4}[/tex]
Area of the valve is 0.00018 [tex]m^{2}[/tex].
From Hooke's law, the force on the safety valve can be determined by;
F = ke
[tex]F_{2}[/tex] = 950 x 0.0085
= 8.075 N
Minimum force, [tex]F_{1}[/tex], required can be determined by;
[tex]\frac{F_{1} }{A_{1} }[/tex] = [tex]\frac{F_{2} }{A_{2} }[/tex]
[tex]\frac{F_{1} }{0.0013}[/tex] = [tex]\frac{8.075}{0.00018}[/tex]
[tex]F_{1}[/tex] = [tex]\frac{0.0013 *8.075}{0.00018}[/tex]
= 58.32
The minimum force that must be exerted on the piston is 58.32 N.
Based on the information in the table, which elements are most likely in the same periods of the periodic table?
Answer:
Just to help, periods on the periodic table are those running horizontally from left to right
Answer:
The answer is A.Boron and carbon are likely together in one period because they have very close atomic numbers, while gallium and germanium are likely together in another period because they have very close atomic numbers.
Explanation:
just took test
A plane travelling at 100 m/s accelerates at 5 m/s² for a distance of 125 m. What is the final velocity of the plane?
Analyzing the question:
We are given:
initial velocity (u) = 100 m/s
final velocity (v) = v m/s
distance (s) = 125 m
acceleration (a) = 5 m/s²
Solving for Final Velocity (v):
from the third equation of motion:
v² - u² = 2as
v² - (100)² = 2(5)(125)
v² - 10000 = 1250
v² = 1250 + 10000
v² = 11250
v = 106.06 m/s
Two equal forces act on two different objects, one of which has a mass ten times as large as the other. The larger object will have _________ acceleration that the less massive object.
Answer:
The larger object will have smaller acceleration that the less massive object.
Explanation:
Generally force is mathematically represented as
[tex]F = ma[/tex]
=> [tex]m = \frac{F}{a }[/tex]
at constant force we have
[tex]m \ \alpha \ \frac{1}{a}[/tex]
So if m is increasing a will be decreasing which means the object with the larger mass will have less acceleration
A mass (m = 30 g) falls onto a spring (k = 7.3 N/m) from a height (h = 25 cm). The spring compresses an additional amount x before temporarily coming to a stop. What is the value of x?
Answer:
x₁ = 0.1878 m
Explanation:
For this exercise we will use conservation of energy
starting point. Highest point
Em₀ = U = m g h
final point. Lowest point with fully compressed spring
Em_f = K_e + U
Em_f = ½ K x² + m g x
energy is conserved
Em₀ = Em_f
m g h = ½ K x² + m g x
½ K x² + mg (x- h) = 0
let's substitute
½ 7.3 x² + 0.030 9.8 (x- 0.25) = 0
3.65 x² + 0.294 (x- 0.25) = 0
x² + 0.080548 (x- 0.25) = 0
x² - 0.020137 + 0.080548 x = 0
x² + 0.080548 x - 0.020137 = 0
let's solve the quadratic equation
x = [0.080548 ±√ (0.080548² + 4 0.020137)] / 2
x = [0.080548 ± 0.29502] / 2
x₁ = 0.1878 m
x₂ = -0.1072 m
These are the compression and extension displacement of the spring
I need help with this answer
decomposition
A decomposition reaction is just the opposite of combination reaction